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An hypothesis is a specific statement of prediction. It describes in concrete (rather than theoretical) terms what you expect will happen in your study. Not all studies have hypotheses. Sometimes a study is designed to be exploratory (see inductive research ). There is no formal hypothesis, and perhaps the purpose of the study is to explore some area more thoroughly in order to develop some specific hypothesis or prediction that can be tested in future research. A single study may have one or many hypotheses.

Actually, whenever I talk about an hypothesis, I am really thinking simultaneously about two hypotheses. Let’s say that you predict that there will be a relationship between two variables in your study. The way we would formally set up the hypothesis test is to formulate two hypothesis statements, one that describes your prediction and one that describes all the other possible outcomes with respect to the hypothesized relationship. Your prediction is that variable A and variable B will be related (you don’t care whether it’s a positive or negative relationship). Then the only other possible outcome would be that variable A and variable B are not related. Usually, we call the hypothesis that you support (your prediction) the alternative hypothesis, and we call the hypothesis that describes the remaining possible outcomes the null hypothesis. Sometimes we use a notation like HA or H1 to represent the alternative hypothesis or your prediction, and HO or H0 to represent the null case. You have to be careful here, though. In some studies, your prediction might very well be that there will be no difference or change. In this case, you are essentially trying to find support for the null hypothesis and you are opposed to the alternative.

If your prediction specifies a direction, and the null therefore is the no difference prediction and the prediction of the opposite direction, we call this a one-tailed hypothesis . For instance, let’s imagine that you are investigating the effects of a new employee training program and that you believe one of the outcomes will be that there will be less employee absenteeism. Your two hypotheses might be stated something like this:

The null hypothesis for this study is:

HO: As a result of the XYZ company employee training program, there will either be no significant difference in employee absenteeism or there will be a significant increase .

which is tested against the alternative hypothesis:

HA: As a result of the XYZ company employee training program, there will be a significant decrease in employee absenteeism.

In the figure on the left, we see this situation illustrated graphically. The alternative hypothesis – your prediction that the program will decrease absenteeism – is shown there. The null must account for the other two possible conditions: no difference, or an increase in absenteeism. The figure shows a hypothetical distribution of absenteeism differences. We can see that the term “one-tailed” refers to the tail of the distribution on the outcome variable.

When your prediction does not specify a direction, we say you have a two-tailed hypothesis . For instance, let’s assume you are studying a new drug treatment for depression. The drug has gone through some initial animal trials, but has not yet been tested on humans. You believe (based on theory and the previous research) that the drug will have an effect, but you are not confident enough to hypothesize a direction and say the drug will reduce depression (after all, you’ve seen more than enough promising drug treatments come along that eventually were shown to have severe side effects that actually worsened symptoms). In this case, you might state the two hypotheses like this:

HO: As a result of 300mg./day of the ABC drug, there will be no significant difference in depression.

HA: As a result of 300mg./day of the ABC drug, there will be a significant difference in depression.

The figure on the right illustrates this two-tailed prediction for this case. Again, notice that the term “two-tailed” refers to the tails of the distribution for your outcome variable.

The important thing to remember about stating hypotheses is that you formulate your prediction (directional or not), and then you formulate a second hypothesis that is mutually exclusive of the first and incorporates all possible alternative outcomes for that case. When your study analysis is completed, the idea is that you will have to choose between the two hypotheses. If your prediction was correct, then you would (usually) reject the null hypothesis and accept the alternative. If your original prediction was not supported in the data, then you will accept the null hypothesis and reject the alternative. The logic of hypothesis testing is based on these two basic principles:

• the formulation of two mutually exclusive hypothesis statements that, together, exhaust all possible outcomes
• the testing of these so that one is necessarily accepted and the other rejected

OK, I know it’s a convoluted, awkward and formalistic way to ask research questions. But it encompasses a long tradition in statistics called the hypothetical-deductive model , and sometimes we just have to do things because they’re traditions. And anyway, if all of this hypothesis testing was easy enough so anybody could understand it, how do you think statisticians would stay employed?

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Hypothesis Testing (cont...)

Hypothesis testing, the structure of hypothesis testing.

Whilst all pieces of quantitative research have some dilemma, issue or problem that they are trying to investigate, the focus in hypothesis testing is to find ways to structure these in such a way that we can test them effectively. Typically, it is important to:

Whilst there are some variations to this structure, it is adopted by most thorough quantitative research studies. We focus on the first five steps in the process, as well as the decision to either reject or fail to reject the null hypothesis. You can get guidance on which statistical test to run by using our Statistical Test Selector .

Operationally defining (measuring) the study

So far, we have simply referred to the outcome of the teaching methods as the "performance" of the students, but what do we mean by "performance". "Performance" could mean how students score in a piece of coursework, how many times they can answer questions in class, what marks they get in their exams, and so on. There are three major reasons why we should be clear about how we operationalize (i.e., measure) what we are studying. First, we simply need to be clear so that people reading our work are in no doubt about what we are studying. This makes it easier for them to repeat the study in future to see if they also get the same (or similar) results; something called internal validity . Second, one of the criteria by which quantitative research is assessed, perhaps by an examiner if you are a student, is how you define what you are measuring (in this case, "performance") and how you choose to measure it. Third, it will determine which statistical test you need to use because the choice of statistical test is largely based on how your variables were measured (e.g., whether the variable, "performance", was measured on a "continuous" scale of 1-100 marks; an "ordinal" scale with groups of marks, such as 0-20, 21-40, 41-60, 61-80 and 81-100; or some of other scale; see the statistical guide, Types of Variable , for more information).

It is worth noting that these choices will sometimes be personal choices (i.e., they are subjective) and at other times they will be guided by some other/external information. For example, if you were to measure intelligence, there may be a number of characteristics that you could use, such as IQ, emotional intelligence, and so forth. What you choose here will likely be a personal choice because all these variables are proxies for intelligence; that is, they are variables used to infer an individual's intelligence, but not everyone would agree that IQ alone is an accurate measure of intelligence. In contrast, if you were measuring company performance, you would find a number of established metrics in the academic and practitioner literature that would determine what you should test, such as "Return on Assets", etc. Therefore, to know what you should measure, it is always worth looking at the literature first to see what other studies have done, whether you use the same measures or not. It is then a matter of making an educated decision whether the variables you choose to examine are accurate proxies for what you are trying to study, as well as discussing the potential limitations of these proxies.

In the case of measuring a statistics student's performance there are a number of proxies that could be used, such as class participation, coursework marks and exam marks, since these are all good measures of performance. However, in this case, we choose exam marks as our measure of performance for two reasons: First, as a statistics tutor, we feel that Sarah's main job is to help her students get the best grade possible since this will affect her students' overall grades in their graduate management degree. Second, the assessment for the statistics course is a single two hour exam. Since there is no coursework and class participation is not assessed in this course, exam marks seem to be the most appropriate proxy for performance. However, it is worth noting that if the assessment for the statistics course was not only a two hour exam, but also a piece of coursework, we would probably have chosen to measure both exam marks and coursework marks as proxies of performance.

The next step is to define the variables that we are using in our study (see the statistical guide, Types of Variable , for more information). Since the study aims to examine the effect that two different teaching methods – providing lectures and seminar classes (Sarah) and providing lectures by themselves (Mike) – had on the performance of Sarah's 50 students and Mike's 50 students, the variables being measured are:

By using a very straightforward example, we have only one dependent variable and one independent variable although studies can examine any number of dependent and independent variables. Now that we know what our variables are, we can look at how to set out the null and alternative hypothesis on the next page .

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How to Write a Hypothesis: The Ultimate Guide with Examples

Hypotheses aren’t about science, experiments, and creating new theories only. While students in science classes formulate a hypothesis every second day, others from non-science fields may find it challenging to write it for an essay or a research paper.

This article is here to reveal the nature of hypothesis writing and help you learn how to write a hypothesis for essays, reports, studies, and any paper type you may need to compose.

We’ve researched all the guides, invited  our top writers  to answer all the FAQs students have on hypothesis writing, gathered hypothesis examples, and put first things first.

Yes, we are ready to make it loud and clear with our essay maker !

Table of Contents:

• Hypothesis vs. prediction
• Theory vs. hypothesis
• Hypothesis characteristics
• Thesis statement vs. hypothesis in an essay
• Main hypothesis sources
• 7 types of hypotheses you may need to write
• Ask a question
• Conduct research
• Write a null hypothesis
• Define variables
• State it using an if-then format
• What is a hypothesis in a research paper?
• How to write a hypothesis: example
• Frequently asked questions

What is a Hypothesis?

A hypothesis is an assumption you make based on existing data and knowledge, stating your predictions about what your research will find. It’s a tentative answer to your research question; it needs to be testable so you could later support or refuse it through further experiments, observations, and any other scientific research methods.

Example of a hypothesis:

Teenagers who get sex education lessons in high school will have lower rates of unplanned pregnancy than those who did not get any sex education.

Your research question here is,  “How effective is high school sex education at reducing teen pregnancies?”  and you formulate a hypothesis to check and explain in your paper.

A hypothesis always proposes a relationship between several variables. As a rule, variables are two – independent and dependent – but it’s also possible to state more variables in your hypothesis essay, to address different aspects of your research question.

• An independent variable  is the one you, as a researcher, can change or control.
• A dependent variable  is the one you, as a researcher, observe and measure based on how an independent variable changes.

In the above example, we can see that an independent variable is “sex education lessons at school” (you assume it is a cause). And a dependent variable here is “lower rates of unplanned pregnancy” (you consider it’s an effect).

Please note that there’s a difference between theory and hypothesis. Also, some guides may tell you that a hypothesis equals a  thesis statement  in essay writing, though a slight difference between these two is yet in place.

More on that below.

Hypothesis vs. Prediction

Given they both are a kind of guess, many people get a hypothesis and a prediction confused. But while a difference is slight, it’s yet critical:

• A hypothesis  explains  why something happens based on  scientific methods  (testing, experiments, data analysis, etc.).
• A prediction  suggests  that something will happen based on  observations .

You write a hypothesis using a statement with variables, while a prediction consists of “if-then” schemes stating about future happenings.

We can also say that a prediction is something you expect to happen if your hypothesis statement is true.

Theory vs. Hypothesis

• A hypothesis states a  suggested  explanation of a phenomenon, which you’ll later support or refuse through testing and other scientific methods.
• A theory is an  already tested , well-substantiated explanation backed by evidence.

You write a hypothesis using a statement with variables, while a theory represents a phenomenon that is already widely accepted and supported by data.

Examples of theories include Einstein’s theory of relativity, the Big Bang theory, Charles Darwin’s theory of evolution, and many others.

For your hypothesis to become a theory, you need to test all the aspects under various circumstances and prove it with well-substantiated facts. You can also use theories to make predictions about something unexplained and then turn those predictions into hypotheses to test and support (or refuse).

It’s worth noting that testings don’t stop once a hypothesis becomes a theory: Science is ongoing, and any theory can become disproved one day.

Hypothesis Characteristics

And now it’s high time to reveal the characteristics of your statement to become a reasonable hypothesis.

They are five:

• A cause-effect relationship between variables . When writing a hypothesis, make sure your one variable causes another one to change (or not change.) There should always be a cause-effect relationship between them.
• Testable nature.  Formulate a hypothesis that you can  test  to support or refuse. You should be able to conduct experiments and control your thesis when working on it.
• Precise and accurate variables.  Your hypothesis’s independent and dependent variables need to be specific and clear for the audience to understand.
• Explained in simple language.   Research papers  and academic writing, in general, are often challenging to understand for an average reader, so do your best to write a hypothesis so there would be no confusion or ambiguity.
• Ethical.  We can test many things, but there’s always a question about  what  we should test or make a subject to experiments. Avoid questionable or taboo topics when thinking about your hypothesis outline.

Thesis Statement vs. Hypothesis in an Essay

When looking for information on writing a hypothesis essay, you can find guides telling that it’s the same with writing a thesis statement for your  argumentative essay . This notion is not entirely true, and there’s still a slight difference between these two:

• A thesis statement is a sentence or two in your essay introduction that summarizes a central claim you’ll  discuss and prove  in the essay body. You’ll use arguments, evidence, and examples for that. 
• A hypothesis is a one-sentence prediction based on the relationships between reliables that you’ll  test   and then  prove or disprove  in the essay body. You’ll use experiments, observation, and quantitative research for that.

Writing a research study should have a thesis statement; if your research intends to prove/disprove something, it will also contain a hypothesis statement.

Feel free to try our  online thesis statement generator  to get a better idea of writing strong thesis statements for your essays.

Main Hypothesis Sources

Once they ask you to write a hypothesis essay, it would be great to have some sources for inspiration at hand, wouldn’t it?

Where to go for  creative ideas ? Where to research hypothesis and come up with new statements for your essay? What sources do science students use?

The primary hypothesis sources are four:

• Scientific theories that already exist
• Some general patterns affecting our thinking process
• Analogies between different phenomena we observe
• The previous knowledge and observations from studies and our experience

Depending on the niche and type of hypothesis you need to cover, you’ll use corresponding sources for research and further hypothesis  outline .

Below you’ll learn what types of hypotheses exist and how to write a hypothesis statement so it would sound scientific.

7 Types of Hypotheses You May Need to Write

So many sources, so many hypothesis classifications they offer. Some specify eight, ten, and even 13  types of hypotheses, depending on the factors like the number of variables you use and the experiment stage you’re in. Some insist that only two significant kinds of hypotheses exist: alternative and null; others call them directional and non-directional hypotheses, respectively.

Let’s put things straight and explain the types of hypotheses you may need to write in essays . They are seven, with examples for you to get a better idea of “who is who,” as they say.

1) Simple hypothesis

It’s the most common type of hypothesis to use in college papers, predicting the direct relationship between two variables in your experiment: a single dependent and a single independent one.

How to write a simple hypothesis? Use an “if-then” format.

For example:

• Everyday smoking leads to lung cancer.  ( If  you smoke every day,  then  you’ll get lung cancer.)
• Covering wounds with a bandage heals with fewer scars.  ( If  you bandage an injury,  then  it will heal with less scarring.)

2) Complex hypothesis

This one also predicts the relationship between variables but has more than two dependent and independent variables to check for supporting or refusing.

• Overweight people who eat junk food have higher chances of getting excessive cholesterol and heart disease.  (Two independent variables are  extra weight  and  junk food consumption ; two dependent variables are  heart disease  and  high cholesterol level .)
• The higher illiteracy in a society, the higher is poverty and crime rate.  (One independent variable is higher  illiteracy , and two dependent variables are higher  poverty  and higher  crime rate .)

3) Null hypothesis

How to write a null hypothesis? It’s the default position stating there’s no relationship between variables, i.e., there will be no difference in the experiment’s results. 

Scientists use null hypotheses to disapprove or reaffirm given statements.

• A person’s productivity doesn’t suffer from getting six instead of eight hours of sleep.
• All daisies are equal in the number of their petals.
• Sex education in high school doesn’t affect unplanned pregnancy rates.

4) Alternative hypothesis

When searching for information on how to write a hypothesis online, you might see queries like “how to write a null and alternative hypothesis.” That’s because alternative hypothesis statements come in place when someone tries to  disprove  a null hypothesis, so these two go hand in hand.

In other words, an alternative hypothesis  directly contradicts  a null one.

Also, an alternative hypothesis is one you may want to develop when the experiment on your initial statement doesn’t bring any result.

• H0 (a null hypothesis): Light color does not affect plant growth.
• H1 (an alternative hypothesis): Light color affects plant growth.
• H0: Cats have no preference for food based on shape.
• H1: Cats prefer round kibbles to other food shapes.

5) Logical hypothesis

This one is a hypothesis you can verify logically, though there’s little to no substantial evidence for it. Here you use reasoning and logical connections instead of proven facts, statistics, or background research.

Logical hypotheses remain assumptions until you put them to the test and support/refuse them after experiments.

• Dogs won’t survive without water.  (Here, you make an assumption based on the fact humans can’t live without water, so dogs, as mammals, won’t do that, either.)
• Creatures from Mars won’t breathe in the Earth’s atmosphere.  (Here, you assume that they won’t because we humans can’t breathe on Mars.)

6) Empirical hypothesis

In plain English, it’s a currently-tested hypothesis that can yet be changed or adjusted according to the results of experiments. It’s a working hypothesis that’s yet to confirm or refuse:

Empirical hypotheses are those going through tests, trials, or errors via observation and experiments right now and can be changed later around the independent variables. As a rule, it’s the opposite of a logical hypothesis.

• Women taking vitamin E grow hair faster than those taking vitamin K.
• Mushrooms grow faster at 22 degrees Celsius than 27 degrees Celsius.

7) Statistical hypothesis

This one is a hypothesis you can test and verify statistically based on data and quantitative research methods.

How to write a statistical hypothesis?

Statistical hypotheses have quantifiable variables and are usually about the nature of a population. It comes in handy when it’s impossible to test or survey every single person in a group. To write such a hypothesis, you’ll need to state the data about your topic using a portion of people.

• 35% of the poor in the USA are illiterate.
• 60% of people talking on the phone while driving have been in at least one car accident.
• 56% of marriages end in divorce.

How to Write a Hypothesis: 5 Steps

First and foremost, it’s worth mentioning that hypothesis writing is the third step of the scientific method scholars, researchers, and science students use to test theories, answer questions, and solve problems.

The steps are six, and they are as follows:

• Observation:  Decide on an issue to solve or a phenomenon to explain. 
• Question:  Develop a research question you’d like to check.
• Hypothesis (we are here!):  Formulate a hypothesis that answers your question and that you can test.
• Prediction:  Determine the experiment’s outcome based on your hypothesis.
• Test:  Do your experiments to test your prediction.
• Analyze:  Review the results to see if your hypothesis was correct. If it wasn’t, you could revise it by formulating another one and going through the whole process again.

In academic writing, hypotheses come as something relating to thesis statements: It’s a sentence or two summarizing a central claim you’ll discuss and prove in your essay.

It stands to reason that hypothesis writing is more common for STEM disciplines like math, chemistry, biology, physics, or economics. Here’s how to craft it, step by step:

1) Ask a Question

This stage is about choosing an  argumentative topic for your essay . Except as assigned by a teacher or a thesis tutor, you can start with an issue of your interest, so your curiosity and questions on it come naturally.

Why is it the way it is?

Why does it happen the way it goes?

What causes this factor you see around?

Your question needs to be  clear ,  specific , and  manageable  so you can research it, test it, and analyze the results. Also, ensure it’s not too broad so you can focus on its particular aspect to formulate your hypothesis.

For example:   How does eating apples affect human dental health?

2) Conduct Research

Now you’ll need to check and collect some information on your question to understand if it’s possible to formulate a research hypothesis. It’s so-called initial research to find an answer to your question.

This stage is not about proving or disproving your hypothesis. Here you’ll collect facts, theories, past studies, and any other information that will help prove or disprove it so that you can make an apparent assumption: Based on the gathered information, you’ll be able to make a logical guess.

Depending on your question, this initial research can  take some time  from you. You may need to read a few books on the topic, find and compare some scientific materials, etc. Or, it may be enough to perform a quick web search to find the answer.

3) Write a Null Hypothesis

To ease the process of hypothesis writing, start with a null hypothesis. As you already know, it’s the default position stating no relationship between variables. (And that’s why it’s so easy to formulate.)

So, take your initial question and write it as a negative statement. In our example with eating apples and dental health, the null hypothesis would sound like that:

Eating apples do not affect a human’s dental health.

(Which means your teeth condition will be the same, whether you eat apples or not.)

4) Define Variables

And now, for your hypothesis to become testable so you can do experiments, make predictions, and analyze the results, think of dependent and independent variables for it.

As you already know, independent variables are the factors you, as a researcher, can control during experiments to check the hypothesis. 

Example:   Eating one apple a day will positively affect a human’s dental health.

“One apple” is the independent variable, and “dental health” is the dependent variable here.

You’ll come up with variables based on your initial research. With some facts and studies already in place, you can predict how your experiment may go and what its results may be. Use this knowledge to shape variables into a clear and concise hypothesis.

And remember:

The way you’ll frame a hypothesis into one sentence depends on a few factors: the type of your project and the type of hypothesis you want to use. 

Simple hypotheses are most common for student research papers , so we use them as examples here. With that in mind, the final stage of hypothesis writing comes:

5) State It Using an If-Then Format

To formulate a hypothesis the best way possible, try framing it with an “if-then” format. Like this:

If a human eats one apple per day, then he gets healthier teeth.

This format becomes tricky when working with complex hypotheses with multiple variables, but it’s reliable when expressing the cause-and-effect relationship. 

The “if-then” format allows you to refine a hypothesis and ensure its final version:

• is clear, specific, and testable;
• has relevant variables;
• identifies the relationship between variables;
• suggests a predicted result of the experiment.

Another way to check if you’ve shaped a hypothesis properly is using the “PICOT” model, best explained via  visual examples . According to this model, a hypothesis should have five components:

P –  population: the specific group or individual of your research

I –  interest: the primary concern of your study

C –  comparison: the leading alternative group

O –  outcome: the expected result

T – time: the length of your experimen t

Always write a hypothesis in  the present tense  because it refers to research that’s currently being conducted.

What is a Hypothesis in a Research Paper?

A hypothesis in a research paper is a statement demonstrating a prediction you believe may happen based on research, evidence, and experimentation.

Often used and associated with science, hypotheses are assumptions (or guesses) for researchers and scholars to prove or disprove via tests and experiments. And they later write a hypothesis essay to analyze and report the experiments’ results to the scientific community.

When writing a hypothesis for a research paper, you should still describe an experiment to prove or disprove it. However, hypothesis essays don’t necessarily have to be on STEM disciplines and tests taken in a lab:

• You can  write a book critique  and state a hypothesis on its or its author’s impact on literature. 
• Or, your hypothesis essay can be about how demographics change a country’s language.
• Or, you’ll  write an autobiography  with a focus on the hypothesis that one particular event influenced your further deeds. 

In such essays, you won’t spend hours in labs to prove that your hypothesis is true; you’ll do that through research, arguments, data, interviews, or previous studies.

Is a thesis statement a hypothesis?

As we already mentioned, there’s a slight difference between these two. While  thesis statements  in essays are about  summarizing  a central claim you’ll discuss,  hypotheses  are about  predictions  or  assumptions  you’ll prove (or disprove) in the essay body.

You don’t have to prove that your hypothesis is correct. The point is to research, test, and experiment to see if you’re right. Even if your hypothesis appears incorrect in  conclusion , it doesn’t mean the quality of your essay is poor.

How to Write a Hypothesis: Example

And now, let’s go to even more hypothesis examples for you to understand the nature of this writing better.

Here goes another example of a hypothesis:

Frequently Asked Questions

What is a hypothesis in an essay.

A hypothesis in an essay is a statement demonstrating a prediction you believe may happen based on research, evidence, and experimentation. As a rule, it predicts the relationship between a few variables; and you can prove or disprove it by the end of your tests and experiments on it.

How long is a hypothesis?

A hypothesis is one-sentence long. It should be clear, direct, and testable through experimentation, predicting a possible outcome.

How to write a hypothesis statement?

First of all, you need to state a problem you’re trying to solve, do some initial research on it to learn the background and predict an outcome, and then think of both dependent and independent variables for your hypothesis. For that, research or brainstorm ideas for your stated problem’s solution. Finally, write your hypothesis as an “if-then” statement, using your variables.

How to write a null hypothesis?

A null hypothesis is the default position stating no relationship between variables. To write it, you need to assume an experiment has no effect regardless of variables; use denying. 

For example, you want to learn whether teens are better at math than adults. In this case, your null hypothesis will be, “ Age does not affect math ability.”

How to write an alternative hypothesis?

An alternative hypothesis directly contradicts   a null one, trying to disprove it. To write it, you need to assume there’s enough evidence to reject the null hypothesis; but never state your claim is already proven true or false.

In contrast with a null hypothesis, typically marked as H0, an alternative one gets an H1 mark. For example:

H0: If I put Mentos into a Coke bottle, there will be no reaction.

H1: If I put Mentos into a Coke bottle, there will be a big explosion.

How to write a simple hypothesis?

A simple hypothesis is the most common one to use in college papers. It predicts the direct relationship between two variables — one dependent and one independent, — so write a simple hypothesis with an “if-then” format.

For example: 

If a postpartum woman has low hemoglobin, then she gets higher risk of infection.

A statistical hypothesis claims the value of a single population characteristic or relationship between several population characteristics. To write it, you first need to specify null and alternative hypotheses, set the significance level, calculate the statistics, and draw a conclusion. Ensure that your variables are quantifiable. For example: 

A population mean is equal to 10.

How to write a hypothesis for a lab report?

To write a hypothesis for a lab report, you should state the issue, predict its outcome based on tests and experiments, define the variables, and formulate a hypothesis as an if-then statement. For example:

If one puts Mentos in a bottle with Coke, there will be an explosion.

How to write a hypothesis for a research paper?

• Decide on a question/problem you want to check/solve.
• Conduct initial research to collect as much background information and observation about your topic as you can.
• Evaluate this information to assume possible causes and possible explanations.
• Define variables you’ll use to confirm or disprove your hypothesis through experimentation.
• Write down a one-sentence hypothesis using the present tense.

Now that you know how to write a hypothesis, it’s high time to give it a try:

• Address your curiosity.
• Ask questions.
• Conduct some initial research.
• Come up with a type of hypothesis that fits your expectations most.

Think of variables for your hypothesis, and ensure it’s clear, concise, and measurable (testable). Then write it in the present tense — and you’ve got it!

Any questions left? Don’t hesitate to write in the comments (yes, we read them and reply!) or ask  Bid4Papers writers  directly!

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Our Writing Guides

9.1 Null and Alternative Hypotheses

The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

H 0 , the — null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.

H a —, the alternative hypothesis: a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are reject H 0 if the sample information favors the alternative hypothesis or do not reject H 0 or decline to reject H 0 if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in H 0 and H a :

H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

Example 9.1

H 0 : No more than 30 percent of the registered voters in Santa Clara County voted in the primary election. p ≤ 30 H a : More than 30 percent of the registered voters in Santa Clara County voted in the primary election. p > 30

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25 percent. State the null and alternative hypotheses.

Example 9.2

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are the following: H 0 : μ = 2.0 H a : μ ≠ 2.0

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : μ __ 66
• H a : μ __ 66

Example 9.3

We want to test if college students take fewer than five years to graduate from college, on the average. The null and alternative hypotheses are the following: H 0 : μ ≥ 5 H a : μ < 5

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : μ __ 45
• H a : μ __ 45

Example 9.4

An article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third of the students pass. The same article stated that 6.6 percent of U.S. students take advanced placement exams and 4.4 percent pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6 percent. State the null and alternative hypotheses. H 0 : p ≤ 0.066 H a : p > 0.066

On a state driver’s test, about 40 percent pass the test on the first try. We want to test if more than 40 percent pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : p __ 0.40
• H a : p __ 0.40

Collaborative Exercise

Bring to class a newspaper, some news magazines, and some internet articles. In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.

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5 Hypothesis Statements and Predictions

5.1 addressing the h ypothes es in an introduction section  .

In certain experiments where you are analyzing quantitative data, you will need to include hypothesis statements. That means presenting your null (H 0 ) and alternative (H A ) hypotheses using proper scientific language is key to the foundation of your investigation. The Null hypothesis (H 0 ) states that the independent variable will have no effect on the dependent variable. The Alternative hypothesis (H A ) states that the independent variable will have an effect on the dependent variable.

To write complete and effective null (H 0 ) and alternative (H A ) hypotheses that contain the proper scientific language you must include: 

• Both the common and Latin (scientific name using binomial nomenclature) name of the organism used in the experiment.
• The name of the independent variable that is being tested (i.e., what the experimenter is manipulating) including appropriate units.
• How the response will be measured or the dependent variable (i.e., what data the experimenter is recording) including appropriate units.

Below is an example of an effective null and alternative hypothesis:

Null hypothesis (H 0 ): Temperature (°C) will have no effect on the pulse rate, measured in beats per minute, of mice ( Mus musculus ).

Alternative hypothesis (H A ): Temperature (°C) will have an effect on the pulse rate, measured in beats per minute, of mice ( Mus musculus ). 

5.2 Activity –Addressing the Predictions in an Introduction Section 

A prediction is a statement of the specific trend you expect (e.g., increase, decrease or no change) to see when you conduct your investigation. The prediction describes the expected relationship between your independent and dependent variable. You should be able to provide sound justification for the reasoning behind your prediction by referencing background information from a peer reviewed source such as a textbook or journal article.

Here is an example of an effective prediction: 

Note how the author uses background information from another study and clearly states their prediction drawing on this information.

Now lets consider the Examples A and B we looked at previously. Here are the paragraphs of the hypotheses and predictions from the 2 examples for you to consider.

Example A  

The paragraphs below reflect how the hypotheses and prediction might be addressed in an introduction section.

Perreault and Whalen (2006) found that the burrowing activity of the endogeic earthworm Aporrectodea caliginosa and the anecic earthworm Lumbricus terrestris was influenced by soil temperature and moisture. They found there was less burrowing, but more weight gain and surface castings produced in wetter soil than in drier soil, suggesting that these worms were burrowing less, but feeding more in wetter soils (Perreault & Whalen, 2006). 

The purpose of this lab is to see if the moisture content of soil affects the rate of movement (cm/minute) of the epigeic earthworm Lumbricus rubellus (red earthworm). The null hypothesis is percent soil moisture content (PMC) will have no effect on the movement rate (cm/minute) of red earthworms ( Lumbricus rubellus ). The alternative hypothesis is percent soil moisture content (PMC) will have an effect on the movement rate (cm/minute) of red earthworms ( Lumbricus rubellus ). We predict that similar to the findings of Perreault and Whalen (2006) the rate of movement of Lumbricus rubellus will increase in drier soils.

Now, rev iew the example below. H ow does it compare to Example A? What advice would you give the author to help them professionally write null (H 0 ) and alternative (H A ) hypotheses? What advice would you give them regarding their prediction?    

Example B  

Perreault and Whalen studied earthworms and saw less burrowing of earthworms as the soil got wetter, but the worms ate more. We predict earth worms will move less and eat more like in the study. We are completing this amazing lab experiment for students to get an idea of how to use the scientific method to study earthworms and see if the water makes earthworms move less or more. The null hypothesis is soil wetness will have no change on the movement of red earthworms ( lumbricus Rubellus ). The alternative hypothesis is wetness will increase the movement of red earthworms. 

Consider what advice you would give these authors to improve their hypothesis statements and prediction.  

Complete the following quiz regarding hypothesis statements and predictions:

Introduction Writing Workshop Copyright © 2022 by KPU Biology Department. All Rights Reserved.

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Hypothesis Testing - Chi Squared Test

Lisa Sullivan, PhD

Professor of Biostatistics

Boston University School of Public Health

Introduction

This module will continue the discussion of hypothesis testing, where a specific statement or hypothesis is generated about a population parameter, and sample statistics are used to assess the likelihood that the hypothesis is true. The hypothesis is based on available information and the investigator's belief about the population parameters. The specific tests considered here are called chi-square tests and are appropriate when the outcome is discrete (dichotomous, ordinal or categorical). For example, in some clinical trials the outcome is a classification such as hypertensive, pre-hypertensive or normotensive. We could use the same classification in an observational study such as the Framingham Heart Study to compare men and women in terms of their blood pressure status - again using the classification of hypertensive, pre-hypertensive or normotensive status.  

The technique to analyze a discrete outcome uses what is called a chi-square test. Specifically, the test statistic follows a chi-square probability distribution. We will consider chi-square tests here with one, two and more than two independent comparison groups.

Learning Objectives

After completing this module, the student will be able to:

• Perform chi-square tests by hand
• Appropriately interpret results of chi-square tests
• Identify the appropriate hypothesis testing procedure based on type of outcome variable and number of samples

Tests with One Sample, Discrete Outcome

Here we consider hypothesis testing with a discrete outcome variable in a single population. Discrete variables are variables that take on more than two distinct responses or categories and the responses can be ordered or unordered (i.e., the outcome can be ordinal or categorical). The procedure we describe here can be used for dichotomous (exactly 2 response options), ordinal or categorical discrete outcomes and the objective is to compare the distribution of responses, or the proportions of participants in each response category, to a known distribution. The known distribution is derived from another study or report and it is again important in setting up the hypotheses that the comparator distribution specified in the null hypothesis is a fair comparison. The comparator is sometimes called an external or a historical control.   

In one sample tests for a discrete outcome, we set up our hypotheses against an appropriate comparator. We select a sample and compute descriptive statistics on the sample data. Specifically, we compute the sample size (n) and the proportions of participants in each response

Test Statistic for Testing H 0 : p 1 = p 10 , p 2 = p 20 , ..., p k = p k0

We find the critical value in a table of probabilities for the chi-square distribution with degrees of freedom (df) = k-1. In the test statistic, O = observed frequency and E=expected frequency in each of the response categories. The observed frequencies are those observed in the sample and the expected frequencies are computed as described below. χ 2 (chi-square) is another probability distribution and ranges from 0 to ∞. The test above statistic formula above is appropriate for large samples, defined as expected frequencies of at least 5 in each of the response categories.  

When we conduct a χ 2 test, we compare the observed frequencies in each response category to the frequencies we would expect if the null hypothesis were true. These expected frequencies are determined by allocating the sample to the response categories according to the distribution specified in H 0 . This is done by multiplying the observed sample size (n) by the proportions specified in the null hypothesis (p 10 , p 20 , ..., p k0 ). To ensure that the sample size is appropriate for the use of the test statistic above, we need to ensure that the following: min(np 10 , n p 20 , ..., n p k0 ) > 5.  

The test of hypothesis with a discrete outcome measured in a single sample, where the goal is to assess whether the distribution of responses follows a known distribution, is called the χ 2 goodness-of-fit test. As the name indicates, the idea is to assess whether the pattern or distribution of responses in the sample "fits" a specified population (external or historical) distribution. In the next example we illustrate the test. As we work through the example, we provide additional details related to the use of this new test statistic.  

A University conducted a survey of its recent graduates to collect demographic and health information for future planning purposes as well as to assess students' satisfaction with their undergraduate experiences. The survey revealed that a substantial proportion of students were not engaging in regular exercise, many felt their nutrition was poor and a substantial number were smoking. In response to a question on regular exercise, 60% of all graduates reported getting no regular exercise, 25% reported exercising sporadically and 15% reported exercising regularly as undergraduates. The next year the University launched a health promotion campaign on campus in an attempt to increase health behaviors among undergraduates. The program included modules on exercise, nutrition and smoking cessation. To evaluate the impact of the program, the University again surveyed graduates and asked the same questions. The survey was completed by 470 graduates and the following data were collected on the exercise question:

Based on the data, is there evidence of a shift in the distribution of responses to the exercise question following the implementation of the health promotion campaign on campus? Run the test at a 5% level of significance.

In this example, we have one sample and a discrete (ordinal) outcome variable (with three response options). We specifically want to compare the distribution of responses in the sample to the distribution reported the previous year (i.e., 60%, 25%, 15% reporting no, sporadic and regular exercise, respectively). We now run the test using the five-step approach.  

• Step 1. Set up hypotheses and determine level of significance.

The null hypothesis again represents the "no change" or "no difference" situation. If the health promotion campaign has no impact then we expect the distribution of responses to the exercise question to be the same as that measured prior to the implementation of the program.

H 0 : p 1 =0.60, p 2 =0.25, p 3 =0.15,  or equivalently H 0 : Distribution of responses is 0.60, 0.25, 0.15  

H 1 :   H 0 is false.          α =0.05

Notice that the research hypothesis is written in words rather than in symbols. The research hypothesis as stated captures any difference in the distribution of responses from that specified in the null hypothesis. We do not specify a specific alternative distribution, instead we are testing whether the sample data "fit" the distribution in H 0 or not. With the χ 2 goodness-of-fit test there is no upper or lower tailed version of the test.

• Step 2. Select the appropriate test statistic.  

The test statistic is:

We must first assess whether the sample size is adequate. Specifically, we need to check min(np 0 , np 1, ..., n p k ) > 5. The sample size here is n=470 and the proportions specified in the null hypothesis are 0.60, 0.25 and 0.15. Thus, min( 470(0.65), 470(0.25), 470(0.15))=min(282, 117.5, 70.5)=70.5. The sample size is more than adequate so the formula can be used.

• Step 3. Set up decision rule.  

The decision rule for the χ 2 test depends on the level of significance and the degrees of freedom, defined as degrees of freedom (df) = k-1 (where k is the number of response categories). If the null hypothesis is true, the observed and expected frequencies will be close in value and the χ 2 statistic will be close to zero. If the null hypothesis is false, then the χ 2 statistic will be large. Critical values can be found in a table of probabilities for the χ 2 distribution. Here we have df=k-1=3-1=2 and a 5% level of significance. The appropriate critical value is 5.99, and the decision rule is as follows: Reject H 0 if χ 2 > 5.99.

• Step 4. Compute the test statistic.  

We now compute the expected frequencies using the sample size and the proportions specified in the null hypothesis. We then substitute the sample data (observed frequencies) and the expected frequencies into the formula for the test statistic identified in Step 2. The computations can be organized as follows.

Notice that the expected frequencies are taken to one decimal place and that the sum of the observed frequencies is equal to the sum of the expected frequencies. The test statistic is computed as follows:

• Step 5. Conclusion.  

We reject H 0 because 8.46 > 5.99. We have statistically significant evidence at α=0.05 to show that H 0 is false, or that the distribution of responses is not 0.60, 0.25, 0.15.  The p-value is p < 0.005.  

In the χ 2 goodness-of-fit test, we conclude that either the distribution specified in H 0 is false (when we reject H 0 ) or that we do not have sufficient evidence to show that the distribution specified in H 0 is false (when we fail to reject H 0 ). Here, we reject H 0 and concluded that the distribution of responses to the exercise question following the implementation of the health promotion campaign was not the same as the distribution prior. The test itself does not provide details of how the distribution has shifted. A comparison of the observed and expected frequencies will provide some insight into the shift (when the null hypothesis is rejected). Does it appear that the health promotion campaign was effective?  

Consider the following: 

If the null hypothesis were true (i.e., no change from the prior year) we would have expected more students to fall in the "No Regular Exercise" category and fewer in the "Regular Exercise" categories. In the sample, 255/470 = 54% reported no regular exercise and 90/470=19% reported regular exercise. Thus, there is a shift toward more regular exercise following the implementation of the health promotion campaign. There is evidence of a statistical difference, is this a meaningful difference? Is there room for improvement?

The National Center for Health Statistics (NCHS) provided data on the distribution of weight (in categories) among Americans in 2002. The distribution was based on specific values of body mass index (BMI) computed as weight in kilograms over height in meters squared. Underweight was defined as BMI< 18.5, Normal weight as BMI between 18.5 and 24.9, overweight as BMI between 25 and 29.9 and obese as BMI of 30 or greater. Americans in 2002 were distributed as follows: 2% Underweight, 39% Normal Weight, 36% Overweight, and 23% Obese. Suppose we want to assess whether the distribution of BMI is different in the Framingham Offspring sample. Using data from the n=3,326 participants who attended the seventh examination of the Offspring in the Framingham Heart Study we created the BMI categories as defined and observed the following:

• Step 1.  Set up hypotheses and determine level of significance.

H 0 : p 1 =0.02, p 2 =0.39, p 3 =0.36, p 4 =0.23     or equivalently

H 0 : Distribution of responses is 0.02, 0.39, 0.36, 0.23

H 1 :   H 0 is false.        α=0.05

The formula for the test statistic is:

We must assess whether the sample size is adequate. Specifically, we need to check min(np 0 , np 1, ..., n p k ) > 5. The sample size here is n=3,326 and the proportions specified in the null hypothesis are 0.02, 0.39, 0.36 and 0.23. Thus, min( 3326(0.02), 3326(0.39), 3326(0.36), 3326(0.23))=min(66.5, 1297.1, 1197.4, 765.0)=66.5. The sample size is more than adequate, so the formula can be used.

Here we have df=k-1=4-1=3 and a 5% level of significance. The appropriate critical value is 7.81 and the decision rule is as follows: Reject H 0 if χ 2 > 7.81.

We now compute the expected frequencies using the sample size and the proportions specified in the null hypothesis. We then substitute the sample data (observed frequencies) into the formula for the test statistic identified in Step 2. We organize the computations in the following table.

The test statistic is computed as follows:

We reject H 0 because 233.53 > 7.81. We have statistically significant evidence at α=0.05 to show that H 0 is false or that the distribution of BMI in Framingham is different from the national data reported in 2002, p < 0.005.  

Again, the χ 2   goodness-of-fit test allows us to assess whether the distribution of responses "fits" a specified distribution. Here we show that the distribution of BMI in the Framingham Offspring Study is different from the national distribution. To understand the nature of the difference we can compare observed and expected frequencies or observed and expected proportions (or percentages). The frequencies are large because of the large sample size, the observed percentages of patients in the Framingham sample are as follows: 0.6% underweight, 28% normal weight, 41% overweight and 30% obese. In the Framingham Offspring sample there are higher percentages of overweight and obese persons (41% and 30% in Framingham as compared to 36% and 23% in the national data), and lower proportions of underweight and normal weight persons (0.6% and 28% in Framingham as compared to 2% and 39% in the national data). Are these meaningful differences?

In the module on hypothesis testing for means and proportions, we discussed hypothesis testing applications with a dichotomous outcome variable in a single population. We presented a test using a test statistic Z to test whether an observed (sample) proportion differed significantly from a historical or external comparator. The chi-square goodness-of-fit test can also be used with a dichotomous outcome and the results are mathematically equivalent.  

In the prior module, we considered the following example. Here we show the equivalence to the chi-square goodness-of-fit test.

The NCHS report indicated that in 2002, 75% of children aged 2 to 17 saw a dentist in the past year. An investigator wants to assess whether use of dental services is similar in children living in the city of Boston. A sample of 125 children aged 2 to 17 living in Boston are surveyed and 64 reported seeing a dentist over the past 12 months. Is there a significant difference in use of dental services between children living in Boston and the national data?

We presented the following approach to the test using a Z statistic. 

• Step 1. Set up hypotheses and determine level of significance

H 0 : p = 0.75

H 1 : p ≠ 0.75                               α=0.05

We must first check that the sample size is adequate. Specifically, we need to check min(np 0 , n(1-p 0 )) = min( 125(0.75), 125(1-0.75))=min(94, 31)=31. The sample size is more than adequate so the following formula can be used

This is a two-tailed test, using a Z statistic and a 5% level of significance. Reject H 0 if Z < -1.960 or if Z > 1.960.

We now substitute the sample data into the formula for the test statistic identified in Step 2. The sample proportion is:

We reject H 0 because -6.15 < -1.960. We have statistically significant evidence at a =0.05 to show that there is a statistically significant difference in the use of dental service by children living in Boston as compared to the national data. (p < 0.0001).  

We now conduct the same test using the chi-square goodness-of-fit test. First, we summarize our sample data as follows:

H 0 : p 1 =0.75, p 2 =0.25     or equivalently H 0 : Distribution of responses is 0.75, 0.25 

We must assess whether the sample size is adequate. Specifically, we need to check min(np 0 , np 1, ...,np k >) > 5. The sample size here is n=125 and the proportions specified in the null hypothesis are 0.75, 0.25. Thus, min( 125(0.75), 125(0.25))=min(93.75, 31.25)=31.25. The sample size is more than adequate so the formula can be used.

Here we have df=k-1=2-1=1 and a 5% level of significance. The appropriate critical value is 3.84, and the decision rule is as follows: Reject H 0 if χ 2 > 3.84. (Note that 1.96 2 = 3.84, where 1.96 was the critical value used in the Z test for proportions shown above.)

(Note that (-6.15) 2 = 37.8, where -6.15 was the value of the Z statistic in the test for proportions shown above.)

We reject H 0 because 37.8 > 3.84. We have statistically significant evidence at α=0.05 to show that there is a statistically significant difference in the use of dental service by children living in Boston as compared to the national data.  (p < 0.0001). This is the same conclusion we reached when we conducted the test using the Z test above. With a dichotomous outcome, Z 2 = χ 2 !   In statistics, there are often several approaches that can be used to test hypotheses. 

Tests for Two or More Independent Samples, Discrete Outcome

Here we extend that application of the chi-square test to the case with two or more independent comparison groups. Specifically, the outcome of interest is discrete with two or more responses and the responses can be ordered or unordered (i.e., the outcome can be dichotomous, ordinal or categorical). We now consider the situation where there are two or more independent comparison groups and the goal of the analysis is to compare the distribution of responses to the discrete outcome variable among several independent comparison groups.  

The test is called the χ 2 test of independence and the null hypothesis is that there is no difference in the distribution of responses to the outcome across comparison groups. This is often stated as follows: The outcome variable and the grouping variable (e.g., the comparison treatments or comparison groups) are independent (hence the name of the test). Independence here implies homogeneity in the distribution of the outcome among comparison groups.    

The null hypothesis in the χ 2 test of independence is often stated in words as: H 0 : The distribution of the outcome is independent of the groups. The alternative or research hypothesis is that there is a difference in the distribution of responses to the outcome variable among the comparison groups (i.e., that the distribution of responses "depends" on the group). In order to test the hypothesis, we measure the discrete outcome variable in each participant in each comparison group. The data of interest are the observed frequencies (or number of participants in each response category in each group). The formula for the test statistic for the χ 2 test of independence is given below.

Test Statistic for Testing H 0 : Distribution of outcome is independent of groups

and we find the critical value in a table of probabilities for the chi-square distribution with df=(r-1)*(c-1).

Here O = observed frequency, E=expected frequency in each of the response categories in each group, r = the number of rows in the two-way table and c = the number of columns in the two-way table.   r and c correspond to the number of comparison groups and the number of response options in the outcome (see below for more details). The observed frequencies are the sample data and the expected frequencies are computed as described below. The test statistic is appropriate for large samples, defined as expected frequencies of at least 5 in each of the response categories in each group.  

The data for the χ 2 test of independence are organized in a two-way table. The outcome and grouping variable are shown in the rows and columns of the table. The sample table below illustrates the data layout. The table entries (blank below) are the numbers of participants in each group responding to each response category of the outcome variable.

Table - Possible outcomes are are listed in the columns; The groups being compared are listed in rows.

In the table above, the grouping variable is shown in the rows of the table; r denotes the number of independent groups. The outcome variable is shown in the columns of the table; c denotes the number of response options in the outcome variable. Each combination of a row (group) and column (response) is called a cell of the table. The table has r*c cells and is sometimes called an r x c ("r by c") table. For example, if there are 4 groups and 5 categories in the outcome variable, the data are organized in a 4 X 5 table. The row and column totals are shown along the right-hand margin and the bottom of the table, respectively. The total sample size, N, can be computed by summing the row totals or the column totals. Similar to ANOVA, N does not refer to a population size here but rather to the total sample size in the analysis. The sample data can be organized into a table like the above. The numbers of participants within each group who select each response option are shown in the cells of the table and these are the observed frequencies used in the test statistic.

The test statistic for the χ 2 test of independence involves comparing observed (sample data) and expected frequencies in each cell of the table. The expected frequencies are computed assuming that the null hypothesis is true. The null hypothesis states that the two variables (the grouping variable and the outcome) are independent. The definition of independence is as follows:

 Two events, A and B, are independent if P(A|B) = P(A), or equivalently, if P(A and B) = P(A) P(B).

The second statement indicates that if two events, A and B, are independent then the probability of their intersection can be computed by multiplying the probability of each individual event. To conduct the χ 2 test of independence, we need to compute expected frequencies in each cell of the table. Expected frequencies are computed by assuming that the grouping variable and outcome are independent (i.e., under the null hypothesis). Thus, if the null hypothesis is true, using the definition of independence:

P(Group 1 and Response Option 1) = P(Group 1) P(Response Option 1).

 The above states that the probability that an individual is in Group 1 and their outcome is Response Option 1 is computed by multiplying the probability that person is in Group 1 by the probability that a person is in Response Option 1. To conduct the χ 2 test of independence, we need expected frequencies and not expected probabilities . To convert the above probability to a frequency, we multiply by N. Consider the following small example.

The data shown above are measured in a sample of size N=150. The frequencies in the cells of the table are the observed frequencies. If Group and Response are independent, then we can compute the probability that a person in the sample is in Group 1 and Response category 1 using:

P(Group 1 and Response 1) = P(Group 1) P(Response 1),

P(Group 1 and Response 1) = (25/150) (62/150) = 0.069.

Thus if Group and Response are independent we would expect 6.9% of the sample to be in the top left cell of the table (Group 1 and Response 1). The expected frequency is 150(0.069) = 10.4.   We could do the same for Group 2 and Response 1:

P(Group 2 and Response 1) = P(Group 2) P(Response 1),

P(Group 2 and Response 1) = (50/150) (62/150) = 0.138.

The expected frequency in Group 2 and Response 1 is 150(0.138) = 20.7.

Thus, the formula for determining the expected cell frequencies in the χ 2 test of independence is as follows:

Expected Cell Frequency = (Row Total * Column Total)/N.

The above computes the expected frequency in one step rather than computing the expected probability first and then converting to a frequency.  

In a prior example we evaluated data from a survey of university graduates which assessed, among other things, how frequently they exercised. The survey was completed by 470 graduates. In the prior example we used the χ 2 goodness-of-fit test to assess whether there was a shift in the distribution of responses to the exercise question following the implementation of a health promotion campaign on campus. We specifically considered one sample (all students) and compared the observed distribution to the distribution of responses the prior year (a historical control). Suppose we now wish to assess whether there is a relationship between exercise on campus and students' living arrangements. As part of the same survey, graduates were asked where they lived their senior year. The response options were dormitory, on-campus apartment, off-campus apartment, and at home (i.e., commuted to and from the university). The data are shown below.

Based on the data, is there a relationship between exercise and student's living arrangement? Do you think where a person lives affect their exercise status? Here we have four independent comparison groups (living arrangement) and a discrete (ordinal) outcome variable with three response options. We specifically want to test whether living arrangement and exercise are independent. We will run the test using the five-step approach.  

H 0 : Living arrangement and exercise are independent

H 1 : H 0 is false.                α=0.05

The null and research hypotheses are written in words rather than in symbols. The research hypothesis is that the grouping variable (living arrangement) and the outcome variable (exercise) are dependent or related.   

• Step 2.  Select the appropriate test statistic.  

The condition for appropriate use of the above test statistic is that each expected frequency is at least 5. In Step 4 we will compute the expected frequencies and we will ensure that the condition is met.

The decision rule depends on the level of significance and the degrees of freedom, defined as df = (r-1)(c-1), where r and c are the numbers of rows and columns in the two-way data table.   The row variable is the living arrangement and there are 4 arrangements considered, thus r=4. The column variable is exercise and 3 responses are considered, thus c=3. For this test, df=(4-1)(3-1)=3(2)=6. Again, with χ 2 tests there are no upper, lower or two-tailed tests. If the null hypothesis is true, the observed and expected frequencies will be close in value and the χ 2 statistic will be close to zero. If the null hypothesis is false, then the χ 2 statistic will be large. The rejection region for the χ 2 test of independence is always in the upper (right-hand) tail of the distribution. For df=6 and a 5% level of significance, the appropriate critical value is 12.59 and the decision rule is as follows: Reject H 0 if c 2 > 12.59.

We now compute the expected frequencies using the formula,

Expected Frequency = (Row Total * Column Total)/N.

The computations can be organized in a two-way table. The top number in each cell of the table is the observed frequency and the bottom number is the expected frequency.   The expected frequencies are shown in parentheses.

Notice that the expected frequencies are taken to one decimal place and that the sums of the observed frequencies are equal to the sums of the expected frequencies in each row and column of the table.  

Recall in Step 2 a condition for the appropriate use of the test statistic was that each expected frequency is at least 5. This is true for this sample (the smallest expected frequency is 9.6) and therefore it is appropriate to use the test statistic.

We reject H 0 because 60.5 > 12.59. We have statistically significant evidence at a =0.05 to show that H 0 is false or that living arrangement and exercise are not independent (i.e., they are dependent or related), p < 0.005.  

Again, the χ 2 test of independence is used to test whether the distribution of the outcome variable is similar across the comparison groups. Here we rejected H 0 and concluded that the distribution of exercise is not independent of living arrangement, or that there is a relationship between living arrangement and exercise. The test provides an overall assessment of statistical significance. When the null hypothesis is rejected, it is important to review the sample data to understand the nature of the relationship. Consider again the sample data. 

Because there are different numbers of students in each living situation, it makes the comparisons of exercise patterns difficult on the basis of the frequencies alone. The following table displays the percentages of students in each exercise category by living arrangement. The percentages sum to 100% in each row of the table. For comparison purposes, percentages are also shown for the total sample along the bottom row of the table.

From the above, it is clear that higher percentages of students living in dormitories and in on-campus apartments reported regular exercise (31% and 23%) as compared to students living in off-campus apartments and at home (10% each).  

Test Yourself

 Pancreaticoduodenectomy (PD) is a procedure that is associated with considerable morbidity. A study was recently conducted on 553 patients who had a successful PD between January 2000 and December 2010 to determine whether their Surgical Apgar Score (SAS) is related to 30-day perioperative morbidity and mortality. The table below gives the number of patients experiencing no, minor, or major morbidity by SAS category.  

Question: What would be an appropriate statistical test to examine whether there is an association between Surgical Apgar Score and patient outcome? Using 14.13 as the value of the test statistic for these data, carry out the appropriate test at a 5% level of significance. Show all parts of your test.

In the module on hypothesis testing for means and proportions, we discussed hypothesis testing applications with a dichotomous outcome variable and two independent comparison groups. We presented a test using a test statistic Z to test for equality of independent proportions. The chi-square test of independence can also be used with a dichotomous outcome and the results are mathematically equivalent.  

In the prior module, we considered the following example. Here we show the equivalence to the chi-square test of independence.

A randomized trial is designed to evaluate the effectiveness of a newly developed pain reliever designed to reduce pain in patients following joint replacement surgery. The trial compares the new pain reliever to the pain reliever currently in use (called the standard of care). A total of 100 patients undergoing joint replacement surgery agreed to participate in the trial. Patients were randomly assigned to receive either the new pain reliever or the standard pain reliever following surgery and were blind to the treatment assignment. Before receiving the assigned treatment, patients were asked to rate their pain on a scale of 0-10 with higher scores indicative of more pain. Each patient was then given the assigned treatment and after 30 minutes was again asked to rate their pain on the same scale. The primary outcome was a reduction in pain of 3 or more scale points (defined by clinicians as a clinically meaningful reduction). The following data were observed in the trial.

We tested whether there was a significant difference in the proportions of patients reporting a meaningful reduction (i.e., a reduction of 3 or more scale points) using a Z statistic, as follows. 

H 0 : p 1 = p 2    

H 1 : p 1 ≠ p 2                             α=0.05

Here the new or experimental pain reliever is group 1 and the standard pain reliever is group 2.

We must first check that the sample size is adequate. Specifically, we need to ensure that we have at least 5 successes and 5 failures in each comparison group or that:

In this example, we have

Therefore, the sample size is adequate, so the following formula can be used:

Reject H 0 if Z < -1.960 or if Z > 1.960.

We now substitute the sample data into the formula for the test statistic identified in Step 2. We first compute the overall proportion of successes:

We now substitute to compute the test statistic.

• Step 5.  Conclusion.  

We now conduct the same test using the chi-square test of independence.  

H 0 : Treatment and outcome (meaningful reduction in pain) are independent

H 1 :   H 0 is false.         α=0.05

The formula for the test statistic is:  

For this test, df=(2-1)(2-1)=1. At a 5% level of significance, the appropriate critical value is 3.84 and the decision rule is as follows: Reject H0 if χ 2 > 3.84. (Note that 1.96 2 = 3.84, where 1.96 was the critical value used in the Z test for proportions shown above.)

We now compute the expected frequencies using:

The computations can be organized in a two-way table. The top number in each cell of the table is the observed frequency and the bottom number is the expected frequency. The expected frequencies are shown in parentheses.

A condition for the appropriate use of the test statistic was that each expected frequency is at least 5. This is true for this sample (the smallest expected frequency is 22.0) and therefore it is appropriate to use the test statistic.

(Note that (2.53) 2 = 6.4, where 2.53 was the value of the Z statistic in the test for proportions shown above.)

Chi-Squared Tests in R

The video below by Mike Marin demonstrates how to perform chi-squared tests in the R programming language.

Answer to Problem on Pancreaticoduodenectomy and Surgical Apgar Scores

We have 3 independent comparison groups (Surgical Apgar Score) and a categorical outcome variable (morbidity/mortality). We can run a Chi-Squared test of independence.

H 0 : Apgar scores and patient outcome are independent of one another.

H A : Apgar scores and patient outcome are not independent.

Chi-squared = 14.3

Since 14.3 is greater than 9.49, we reject H 0.

There is an association between Apgar scores and patient outcome. The lowest Apgar score group (0 to 4) experienced the highest percentage of major morbidity or mortality (16 out of 57=28%) compared to the other Apgar score groups.

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9: Hypothesis Testing for a Single Variable and Population

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One job of a statistician is to make statistical inferences about populations based on samples taken from the population. Confidence intervals are one way to estimate a population parameter. Another way to make a statistical inference is to make a decision about a parameter. For instance, a car dealer advertises that its new small truck gets 35 miles per gallon, on average. A tutoring service claims that its method of tutoring helps 90% of its students get an A or a B. A company says that women managers in their company earn an average of $60,000 per year.

• 9.1: Hypothesis Tests- An Introduction The actual test begins by considering two hypotheses. They are called the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints. Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not.
• 9.2: Type I and Type II Errors In every hypothesis test, the outcomes are dependent on a correct interpretation of the data. Incorrect calculations or misunderstood summary statistics can yield errors that affect the results. A Type I error occurs when a true null hypothesis is rejected. A Type II error occurs when a false null hypothesis is not rejected.
• 9.3: Hypothesis Tests about μ- p-value Approach When testing for a single population mean: A Student's t-test should be used if the data come from a simple, random sample and the population is approximately normally distributed, or the sample size is large, with an unknown standard deviation. The normal test will work if the data come from a simple, random sample and the population is approximately normally distributed, or the sample size is large, with a known standard deviation.
• 9.4: Hypothesis Tests about μ- Critical Region Approach When the probability of an event occurring is low, and it happens, it is called a rare event. Rare events are important to consider in hypothesis testing because they can inform your willingness not to reject or to reject a null hypothesis. To test a null hypothesis, find the p-value for the sample data and graph the results.
• 9.5: Hypothesis Tests for a Proportion A statistics Worksheet:  The student will select the appropriate distributions to use in each case. The student will conduct hypothesis tests and interpret the results.

Contributors and Attributions

Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/[email protected] .

Hypothesis Testing: A Step-by-Step Guide With Easy Examples

Introduction  

When we hear the word ‘hypothesis,’ the first thing that comes to our mind is a kind of theory. Assuming and explaining theories is a fundamental part of Business Analytics. In the past few years, the field of Business Analytics has proliferated and made several advancements. As the number of people interested in its statistical applications in business has increased, the concept of hypothesis testing has grabbed everyone’s attention.

Let us find out more about testing of hypothesis and the different steps through which you can write a hypothesis.  

What is Hypothesis?  

A hypothesis’s general definition says, “Hypothesis is an assumption made based on some evidence.” It is a theory you propose about what will happen in the future based on current circumstances. Proposing a hypothesis is the first and most important step of any research or investigation as it decides the future path of the research/investigation and can lead it to a faithful and acceptable answer.  

Key Points of a Hypothesis  

• The assumptions made while proposing the theory should be precise and based on proper evidence.  
• The hypothesis should target a specific topic only and should have the scope to conduct various experiments for proving the assumptions.  
• The sources used for developing a hypothesis must be based on scientific theories, common patterns that affect the thought process of the people, and observations made in past research programs on the same topic.  

Types of Hypotheses With Examples  

There are multiple types of hypotheses which are described below.  

1. Simple Hypothesis

As the name suggests, a simple hypothesis is pretty simple to work on. It just deals with a single independent variable and one dependent variable. While proving a simple hypothesis, you just have to confirm that these two variables are linked.  

Example: If you eat more vegetables, you will be safe from heart disease. Here eating vegetables is an independent variable and staying safe from heart disease is a dependent variable.  

2. Complex Hypothesis  

Unlike a simple hypothesis, a complex hypothesis deals with multiple dependent and independent variables in the assumption simultaneously. The involvement of multiple variables makes the hypothesis more accurate and more difficult to prove simultaneously.  

Example: Age, diet, and weight affect the chances of diseases like diabetes or blood pressure. Age, diet, and weight are independent variables, and diabetes and blood pressure are dependent variables.  

3. Null Hypothesis  

The null hypothesis is the opposite of the simple hypothesis. Where a simple hypothesis tries to establish a link between the dependent and the independent variables, the Null hypothesis tries to prove that there’s no link between the given variables. Simply put, it tries to prove a statement opposite to the proposed hypothesis. It is represented as H0.  

Example: Age and daily routine affect the chances of heart disease. In a Null hypothesis, you will try to prove that there is no relation between the given factors, i.e., age, weight, and heart disease.  

4. Alternative Hypothesis  

An alternative hypothesis tries to disapprove the assumptions or statements proposed in a null hypothesis. Generally, alternative and null hypotheses are used together. An alternative hypothesis is represented as HA.  

  It is to be noted that H0 ≠ H A.   The alternate hypothesis further branches into two categories:  

• Directional Hypothesis: The result obtained through this type of alternative hypothesis is either negative or positive. It is represented by adding ‘>’ or ‘<‘ along with the HA symbol.
• Non-Directional Hypothesis: This type of hypothesis only clarifies the dependency of the dependent variables on the independent variable. It does not state anything about the result being positive or negative.  

  Example:  

Age and daily routine affect the chances of heart disease. In an Alternative Hypothesis, you will try to prove that age and daily routine affect heart disease chances.  

• If you prove the result is positive or negative, i.e., age and daily routine do or do not affect the chances of heart disease, it is a directional hypothesis  
• If you only prove that the chances of heart disease depend on variables like age and daily routine, it is a non-directional hypothesis.  

5. Logical Hypothesis  

Logical hypotheses cannot be proved with the help of scientific evidence. The assumptions made in a logical hypothesis are based on some logical explanation that backs up our assumptions. Logical hypotheses are mostly used in philosophy, and as the assumptions made are often too complex or simply unrealistic, they are untestable, and we have to rely on logical explanations.  

Example:  

Dinosaurs are related to the reptile family as both have scales. As the dinosaurs are extinct, we cannot test the given hypothesis and rely on our logical explanation on, not the experimental data.  

6. Empirical Hypothesis  

It is the complete opposite of the Logical Hypothesis. The assumptions made in an Empirical Hypothesis are based on empirical data and proved through scientific testing and analysis.    

It is divided into two parts, namely theoretical and empirical. Both methods of research rely on testing that can be verified through experimental data. So, unlike logical hypotheses, an empirical hypothesis can be and will be tested.  

Vegetables grow faster in cold climates as compared to warm and humid climates. The assumption stated here can be thoroughly tested through scientific methods.  

7. Statistical Hypothesis  

Statistical Hypothesis makes use of large statistical datasets to obtain results that consider larger populations.  This type of hypothesis is used when we have to take into consideration all the possible cases present in the assumptions made in the hypothesis. It makes use of datasets or samples so that conclusions can be drawn from the broader dataset. For this, you may conduct tests for sufficient samples and obtain results with high accuracy that would remain stable across all the datasets.  

Men in the U.S.A. are taller than men in India. It is simply impossible to measure the height of all the men present in India and the U.S.A., but by conducting the test on sufficient samples, you can obtain results with high accuracy that would remain constant over different samples.  

What Makes a Good Hypothesis?  

Before developing a good hypothesis, you must consider a few points.  

• Do the assumptions made in the hypothesis consist of dependent or independent variables?  
• Can you conduct safety tests for your assumptions in the hypothesis?  
• Are there any other alternative assumptions present that you can take into consideration?  

Characteristics of a Good Hypothesis –  

1. Candid Language  

Make use of simple language in your hypothesis instead of being vague. Try to focus on the given topic through your assumptions; it should be simple yet justifiable. The use of candid language makes the hypothesis more understandable and reachable to the common people.  

2. Cause and Effect  

Understand the assumptions made in the hypothesis. For example, the cause of the assumption, the effect of the assumption being accepted or rejected, etc. Try to back up your assumptions with the help of proper scientific data and explanations.  

3. The Independent and Dependent Variables  

Before starting to write a hypothesis, figure out the number of dependent and independent variables in the hypothesis. This will help you make proper assumptions to establish a link between these variables or to prove that these variables are not interlinked. It will also help you to prepare a mind map for your hypothesis.  

4. Accurate Results  

One of the most important characteristics of a good hypothesis is the accuracy of the results. Hypotheses are generally used to predict the future based on current scenarios. This can help to figure out the problems that may arise in the future and find solutions accordingly.  

5. Adherence to Ethics  

Sticking to ethics while working on any research project is very important. You get an idea about the research structure through the generally followed ethics beforehand. It helps to guide the research project or hypothesis in a fruitful direction.  

6. Testable Predictions  

The conditions used in the hypothesis research project should be easily testable. This helps to make the results of the hypothesis more accurate and reliable. Before starting the research on the assumptions in the hypothesis, you should be aware of all the different ways that can be used to make the hypothesis applicable to modern testing methodologies.  

How to Write a Hypothesis?  

Well, there are many ways to write a hypothesis; here are the six most efficient and important steps that will help you craft a strong hypothesis:  

Step 1: Ask a Question  

The first and most important step of writing a hypothesis is deciding upon the questions or assumptions you will implement in your research. A hypothesis can’t be based on random questions or general thoughts. The questions you decide must be approachable and testable as it forms the foundation of your project.  

Step 2: Carry out Preliminary Research  

Once you have decided on the questions and assumptions to be included in your hypothesis, you should start your preliminary research on the same. For that, you should start reading older research papers on the topic, go through the web, collect the data, prepare the dataset for the experiments, etc.  

Step 3: Define Your Variables  

After conducting the preliminary research, you need to define the number of variables present in your assumption and classify them into dependent and independent variables. It will help you to conduct further research and establish a link between them or prove that there is no link between them.  

Step-4: Collect Data to Support Your Hypothesis  

After classifying the variables and conducting the basic preliminary research, you need to start collecting evidence and data that will help you support your hypothesis. This data will help you test your assumptions and infer statistical results about your interesting dataset.

Step-5: Perform Statistical Tests  

The data you have collected from the above step can be used to perform different statistical tests.   The type of tests you perform depends on the data you collect. All the different tests are based on in-group variance and between-group variance. Depending on the variance, your statistical test will reflect a high or low p-value.    

After performing the tests, you should prepare a draft for writing down your hypothesis.  

Step-6: Present It in an If-Then Form  

Now that everything has been done, it is time to write down your hypothesis. Considering your draft, you should write down the hypothesis accordingly and ensure that it satisfies all the conditions like simple and to-the-point language, accurate results, relevant evidence and data sources, etc. The final hypothesis should be well-framed and address the topic clearly.  

Conclusion  

Research and hypothesis testing are an important part of the Business Analytics field. To write a good hypothesis or research, you need to conduct a good amount of research. Since you know about the different types of hypotheses and how to write a good hypothesis, writing a good and strong hypothesis by yourself is now much easier! If you want to pursue a career in the field of Business Analytics, you can check out the Integrated Program In Business Analytics by UNext Jigsaw. We hope now you understand “ what is hypothesis testing ?” and hypothesis testing steps in detail.

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26 Hypothesis and Variables – Meaning, Classification and Uses

C. Parvathi

INTRODUCTION

Today, we are going to see the meaning of the hypothesis, steps involved to write a hypothesis, its characteristics, types and errors in formulating hypothesis. It involves different errors of hypothesis for which we have to identify the variables which will enable the research scholars to justify the area of research and design of the research work under taken by the investigator.

Hypothesis is usually considered as the principal instrument in research. Its main function is to suggest new experiments and observations. In fact, many experiments are carried out with the deliberate objective of testing hypotheses. Decision-makers often face situations wherein they are interested in testing hypotheses on the basis of available information and then take decisions on the basis of such testing. In social science, where direct knowledge of population parameter(s) is rare, hypothesis testing is often used strategy for deciding whether a sample data offers such support for a hypothesis from which generalization can be made. Thus hypothesis testing enables us to make probability statements about population parameter(s). The hypothesis may not be proved absolutely, but in practice it is accepted if it has withstood a critical testing. Before we explain how hypotheses are tested through different tests meant for this purpose, it will be appropriate to explain clearly the meaning of a hypothesis and the related concepts for better understanding of the hypothesis testing techniques.

WHAT IS HYPOTHESIS?

Generally, when one talks about hypothesis, one simply means mere assumption or some supposition to be proved or disproved. Thus a hypothesis may be defined as a proposition or a set of proposition set forth as an explanation for the occurrence of some specified group of phenomena either asserted merely as a provisional conjecture to guide some investigation or accepted a highly probable in the light of established facts. Research hypothesis is a predictive  statement, capable of being tested by scientific methods that relate an independent variable to some dependant variable. For example, consider statement like the following ones:

“Students who receive counseling will show better performance increase in creativity than students not receiving counseling” or “the automobile  A is performing better than automobile B .”

The above hypothesis is capable of being objectively verified and tested. It is a proposition which can be put to a test to determine its validity.

Here, we are examining the truth or otherwise of the hypothesis (guess, claim or assumptions, etc.) about some feature about one or more populations on the basis of samples drawn from these populations. Testing plays a major role in statistical investigation. Generally, a statistical hypothesis is a statement or a conclusion or an assumption about certain characteristic populations which is drawn on a logical basis and it can be tested based on the sample evidences. Test of hypothesis means either accept or reject the hypothesis under a valid reason. The test of significance enables a researcher to decide either to accept or reject the statistical hypothesis. For example, a manufacturing company producing bolts of different sizes and claims that not more than 2 per cent bolts are defective. In order to verify the claim as true or not, we have to check it on the basis of sample of bolts. A company wants to verify the effectiveness of advertisement given through print media is less effective than audio-visual media or not. There are wide ranges of areas in business where we have to come across situations of arriving at a decision of accepting or rejecting hypothesis. So, it is very much important to have knowledge about the logical basis of such decisions and it is provided by hypothesis testing, which is the objective of this chapter.

It is a usual procedure that sample is drawn from the population an estimate of population parameter which is in other words, called sample statistic. Estimate of population parameters thus obtained may or may not exactly match with true values. To take the sample statistic as the estimate of population parameter is involved with risk. So, it is worthwhile to find whether the  difference between the estimated value of the parameter or the true value is significantly different or it could have arisen due to fluctuation of sampling. For this reason only, a hypothesis is formulated and then tested for validity.

Meaning of Hypothesis:

Hypothesis simply means a mere assumption to be proved or disproved. But for a researcher hypothesis is a formal question that he intends to resolve. It is a testable statement; hypotheses are generally either derived theory of from direct observation of data

Types of Hypothesis

Null hypothesis

Null hypothesis is the statement about the parameters, which is usually a hypothesis of no difference and is denoted by Ho.

Alternative Hypothesis

Any hypothesis, which is complementary to the null hypothesis, is called an alternative hypothesis, usually denoted by H1.

BASIC CONCEPTS ON TESTING OF HYPOTHESES

a) NULL HYPOTHESIS

In the context of statistical analysis, we often talk about null hypothesis and alternative hypothesis. If we are to compare method A with method B about its superiority and if we proceed on the assumption that both methods are equally good, then this assumption is termed as the null hypothesis. The null hypothesis is generally symbolized as Ho and the alternative hypothesis as Ha.

In the choice of null hypothesis, the following considerations are usually kept in view:

Alternative hypothesis is usually the one which one wishes to prove and the null hypothesis is the one which one wishes to disprove. Thus, a null hypothesis represents the hypothesis we are trying to reject, and the alternative hypothesis represents all other possibilities.

  If the rejection of a certain hypothesis when it actually true involves great risk, it is taken as null hypothesis.

Null hypothesis should always be specific hypothesis i.e., it should not state about or approximately a certain value.

b)   THE LEVEL OF SIGNIFICANCE

This is a very important concept in the context of hypothesis testing. It is always some percentage (usually 5%) which should be chosen with great care. In case we take the significance level at 5 percent, then this implies that Ho will be rejected when the sampling result (i.e., observed evidence) has a less than 0.05 probability of occurring if Ho is true. In other words, the 5 percent level of significance means that researcher is willing to take as much as 5 percent risk of rejecting the null hypothesis when it (Ho) happens to be true.

c) DECISION RULE OF TEST OF HYPOTHESIS

Given a hypothesis Ho and an alternative hypothesis Ha, we make a rule which is known as decision rule according to which we accept Ho (i.e., reject Ha) or reject Ho (i.e., accept Ha).

d) TYPE I ERROR AND TYPE II ERRORS

In the context of testing of hypotheses, there are basically two types of errors. We may reject Ho when Ho is true and we may accept Ho when Ho is not true. The former is known as Type I error and the latter as Type II error. In other words, Type I error means rejection of hypothesis which should have been accepted and Type II error means accepting the hypothesis which should have been rejected. Type I error is denoted by α (alpha) known as α error, also called as the level of significance of test; and Type II error is denoted by β (beta) known as β error.

e) TWO-TAILED AND ONE-TAILED TESTS

In the content of hypothesis testing, these two terms are quite important and must be clearly understood. A two-tailed test rejects the null hypothesis if, say, the sample mean is significantly higher or lower than the hypothesized value of the mean of the population. Such a test is appropriate when the null hypothesis is some specified value and the alternative hypothesis is a value not equal to the specified value of the null hypothesis.

ERRORS IN TESTING OF HYPOTHESIS

In the procedure of testing of hypothesis, a decision is taken about the acceptance or rejection of null hypothesis. The possible decisions can be written in a tabular form.

There is always some possibility of committing the following two types of errors in taking such as decision as

Type I Error: Reject the null hypothesis Ho when it is true.

Type II Error: Accept the null hypothesis Ho when it is false.

Now, we write α = Probability of committing Type I error

And β = Probability of committing Type II error

The compliment of Type II error is called as the power of the test and is given by (1- β) and the size of Type I error (α) is also called as level of significance . The level of significance is  the quantity of risk, which can be readily tolerated in making a decision Ho. Usually the value of α, is chosen depending upon the desired degree of precession and it and its value varies between 0.05 (for moderate precision) to 0.01 (for high precision).

PROCEDURE FOR HYPOTHESIS TESTING

In hypothesis testing the main question is: whether to accept the null hypothesis or not. Procedure for hypothesis testing refers to all those steps that we undertake for making a choice between the two actions i.e., rejection and acceptance of a null hypothesis.

The various steps involved in hypothesis testing are stated below:

(i)  Selection of Variables

DEPENDENT VARIABLE

The variable that depends on other factors is called dependent variable. These variables are expected to change a result of an experimental manipulation of the independent variable or variables. The outcome variable measured in each subject, who may be influenced by manipulation of the independent variable, is termed the dependent variable.

INDEPENDENT VARIABLE

The variable that is stable and unaffected by other variables is called independent variable. It refers to the condition of an experiment that is systematically manipulated by the investigator. In experimental research, an investigator manipulates one variable and measures the effect of that manipulation on another variable. For example, let’s take a study in which the investigators want to determine how often an exercise must be done to increase strength.

Check your progress

Fill in the blanks

F  Hypothesis is usually considered as the principal instrument of _________________

F   The null hypothesis is generally symbolized as_________

F   The variable that depends on other factor is called _____________ Variable.

IDENTIFYING THE KEY VARIABLES FOR ANALYSIS

• The key variables provide focus when writing the Introduction section
• The key variables are the major terms to be used in methodology.
• The key variables are the terms to be operationally defined if an Operational Definition of Terms section is necessary.
• The key variables must be directly measured or manipulated for the research study to be valid

     (ii)   Making a formal statement

(iii) Selecting a significance level

(iv) Deciding the distribution to use

(v) Selecting a random sample and computing an appropriate value

(vi) Calculation of the probability; and

(vii) Comparing the probability

FLOW DIAGRAM FOR HYPOTHESIS TESTING

TEST OF HYPOTHESIS

Statisticians have developed several tests of hypotheses (also known as the tests of significance) for the purpose of testing of hypotheses which can be classified as: (a) Parametric tests or standard test of hypothesis and (b) Non-parametric tests or distribution-free test of hypotheses.

Parametric tests are usually assuming certain properties of the parent population from which we draw samples. Assumptions like observations come from a normal population, sample size is large, assumptions about the population parameters like mean, variance, etc., must hold good before parametric tests can be used.

Non-parametric tests assume only nominal or ordinal data, whereas parameters tests require measurement equivalent to at least an interval scale.

IMPORTANT PARAMETRIC TESTS

The important parametric tests are:

(i)   Z-test

Z-test is based on the normal probability distribution and is used for judging the significance of several statistical measures, particularly the mean.

(ii)   t-test

t-test is based on t-distribution and is considered an appropriate test for judging the significance of an sample mean or for judging the significance of difference between the means of two samples in case of small sample(s) when population variance is not known (in which we use variance of the samples as an estimate of the population variance).

(iii)   X 2 -test

X2-test is also used as a test of goodness of fit and also as a test of independence in which case it is a non-parametric test. X2-test is based on chi-square distribution and as a parametric test is used for comparing a sample variance to a theoretical population variance.

(iv)   F-test

F-test is based on F-distribution and is used to compare the variance of the two-independent samples.

LIMITATIONS OF THE TESTS OF HYPOTHESES

Limitations of test of hypothesis are as follows:

i) The tests should not be used in a mechanical fashion. It should be kept in view that testing is not decision- making itself; the tests are only useful aids for decision-making.

ii) Tests do not explain the reasons as to why does the difference exist, like between the means of the two samples. They simply indicate whether the difference is due to fluctuations of sampling or because of other reasons.

 iii) Results of test of significance are based on probabilities which cannot be expressed with full certainty. When a test shows that a difference is statistically significant, then it simply suggests that the difference is probably not due to chance.

iv) Statistical inferences based on the significance tests cannot be said to be entirely correct evidences concerning the truth of the hypotheses. This is specially so in case of small samples where the probability of drawing inferences happens to be generally higher. For greater reliability, the size of samples is sufficiently enlarged.

To conclude, we have seen the meaning, steps, and characteristics of hypothesis in a detailed manner. Framing and testing of the hypothesis is the major part of the research work with which investigator will be able to test by scientific method(s), to apply econometric models to establish a strong relationship between the theory and the analysis of the research work which will strengthen the findings of the study. Therefore, in social science, framing the hypothesis occupies a significant place to proceed with the research work. Hence, the present E-module will be very useful for the project investigators and thereby conclusions drawn will enable the government to take decision at policy level.

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• Keeping, E.S. Introduction to Statistical Inference (Chs.8,11). Van Nostrand, 1962 and Affiliated East-West PressModd, A.M.,
• Graybill, F.a. and Boes, D.GIntroduction to the Theory of Statistics (Chs. 7, 8, 11,12). McGraw-Hill, 1963,and Kogakusha Rao, C.R. Advanced Statistical Methods in Biometric Research (Chs. 4, 8a). John Wiley, 1952.
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Frequently asked questions

What is the definition of a hypothesis.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess. It should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

Frequently asked questions: Methodology

Quantitative observations involve measuring or counting something and expressing the result in numerical form, while qualitative observations involve describing something in non-numerical terms, such as its appearance, texture, or color.

To make quantitative observations , you need to use instruments that are capable of measuring the quantity you want to observe. For example, you might use a ruler to measure the length of an object or a thermometer to measure its temperature.

Scope of research is determined at the beginning of your research process , prior to the data collection stage. Sometimes called “scope of study,” your scope delineates what will and will not be covered in your project. It helps you focus your work and your time, ensuring that you’ll be able to achieve your goals and outcomes.

Defining a scope can be very useful in any research project, from a research proposal to a thesis or dissertation . A scope is needed for all types of research: quantitative , qualitative , and mixed methods .

To define your scope of research, consider the following:

• Budget constraints or any specifics of grant funding
• Your proposed timeline and duration
• Specifics about your population of study, your proposed sample size , and the research methodology you’ll pursue
• Any inclusion and exclusion criteria
• Any anticipated control , extraneous , or confounding variables that could bias your research if not accounted for properly.

Inclusion and exclusion criteria are predominantly used in non-probability sampling . In purposive sampling and snowball sampling , restrictions apply as to who can be included in the sample .

Inclusion and exclusion criteria are typically presented and discussed in the methodology section of your thesis or dissertation .

The purpose of theory-testing mode is to find evidence in order to disprove, refine, or support a theory. As such, generalisability is not the aim of theory-testing mode.

Due to this, the priority of researchers in theory-testing mode is to eliminate alternative causes for relationships between variables . In other words, they prioritise internal validity over external validity , including ecological validity .

Convergent validity shows how much a measure of one construct aligns with other measures of the same or related constructs .

On the other hand, concurrent validity is about how a measure matches up to some known criterion or gold standard, which can be another measure.

Although both types of validity are established by calculating the association or correlation between a test score and another variable , they represent distinct validation methods.

Validity tells you how accurately a method measures what it was designed to measure. There are 4 main types of validity :

• Construct validity : Does the test measure the construct it was designed to measure?
• Face validity : Does the test appear to be suitable for its objectives ?
• Content validity : Does the test cover all relevant parts of the construct it aims to measure.
• Criterion validity : Do the results accurately measure the concrete outcome they are designed to measure?

Criterion validity evaluates how well a test measures the outcome it was designed to measure. An outcome can be, for example, the onset of a disease.

Criterion validity consists of two subtypes depending on the time at which the two measures (the criterion and your test) are obtained:

• Concurrent validity is a validation strategy where the the scores of a test and the criterion are obtained at the same time
• Predictive validity is a validation strategy where the criterion variables are measured after the scores of the test

Attrition refers to participants leaving a study. It always happens to some extent – for example, in randomised control trials for medical research.

Differential attrition occurs when attrition or dropout rates differ systematically between the intervention and the control group . As a result, the characteristics of the participants who drop out differ from the characteristics of those who stay in the study. Because of this, study results may be biased .

Criterion validity and construct validity are both types of measurement validity . In other words, they both show you how accurately a method measures something.

While construct validity is the degree to which a test or other measurement method measures what it claims to measure, criterion validity is the degree to which a test can predictively (in the future) or concurrently (in the present) measure something.

Construct validity is often considered the overarching type of measurement validity . You need to have face validity , content validity , and criterion validity in order to achieve construct validity.

Convergent validity and discriminant validity are both subtypes of construct validity . Together, they help you evaluate whether a test measures the concept it was designed to measure.

• Convergent validity indicates whether a test that is designed to measure a particular construct correlates with other tests that assess the same or similar construct.
• Discriminant validity indicates whether two tests that should not be highly related to each other are indeed not related. This type of validity is also called divergent validity .

You need to assess both in order to demonstrate construct validity. Neither one alone is sufficient for establishing construct validity.

Face validity and content validity are similar in that they both evaluate how suitable the content of a test is. The difference is that face validity is subjective, and assesses content at surface level.

When a test has strong face validity, anyone would agree that the test’s questions appear to measure what they are intended to measure.

For example, looking at a 4th grade math test consisting of problems in which students have to add and multiply, most people would agree that it has strong face validity (i.e., it looks like a math test).

On the other hand, content validity evaluates how well a test represents all the aspects of a topic. Assessing content validity is more systematic and relies on expert evaluation. of each question, analysing whether each one covers the aspects that the test was designed to cover.

A 4th grade math test would have high content validity if it covered all the skills taught in that grade. Experts(in this case, math teachers), would have to evaluate the content validity by comparing the test to the learning objectives.

Content validity shows you how accurately a test or other measurement method taps  into the various aspects of the specific construct you are researching.

In other words, it helps you answer the question: “does the test measure all aspects of the construct I want to measure?” If it does, then the test has high content validity.

The higher the content validity, the more accurate the measurement of the construct.

If the test fails to include parts of the construct, or irrelevant parts are included, the validity of the instrument is threatened, which brings your results into question.

Construct validity refers to how well a test measures the concept (or construct) it was designed to measure. Assessing construct validity is especially important when you’re researching concepts that can’t be quantified and/or are intangible, like introversion. To ensure construct validity your test should be based on known indicators of introversion ( operationalisation ).

On the other hand, content validity assesses how well the test represents all aspects of the construct. If some aspects are missing or irrelevant parts are included, the test has low content validity.

• Discriminant validity indicates whether two tests that should not be highly related to each other are indeed not related

Construct validity has convergent and discriminant subtypes. They assist determine if a test measures the intended notion.

The reproducibility and replicability of a study can be ensured by writing a transparent, detailed method section and using clear, unambiguous language.

Reproducibility and replicability are related terms.

• A successful reproduction shows that the data analyses were conducted in a fair and honest manner.
• A successful replication shows that the reliability of the results is high.
• Reproducing research entails reanalysing the existing data in the same manner.
• Replicating (or repeating ) the research entails reconducting the entire analysis, including the collection of new data . 

Snowball sampling is a non-probability sampling method . Unlike probability sampling (which involves some form of random selection ), the initial individuals selected to be studied are the ones who recruit new participants.

Because not every member of the target population has an equal chance of being recruited into the sample, selection in snowball sampling is non-random.

Snowball sampling is a non-probability sampling method , where there is not an equal chance for every member of the population to be included in the sample .

This means that you cannot use inferential statistics and make generalisations – often the goal of quantitative research . As such, a snowball sample is not representative of the target population, and is usually a better fit for qualitative research .

Snowball sampling relies on the use of referrals. Here, the researcher recruits one or more initial participants, who then recruit the next ones. 

Participants share similar characteristics and/or know each other. Because of this, not every member of the population has an equal chance of being included in the sample, giving rise to sampling bias .

Snowball sampling is best used in the following cases:

• If there is no sampling frame available (e.g., people with a rare disease)
• If the population of interest is hard to access or locate (e.g., people experiencing homelessness)
• If the research focuses on a sensitive topic (e.g., extra-marital affairs)

Stratified sampling and quota sampling both involve dividing the population into subgroups and selecting units from each subgroup. The purpose in both cases is to select a representative sample and/or to allow comparisons between subgroups.

The main difference is that in stratified sampling, you draw a random sample from each subgroup ( probability sampling ). In quota sampling you select a predetermined number or proportion of units, in a non-random manner ( non-probability sampling ).

Random sampling or probability sampling is based on random selection. This means that each unit has an equal chance (i.e., equal probability) of being included in the sample.

On the other hand, convenience sampling involves stopping people at random, which means that not everyone has an equal chance of being selected depending on the place, time, or day you are collecting your data.

Convenience sampling and quota sampling are both non-probability sampling methods. They both use non-random criteria like availability, geographical proximity, or expert knowledge to recruit study participants.

However, in convenience sampling, you continue to sample units or cases until you reach the required sample size.

In quota sampling, you first need to divide your population of interest into subgroups (strata) and estimate their proportions (quota) in the population. Then you can start your data collection , using convenience sampling to recruit participants, until the proportions in each subgroup coincide with the estimated proportions in the population.

A sampling frame is a list of every member in the entire population . It is important that the sampling frame is as complete as possible, so that your sample accurately reflects your population.

Stratified and cluster sampling may look similar, but bear in mind that groups created in cluster sampling are heterogeneous , so the individual characteristics in the cluster vary. In contrast, groups created in stratified sampling are homogeneous , as units share characteristics.

Relatedly, in cluster sampling you randomly select entire groups and include all units of each group in your sample. However, in stratified sampling, you select some units of all groups and include them in your sample. In this way, both methods can ensure that your sample is representative of the target population .

When your population is large in size, geographically dispersed, or difficult to contact, it’s necessary to use a sampling method .

This allows you to gather information from a smaller part of the population, i.e. the sample, and make accurate statements by using statistical analysis. A few sampling methods include simple random sampling , convenience sampling , and snowball sampling .

The two main types of social desirability bias are:

• Self-deceptive enhancement (self-deception): The tendency to see oneself in a favorable light without realizing it.
• Impression managemen t (other-deception): The tendency to inflate one’s abilities or achievement in order to make a good impression on other people.

Response bias refers to conditions or factors that take place during the process of responding to surveys, affecting the responses. One type of response bias is social desirability bias .

Demand characteristics are aspects of experiments that may give away the research objective to participants. Social desirability bias occurs when participants automatically try to respond in ways that make them seem likeable in a study, even if it means misrepresenting how they truly feel.

Participants may use demand characteristics to infer social norms or experimenter expectancies and act in socially desirable ways, so you should try to control for demand characteristics wherever possible.

A systematic review is secondary research because it uses existing research. You don’t collect new data yourself.

Ethical considerations in research are a set of principles that guide your research designs and practices. These principles include voluntary participation, informed consent, anonymity, confidentiality, potential for harm, and results communication.

Scientists and researchers must always adhere to a certain code of conduct when collecting data from others .

These considerations protect the rights of research participants, enhance research validity , and maintain scientific integrity.

Research ethics matter for scientific integrity, human rights and dignity, and collaboration between science and society. These principles make sure that participation in studies is voluntary, informed, and safe.

Research misconduct means making up or falsifying data, manipulating data analyses, or misrepresenting results in research reports. It’s a form of academic fraud.

These actions are committed intentionally and can have serious consequences; research misconduct is not a simple mistake or a point of disagreement but a serious ethical failure.

Anonymity means you don’t know who the participants are, while confidentiality means you know who they are but remove identifying information from your research report. Both are important ethical considerations .

You can only guarantee anonymity by not collecting any personally identifying information – for example, names, phone numbers, email addresses, IP addresses, physical characteristics, photos, or videos.

You can keep data confidential by using aggregate information in your research report, so that you only refer to groups of participants rather than individuals.

Peer review is a process of evaluating submissions to an academic journal. Utilising rigorous criteria, a panel of reviewers in the same subject area decide whether to accept each submission for publication.

For this reason, academic journals are often considered among the most credible sources you can use in a research project – provided that the journal itself is trustworthy and well regarded.

In general, the peer review process follows the following steps:

• First, the author submits the manuscript to the editor.
• Reject the manuscript and send it back to author, or
• Send it onward to the selected peer reviewer(s)
• Next, the peer review process occurs. The reviewer provides feedback, addressing any major or minor issues with the manuscript, and gives their advice regarding what edits should be made.
• Lastly, the edited manuscript is sent back to the author. They input the edits, and resubmit it to the editor for publication.

Peer review can stop obviously problematic, falsified, or otherwise untrustworthy research from being published. It also represents an excellent opportunity to get feedback from renowned experts in your field.

It acts as a first defence, helping you ensure your argument is clear and that there are no gaps, vague terms, or unanswered questions for readers who weren’t involved in the research process.

Peer-reviewed articles are considered a highly credible source due to this stringent process they go through before publication.

Many academic fields use peer review , largely to determine whether a manuscript is suitable for publication. Peer review enhances the credibility of the published manuscript.

However, peer review is also common in non-academic settings. The United Nations, the European Union, and many individual nations use peer review to evaluate grant applications. It is also widely used in medical and health-related fields as a teaching or quality-of-care measure.

Peer assessment is often used in the classroom as a pedagogical tool. Both receiving feedback and providing it are thought to enhance the learning process, helping students think critically and collaboratively.

• In a single-blind study , only the participants are blinded.
• In a double-blind study , both participants and experimenters are blinded.
• In a triple-blind study , the assignment is hidden not only from participants and experimenters, but also from the researchers analysing the data.

Blinding is important to reduce bias (e.g., observer bias , demand characteristics ) and ensure a study’s internal validity .

If participants know whether they are in a control or treatment group , they may adjust their behaviour in ways that affect the outcome that researchers are trying to measure. If the people administering the treatment are aware of group assignment, they may treat participants differently and thus directly or indirectly influence the final results.

Blinding means hiding who is assigned to the treatment group and who is assigned to the control group in an experiment .

Explanatory research is a research method used to investigate how or why something occurs when only a small amount of information is available pertaining to that topic. It can help you increase your understanding of a given topic.

Explanatory research is used to investigate how or why a phenomenon occurs. Therefore, this type of research is often one of the first stages in the research process , serving as a jumping-off point for future research.

Exploratory research is a methodology approach that explores research questions that have not previously been studied in depth. It is often used when the issue you’re studying is new, or the data collection process is challenging in some way.

Exploratory research is often used when the issue you’re studying is new or when the data collection process is challenging for some reason.

You can use exploratory research if you have a general idea or a specific question that you want to study but there is no preexisting knowledge or paradigm with which to study it.

To implement random assignment , assign a unique number to every member of your study’s sample .

Then, you can use a random number generator or a lottery method to randomly assign each number to a control or experimental group. You can also do so manually, by flipping a coin or rolling a die to randomly assign participants to groups.

Random selection, or random sampling , is a way of selecting members of a population for your study’s sample.

In contrast, random assignment is a way of sorting the sample into control and experimental groups.

Random sampling enhances the external validity or generalisability of your results, while random assignment improves the internal validity of your study.

Random assignment is used in experiments with a between-groups or independent measures design. In this research design, there’s usually a control group and one or more experimental groups. Random assignment helps ensure that the groups are comparable.

In general, you should always use random assignment in this type of experimental design when it is ethically possible and makes sense for your study topic.

Clean data are valid, accurate, complete, consistent, unique, and uniform. Dirty data include inconsistencies and errors.

Dirty data can come from any part of the research process, including poor research design , inappropriate measurement materials, or flawed data entry.

Data cleaning takes place between data collection and data analyses. But you can use some methods even before collecting data.

For clean data, you should start by designing measures that collect valid data. Data validation at the time of data entry or collection helps you minimize the amount of data cleaning you’ll need to do.

After data collection, you can use data standardisation and data transformation to clean your data. You’ll also deal with any missing values, outliers, and duplicate values.

Data cleaning involves spotting and resolving potential data inconsistencies or errors to improve your data quality. An error is any value (e.g., recorded weight) that doesn’t reflect the true value (e.g., actual weight) of something that’s being measured.

In this process, you review, analyse, detect, modify, or remove ‘dirty’ data to make your dataset ‘clean’. Data cleaning is also called data cleansing or data scrubbing.

Data cleaning is necessary for valid and appropriate analyses. Dirty data contain inconsistencies or errors , but cleaning your data helps you minimise or resolve these.

Without data cleaning, you could end up with a Type I or II error in your conclusion. These types of erroneous conclusions can be practically significant with important consequences, because they lead to misplaced investments or missed opportunities.

Observer bias occurs when a researcher’s expectations, opinions, or prejudices influence what they perceive or record in a study. It usually affects studies when observers are aware of the research aims or hypotheses. This type of research bias is also called detection bias or ascertainment bias .

The observer-expectancy effect occurs when researchers influence the results of their own study through interactions with participants.

Researchers’ own beliefs and expectations about the study results may unintentionally influence participants through demand characteristics .

You can use several tactics to minimise observer bias .

• Use masking (blinding) to hide the purpose of your study from all observers.
• Triangulate your data with different data collection methods or sources.
• Use multiple observers and ensure inter-rater reliability.
• Train your observers to make sure data is consistently recorded between them.
• Standardise your observation procedures to make sure they are structured and clear.

Naturalistic observation is a valuable tool because of its flexibility, external validity , and suitability for topics that can’t be studied in a lab setting.

The downsides of naturalistic observation include its lack of scientific control , ethical considerations , and potential for bias from observers and subjects.

Naturalistic observation is a qualitative research method where you record the behaviours of your research subjects in real-world settings. You avoid interfering or influencing anything in a naturalistic observation.

You can think of naturalistic observation as ‘people watching’ with a purpose.

Closed-ended, or restricted-choice, questions offer respondents a fixed set of choices to select from. These questions are easier to answer quickly.

Open-ended or long-form questions allow respondents to answer in their own words. Because there are no restrictions on their choices, respondents can answer in ways that researchers may not have otherwise considered.

You can organise the questions logically, with a clear progression from simple to complex, or randomly between respondents. A logical flow helps respondents process the questionnaire easier and quicker, but it may lead to bias. Randomisation can minimise the bias from order effects.

Questionnaires can be self-administered or researcher-administered.

Self-administered questionnaires can be delivered online or in paper-and-pen formats, in person or by post. All questions are standardised so that all respondents receive the same questions with identical wording.

Researcher-administered questionnaires are interviews that take place by phone, in person, or online between researchers and respondents. You can gain deeper insights by clarifying questions for respondents or asking follow-up questions.

In a controlled experiment , all extraneous variables are held constant so that they can’t influence the results. Controlled experiments require:

• A control group that receives a standard treatment, a fake treatment, or no treatment
• Random assignment of participants to ensure the groups are equivalent

Depending on your study topic, there are various other methods of controlling variables .

An experimental group, also known as a treatment group, receives the treatment whose effect researchers wish to study, whereas a control group does not. They should be identical in all other ways.

A true experiment (aka a controlled experiment) always includes at least one control group that doesn’t receive the experimental treatment.

However, some experiments use a within-subjects design to test treatments without a control group. In these designs, you usually compare one group’s outcomes before and after a treatment (instead of comparing outcomes between different groups).

For strong internal validity , it’s usually best to include a control group if possible. Without a control group, it’s harder to be certain that the outcome was caused by the experimental treatment and not by other variables.

A questionnaire is a data collection tool or instrument, while a survey is an overarching research method that involves collecting and analysing data from people using questionnaires.

A Likert scale is a rating scale that quantitatively assesses opinions, attitudes, or behaviours. It is made up of four or more questions that measure a single attitude or trait when response scores are combined.

To use a Likert scale in a survey , you present participants with Likert-type questions or statements, and a continuum of items, usually with five or seven possible responses, to capture their degree of agreement.

Individual Likert-type questions are generally considered ordinal data , because the items have clear rank order, but don’t have an even distribution.

Overall Likert scale scores are sometimes treated as interval data. These scores are considered to have directionality and even spacing between them.

The type of data determines what statistical tests you should use to analyse your data.

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (‘ x affects y because …’).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses. In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

Cross-sectional studies are less expensive and time-consuming than many other types of study. They can provide useful insights into a population’s characteristics and identify correlations for further research.

Sometimes only cross-sectional data are available for analysis; other times your research question may only require a cross-sectional study to answer it.

Cross-sectional studies cannot establish a cause-and-effect relationship or analyse behaviour over a period of time. To investigate cause and effect, you need to do a longitudinal study or an experimental study .

Longitudinal studies and cross-sectional studies are two different types of research design . In a cross-sectional study you collect data from a population at a specific point in time; in a longitudinal study you repeatedly collect data from the same sample over an extended period of time.

Longitudinal studies are better to establish the correct sequence of events, identify changes over time, and provide insight into cause-and-effect relationships, but they also tend to be more expensive and time-consuming than other types of studies.

The 1970 British Cohort Study , which has collected data on the lives of 17,000 Brits since their births in 1970, is one well-known example of a longitudinal study .

Longitudinal studies can last anywhere from weeks to decades, although they tend to be at least a year long.

A correlation reflects the strength and/or direction of the association between two or more variables.

• A positive correlation means that both variables change in the same direction.
• A negative correlation means that the variables change in opposite directions.
• A zero correlation means there’s no relationship between the variables.

A correlational research design investigates relationships between two variables (or more) without the researcher controlling or manipulating any of them. It’s a non-experimental type of quantitative research .

A correlation coefficient is a single number that describes the strength and direction of the relationship between your variables.

Different types of correlation coefficients might be appropriate for your data based on their levels of measurement and distributions . The Pearson product-moment correlation coefficient (Pearson’s r ) is commonly used to assess a linear relationship between two quantitative variables.

Controlled experiments establish causality, whereas correlational studies only show associations between variables.

• In an experimental design , you manipulate an independent variable and measure its effect on a dependent variable. Other variables are controlled so they can’t impact the results.
• In a correlational design , you measure variables without manipulating any of them. You can test whether your variables change together, but you can’t be sure that one variable caused a change in another.

In general, correlational research is high in external validity while experimental research is high in internal validity .

The third variable and directionality problems are two main reasons why correlation isn’t causation .

The third variable problem means that a confounding variable affects both variables to make them seem causally related when they are not.

The directionality problem is when two variables correlate and might actually have a causal relationship, but it’s impossible to conclude which variable causes changes in the other.

As a rule of thumb, questions related to thoughts, beliefs, and feelings work well in focus groups . Take your time formulating strong questions, paying special attention to phrasing. Be careful to avoid leading questions , which can bias your responses.

Overall, your focus group questions should be:

• Open-ended and flexible
• Impossible to answer with ‘yes’ or ‘no’ (questions that start with ‘why’ or ‘how’ are often best)
• Unambiguous, getting straight to the point while still stimulating discussion
• Unbiased and neutral

Social desirability bias is the tendency for interview participants to give responses that will be viewed favourably by the interviewer or other participants. It occurs in all types of interviews and surveys , but is most common in semi-structured interviews , unstructured interviews , and focus groups .

Social desirability bias can be mitigated by ensuring participants feel at ease and comfortable sharing their views. Make sure to pay attention to your own body language and any physical or verbal cues, such as nodding or widening your eyes.

This type of bias in research can also occur in observations if the participants know they’re being observed. They might alter their behaviour accordingly.

A focus group is a research method that brings together a small group of people to answer questions in a moderated setting. The group is chosen due to predefined demographic traits, and the questions are designed to shed light on a topic of interest. It is one of four types of interviews .

The four most common types of interviews are:

• Structured interviews : The questions are predetermined in both topic and order.
• Semi-structured interviews : A few questions are predetermined, but other questions aren’t planned.
• Unstructured interviews : None of the questions are predetermined.
• Focus group interviews : The questions are presented to a group instead of one individual.

An unstructured interview is the most flexible type of interview, but it is not always the best fit for your research topic.

Unstructured interviews are best used when:

• You are an experienced interviewer and have a very strong background in your research topic, since it is challenging to ask spontaneous, colloquial questions
• Your research question is exploratory in nature. While you may have developed hypotheses, you are open to discovering new or shifting viewpoints through the interview process.
• You are seeking descriptive data, and are ready to ask questions that will deepen and contextualise your initial thoughts and hypotheses
• Your research depends on forming connections with your participants and making them feel comfortable revealing deeper emotions, lived experiences, or thoughts

A semi-structured interview is a blend of structured and unstructured types of interviews. Semi-structured interviews are best used when:

• You have prior interview experience. Spontaneous questions are deceptively challenging, and it’s easy to accidentally ask a leading question or make a participant uncomfortable.
• Your research question is exploratory in nature. Participant answers can guide future research questions and help you develop a more robust knowledge base for future research.

The interviewer effect is a type of bias that emerges when a characteristic of an interviewer (race, age, gender identity, etc.) influences the responses given by the interviewee.

There is a risk of an interviewer effect in all types of interviews , but it can be mitigated by writing really high-quality interview questions.

A structured interview is a data collection method that relies on asking questions in a set order to collect data on a topic. They are often quantitative in nature. Structured interviews are best used when:

• You already have a very clear understanding of your topic. Perhaps significant research has already been conducted, or you have done some prior research yourself, but you already possess a baseline for designing strong structured questions.
• You are constrained in terms of time or resources and need to analyse your data quickly and efficiently
• Your research question depends on strong parity between participants, with environmental conditions held constant

More flexible interview options include semi-structured interviews , unstructured interviews , and focus groups .

When conducting research, collecting original data has significant advantages:

• You can tailor data collection to your specific research aims (e.g., understanding the needs of your consumers or user testing your website).
• You can control and standardise the process for high reliability and validity (e.g., choosing appropriate measurements and sampling methods ).

However, there are also some drawbacks: data collection can be time-consuming, labour-intensive, and expensive. In some cases, it’s more efficient to use secondary data that has already been collected by someone else, but the data might be less reliable.

Data collection is the systematic process by which observations or measurements are gathered in research. It is used in many different contexts by academics, governments, businesses, and other organisations.

A mediator variable explains the process through which two variables are related, while a moderator variable affects the strength and direction of that relationship.

A confounder is a third variable that affects variables of interest and makes them seem related when they are not. In contrast, a mediator is the mechanism of a relationship between two variables: it explains the process by which they are related.

If something is a mediating variable :

• It’s caused by the independent variable
• It influences the dependent variable
• When it’s taken into account, the statistical correlation between the independent and dependent variables is higher than when it isn’t considered

Including mediators and moderators in your research helps you go beyond studying a simple relationship between two variables for a fuller picture of the real world. They are important to consider when studying complex correlational or causal relationships.

Mediators are part of the causal pathway of an effect, and they tell you how or why an effect takes place. Moderators usually help you judge the external validity of your study by identifying the limitations of when the relationship between variables holds.

You can think of independent and dependent variables in terms of cause and effect: an independent variable is the variable you think is the cause , while a dependent variable is the effect .

In an experiment, you manipulate the independent variable and measure the outcome in the dependent variable. For example, in an experiment about the effect of nutrients on crop growth:

• The  independent variable  is the amount of nutrients added to the crop field.
• The  dependent variable is the biomass of the crops at harvest time.

Defining your variables, and deciding how you will manipulate and measure them, is an important part of experimental design .

Discrete and continuous variables are two types of quantitative variables :

• Discrete variables represent counts (e.g., the number of objects in a collection).
• Continuous variables represent measurable amounts (e.g., water volume or weight).

Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).

Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).

You need to know what type of variables you are working with to choose the right statistical test for your data and interpret your results .

Determining cause and effect is one of the most important parts of scientific research. It’s essential to know which is the cause – the independent variable – and which is the effect – the dependent variable.

You want to find out how blood sugar levels are affected by drinking diet cola and regular cola, so you conduct an experiment .

• The type of cola – diet or regular – is the independent variable .
• The level of blood sugar that you measure is the dependent variable – it changes depending on the type of cola.

No. The value of a dependent variable depends on an independent variable, so a variable cannot be both independent and dependent at the same time. It must be either the cause or the effect, not both.

Yes, but including more than one of either type requires multiple research questions .

For example, if you are interested in the effect of a diet on health, you can use multiple measures of health: blood sugar, blood pressure, weight, pulse, and many more. Each of these is its own dependent variable with its own research question.

You could also choose to look at the effect of exercise levels as well as diet, or even the additional effect of the two combined. Each of these is a separate independent variable .

To ensure the internal validity of an experiment , you should only change one independent variable at a time.

To ensure the internal validity of your research, you must consider the impact of confounding variables. If you fail to account for them, you might over- or underestimate the causal relationship between your independent and dependent variables , or even find a causal relationship where none exists.

A confounding variable is closely related to both the independent and dependent variables in a study. An independent variable represents the supposed cause , while the dependent variable is the supposed effect . A confounding variable is a third variable that influences both the independent and dependent variables.

Failing to account for confounding variables can cause you to wrongly estimate the relationship between your independent and dependent variables.

There are several methods you can use to decrease the impact of confounding variables on your research: restriction, matching, statistical control, and randomisation.

In restriction , you restrict your sample by only including certain subjects that have the same values of potential confounding variables.

In matching , you match each of the subjects in your treatment group with a counterpart in the comparison group. The matched subjects have the same values on any potential confounding variables, and only differ in the independent variable .

In statistical control , you include potential confounders as variables in your regression .

In randomisation , you randomly assign the treatment (or independent variable) in your study to a sufficiently large number of subjects, which allows you to control for all potential confounding variables.

In scientific research, concepts are the abstract ideas or phenomena that are being studied (e.g., educational achievement). Variables are properties or characteristics of the concept (e.g., performance at school), while indicators are ways of measuring or quantifying variables (e.g., yearly grade reports).

The process of turning abstract concepts into measurable variables and indicators is called operationalisation .

In statistics, ordinal and nominal variables are both considered categorical variables .

Even though ordinal data can sometimes be numerical, not all mathematical operations can be performed on them.

A control variable is any variable that’s held constant in a research study. It’s not a variable of interest in the study, but it’s controlled because it could influence the outcomes.

Control variables help you establish a correlational or causal relationship between variables by enhancing internal validity .

If you don’t control relevant extraneous variables , they may influence the outcomes of your study, and you may not be able to demonstrate that your results are really an effect of your independent variable .

‘Controlling for a variable’ means measuring extraneous variables and accounting for them statistically to remove their effects on other variables.

Researchers often model control variable data along with independent and dependent variable data in regression analyses and ANCOVAs . That way, you can isolate the control variable’s effects from the relationship between the variables of interest.

An extraneous variable is any variable that you’re not investigating that can potentially affect the dependent variable of your research study.

A confounding variable is a type of extraneous variable that not only affects the dependent variable, but is also related to the independent variable.

There are 4 main types of extraneous variables :

• Demand characteristics : Environmental cues that encourage participants to conform to researchers’ expectations
• Experimenter effects : Unintentional actions by researchers that influence study outcomes
• Situational variables : Eenvironmental variables that alter participants’ behaviours
• Participant variables : Any characteristic or aspect of a participant’s background that could affect study results

The difference between explanatory and response variables is simple:

• An explanatory variable is the expected cause, and it explains the results.
• A response variable is the expected effect, and it responds to other variables.

The term ‘ explanatory variable ‘ is sometimes preferred over ‘ independent variable ‘ because, in real-world contexts, independent variables are often influenced by other variables. This means they aren’t totally independent.

Multiple independent variables may also be correlated with each other, so ‘explanatory variables’ is a more appropriate term.

On graphs, the explanatory variable is conventionally placed on the x -axis, while the response variable is placed on the y -axis.

• If you have quantitative variables , use a scatterplot or a line graph.
• If your response variable is categorical, use a scatterplot or a line graph.
• If your explanatory variable is categorical, use a bar graph.

A correlation is usually tested for two variables at a time, but you can test correlations between three or more variables.

An independent variable is the variable you manipulate, control, or vary in an experimental study to explore its effects. It’s called ‘independent’ because it’s not influenced by any other variables in the study.

Independent variables are also called:

• Explanatory variables (they explain an event or outcome)
• Predictor variables (they can be used to predict the value of a dependent variable)
• Right-hand-side variables (they appear on the right-hand side of a regression equation)

A dependent variable is what changes as a result of the independent variable manipulation in experiments . It’s what you’re interested in measuring, and it ‘depends’ on your independent variable.

In statistics, dependent variables are also called:

• Response variables (they respond to a change in another variable)
• Outcome variables (they represent the outcome you want to measure)
• Left-hand-side variables (they appear on the left-hand side of a regression equation)

Deductive reasoning is commonly used in scientific research, and it’s especially associated with quantitative research .

In research, you might have come across something called the hypothetico-deductive method . It’s the scientific method of testing hypotheses to check whether your predictions are substantiated by real-world data.

Deductive reasoning is a logical approach where you progress from general ideas to specific conclusions. It’s often contrasted with inductive reasoning , where you start with specific observations and form general conclusions.

Deductive reasoning is also called deductive logic.

Inductive reasoning is a method of drawing conclusions by going from the specific to the general. It’s usually contrasted with deductive reasoning, where you proceed from general information to specific conclusions.

Inductive reasoning is also called inductive logic or bottom-up reasoning.

In inductive research , you start by making observations or gathering data. Then, you take a broad scan of your data and search for patterns. Finally, you make general conclusions that you might incorporate into theories.

Inductive reasoning is a bottom-up approach, while deductive reasoning is top-down.

Inductive reasoning takes you from the specific to the general, while in deductive reasoning, you make inferences by going from general premises to specific conclusions.

There are many different types of inductive reasoning that people use formally or informally.

Here are a few common types:

• Inductive generalisation : You use observations about a sample to come to a conclusion about the population it came from.
• Statistical generalisation: You use specific numbers about samples to make statements about populations.
• Causal reasoning: You make cause-and-effect links between different things.
• Sign reasoning: You make a conclusion about a correlational relationship between different things.
• Analogical reasoning: You make a conclusion about something based on its similarities to something else.

It’s often best to ask a variety of people to review your measurements. You can ask experts, such as other researchers, or laypeople, such as potential participants, to judge the face validity of tests.

While experts have a deep understanding of research methods , the people you’re studying can provide you with valuable insights you may have missed otherwise.

Face validity is important because it’s a simple first step to measuring the overall validity of a test or technique. It’s a relatively intuitive, quick, and easy way to start checking whether a new measure seems useful at first glance.

Good face validity means that anyone who reviews your measure says that it seems to be measuring what it’s supposed to. With poor face validity, someone reviewing your measure may be left confused about what you’re measuring and why you’re using this method.

Face validity is about whether a test appears to measure what it’s supposed to measure. This type of validity is concerned with whether a measure seems relevant and appropriate for what it’s assessing only on the surface.

Statistical analyses are often applied to test validity with data from your measures. You test convergent validity and discriminant validity with correlations to see if results from your test are positively or negatively related to those of other established tests.

You can also use regression analyses to assess whether your measure is actually predictive of outcomes that you expect it to predict theoretically. A regression analysis that supports your expectations strengthens your claim of construct validity .

When designing or evaluating a measure, construct validity helps you ensure you’re actually measuring the construct you’re interested in. If you don’t have construct validity, you may inadvertently measure unrelated or distinct constructs and lose precision in your research.

Construct validity is often considered the overarching type of measurement validity ,  because it covers all of the other types. You need to have face validity , content validity, and criterion validity to achieve construct validity.

Construct validity is about how well a test measures the concept it was designed to evaluate. It’s one of four types of measurement validity , which includes construct validity, face validity , and criterion validity.

There are two subtypes of construct validity.

• Convergent validity : The extent to which your measure corresponds to measures of related constructs
• Discriminant validity: The extent to which your measure is unrelated or negatively related to measures of distinct constructs

Attrition bias can skew your sample so that your final sample differs significantly from your original sample. Your sample is biased because some groups from your population are underrepresented.

With a biased final sample, you may not be able to generalise your findings to the original population that you sampled from, so your external validity is compromised.

There are seven threats to external validity : selection bias , history, experimenter effect, Hawthorne effect , testing effect, aptitude-treatment, and situation effect.

The two types of external validity are population validity (whether you can generalise to other groups of people) and ecological validity (whether you can generalise to other situations and settings).

The external validity of a study is the extent to which you can generalise your findings to different groups of people, situations, and measures.

Attrition bias is a threat to internal validity . In experiments, differential rates of attrition between treatment and control groups can skew results.

This bias can affect the relationship between your independent and dependent variables . It can make variables appear to be correlated when they are not, or vice versa.

Internal validity is the extent to which you can be confident that a cause-and-effect relationship established in a study cannot be explained by other factors.

There are eight threats to internal validity : history, maturation, instrumentation, testing, selection bias , regression to the mean, social interaction, and attrition .

A sampling error is the difference between a population parameter and a sample statistic .

A statistic refers to measures about the sample , while a parameter refers to measures about the population .

Populations are used when a research question requires data from every member of the population. This is usually only feasible when the population is small and easily accessible.

Systematic sampling is a probability sampling method where researchers select members of the population at a regular interval – for example, by selecting every 15th person on a list of the population. If the population is in a random order, this can imitate the benefits of simple random sampling .

There are three key steps in systematic sampling :

• Define and list your population , ensuring that it is not ordered in a cyclical or periodic order.
• Decide on your sample size and calculate your interval, k , by dividing your population by your target sample size.
• Choose every k th member of the population as your sample.

Yes, you can create a stratified sample using multiple characteristics, but you must ensure that every participant in your study belongs to one and only one subgroup. In this case, you multiply the numbers of subgroups for each characteristic to get the total number of groups.

For example, if you were stratifying by location with three subgroups (urban, rural, or suburban) and marital status with five subgroups (single, divorced, widowed, married, or partnered), you would have 3 × 5 = 15 subgroups.

You should use stratified sampling when your sample can be divided into mutually exclusive and exhaustive subgroups that you believe will take on different mean values for the variable that you’re studying.

Using stratified sampling will allow you to obtain more precise (with lower variance ) statistical estimates of whatever you are trying to measure.

For example, say you want to investigate how income differs based on educational attainment, but you know that this relationship can vary based on race. Using stratified sampling, you can ensure you obtain a large enough sample from each racial group, allowing you to draw more precise conclusions.

In stratified sampling , researchers divide subjects into subgroups called strata based on characteristics that they share (e.g., race, gender, educational attainment).

Once divided, each subgroup is randomly sampled using another probability sampling method .

Multistage sampling can simplify data collection when you have large, geographically spread samples, and you can obtain a probability sample without a complete sampling frame.

But multistage sampling may not lead to a representative sample, and larger samples are needed for multistage samples to achieve the statistical properties of simple random samples .

In multistage sampling , you can use probability or non-probability sampling methods.

For a probability sample, you have to probability sampling at every stage. You can mix it up by using simple random sampling , systematic sampling , or stratified sampling to select units at different stages, depending on what is applicable and relevant to your study.

Cluster sampling is a probability sampling method in which you divide a population into clusters, such as districts or schools, and then randomly select some of these clusters as your sample.

The clusters should ideally each be mini-representations of the population as a whole.

There are three types of cluster sampling : single-stage, double-stage and multi-stage clustering. In all three types, you first divide the population into clusters, then randomly select clusters for use in your sample.

• In single-stage sampling , you collect data from every unit within the selected clusters.
• In double-stage sampling , you select a random sample of units from within the clusters.
• In multi-stage sampling , you repeat the procedure of randomly sampling elements from within the clusters until you have reached a manageable sample.

Cluster sampling is more time- and cost-efficient than other probability sampling methods , particularly when it comes to large samples spread across a wide geographical area.

However, it provides less statistical certainty than other methods, such as simple random sampling , because it is difficult to ensure that your clusters properly represent the population as a whole.

If properly implemented, simple random sampling is usually the best sampling method for ensuring both internal and external validity . However, it can sometimes be impractical and expensive to implement, depending on the size of the population to be studied,

If you have a list of every member of the population and the ability to reach whichever members are selected, you can use simple random sampling.

The American Community Survey  is an example of simple random sampling . In order to collect detailed data on the population of the US, the Census Bureau officials randomly select 3.5 million households per year and use a variety of methods to convince them to fill out the survey.

Simple random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population . Each member of the population has an equal chance of being selected. Data are then collected from as large a percentage as possible of this random subset.

Sampling bias occurs when some members of a population are systematically more likely to be selected in a sample than others.

In multistage sampling , or multistage cluster sampling, you draw a sample from a population using smaller and smaller groups at each stage.

This method is often used to collect data from a large, geographically spread group of people in national surveys, for example. You take advantage of hierarchical groupings (e.g., from county to city to neighbourhood) to create a sample that’s less expensive and time-consuming to collect data from.

In non-probability sampling , the sample is selected based on non-random criteria, and not every member of the population has a chance of being included.

Common non-probability sampling methods include convenience sampling , voluntary response sampling, purposive sampling , snowball sampling , and quota sampling .

Probability sampling means that every member of the target population has a known chance of being included in the sample.

Probability sampling methods include simple random sampling , systematic sampling , stratified sampling , and cluster sampling .

Samples are used to make inferences about populations . Samples are easier to collect data from because they are practical, cost-effective, convenient, and manageable.

While a between-subjects design has fewer threats to internal validity , it also requires more participants for high statistical power than a within-subjects design .

Advantages:

• Prevents carryover effects of learning and fatigue.
• Shorter study duration.

Disadvantages:

• Needs larger samples for high power.
• Uses more resources to recruit participants, administer sessions, cover costs, etc.
• Individual differences may be an alternative explanation for results.

In a factorial design, multiple independent variables are tested.

If you test two variables, each level of one independent variable is combined with each level of the other independent variable to create different conditions.

Yes. Between-subjects and within-subjects designs can be combined in a single study when you have two or more independent variables (a factorial design). In a mixed factorial design, one variable is altered between subjects and another is altered within subjects.

Within-subjects designs have many potential threats to internal validity , but they are also very statistically powerful .

• Only requires small samples
• Statistically powerful
• Removes the effects of individual differences on the outcomes
• Internal validity threats reduce the likelihood of establishing a direct relationship between variables
• Time-related effects, such as growth, can influence the outcomes
• Carryover effects mean that the specific order of different treatments affect the outcomes

Quasi-experimental design is most useful in situations where it would be unethical or impractical to run a true experiment .

Quasi-experiments have lower internal validity than true experiments, but they often have higher external validity  as they can use real-world interventions instead of artificial laboratory settings.

In experimental research, random assignment is a way of placing participants from your sample into different groups using randomisation. With this method, every member of the sample has a known or equal chance of being placed in a control group or an experimental group.

A quasi-experiment is a type of research design that attempts to establish a cause-and-effect relationship. The main difference between this and a true experiment is that the groups are not randomly assigned.

In a between-subjects design , every participant experiences only one condition, and researchers assess group differences between participants in various conditions.

In a within-subjects design , each participant experiences all conditions, and researchers test the same participants repeatedly for differences between conditions.

The word ‘between’ means that you’re comparing different conditions between groups, while the word ‘within’ means you’re comparing different conditions within the same group.

A confounding variable , also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.

A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.

In your research design , it’s important to identify potential confounding variables and plan how you will reduce their impact.

Triangulation can help:

• Reduce bias that comes from using a single method, theory, or investigator
• Enhance validity by approaching the same topic with different tools
• Establish credibility by giving you a complete picture of the research problem

But triangulation can also pose problems:

• It’s time-consuming and labour-intensive, often involving an interdisciplinary team.
• Your results may be inconsistent or even contradictory.

There are four main types of triangulation :

• Data triangulation : Using data from different times, spaces, and people
• Investigator triangulation : Involving multiple researchers in collecting or analysing data
• Theory triangulation : Using varying theoretical perspectives in your research
• Methodological triangulation : Using different methodologies to approach the same topic

Experimental designs are a set of procedures that you plan in order to examine the relationship between variables that interest you.

To design a successful experiment, first identify:

• A testable hypothesis
• One or more independent variables that you will manipulate
• One or more dependent variables that you will measure

When designing the experiment, first decide:

• How your variable(s) will be manipulated
• How you will control for any potential confounding or lurking variables
• How many subjects you will include
• How you will assign treatments to your subjects

Exploratory research explores the main aspects of a new or barely researched question.

Explanatory research explains the causes and effects of an already widely researched question.

The key difference between observational studies and experiments is that, done correctly, an observational study will never influence the responses or behaviours of participants. Experimental designs will have a treatment condition applied to at least a portion of participants.

An observational study could be a good fit for your research if your research question is based on things you observe. If you have ethical, logistical, or practical concerns that make an experimental design challenging, consider an observational study. Remember that in an observational study, it is critical that there be no interference or manipulation of the research subjects. Since it’s not an experiment, there are no control or treatment groups either.

These are four of the most common mixed methods designs :

• Convergent parallel: Quantitative and qualitative data are collected at the same time and analysed separately. After both analyses are complete, compare your results to draw overall conclusions. 
• Embedded: Quantitative and qualitative data are collected at the same time, but within a larger quantitative or qualitative design. One type of data is secondary to the other.
• Explanatory sequential: Quantitative data is collected and analysed first, followed by qualitative data. You can use this design if you think your qualitative data will explain and contextualise your quantitative findings.
• Exploratory sequential: Qualitative data is collected and analysed first, followed by quantitative data. You can use this design if you think the quantitative data will confirm or validate your qualitative findings.

Triangulation in research means using multiple datasets, methods, theories and/or investigators to address a research question. It’s a research strategy that can help you enhance the validity and credibility of your findings.

Triangulation is mainly used in qualitative research , but it’s also commonly applied in quantitative research . Mixed methods research always uses triangulation.

Operationalisation means turning abstract conceptual ideas into measurable observations.

For example, the concept of social anxiety isn’t directly observable, but it can be operationally defined in terms of self-rating scores, behavioural avoidance of crowded places, or physical anxiety symptoms in social situations.

Before collecting data , it’s important to consider how you will operationalise the variables that you want to measure.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

There are five common approaches to qualitative research :

• Grounded theory involves collecting data in order to develop new theories.
• Ethnography involves immersing yourself in a group or organisation to understand its culture.
• Narrative research involves interpreting stories to understand how people make sense of their experiences and perceptions.
• Phenomenological research involves investigating phenomena through people’s lived experiences.
• Action research links theory and practice in several cycles to drive innovative changes.

There are various approaches to qualitative data analysis , but they all share five steps in common:

• Prepare and organise your data.
• Review and explore your data.
• Develop a data coding system.
• Assign codes to the data.
• Identify recurring themes.

The specifics of each step depend on the focus of the analysis. Some common approaches include textual analysis , thematic analysis , and discourse analysis .

In mixed methods research , you use both qualitative and quantitative data collection and analysis methods to answer your research question .

Methodology refers to the overarching strategy and rationale of your research project . It involves studying the methods used in your field and the theories or principles behind them, in order to develop an approach that matches your objectives.

Methods are the specific tools and procedures you use to collect and analyse data (e.g. experiments, surveys , and statistical tests ).

In shorter scientific papers, where the aim is to report the findings of a specific study, you might simply describe what you did in a methods section .

In a longer or more complex research project, such as a thesis or dissertation , you will probably include a methodology section , where you explain your approach to answering the research questions and cite relevant sources to support your choice of methods.

The research methods you use depend on the type of data you need to answer your research question .

• If you want to measure something or test a hypothesis , use quantitative methods . If you want to explore ideas, thoughts, and meanings, use qualitative methods .
• If you want to analyse a large amount of readily available data, use secondary data. If you want data specific to your purposes with control over how they are generated, collect primary data.
• If you want to establish cause-and-effect relationships between variables , use experimental methods. If you want to understand the characteristics of a research subject, use descriptive methods.

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How to Write a Hypothesis for Correlation

How to Calculate a P-Value

A hypothesis is a testable statement about how something works in the natural world. While some hypotheses predict a causal relationship between two variables, other hypotheses predict a correlation between them. According to the Research Methods Knowledge Base, a correlation is a single number that describes the relationship between two variables. If you do not predict a causal relationship or cannot measure one objectively, state clearly in your hypothesis that you are merely predicting a correlation.

Research the topic in depth before forming a hypothesis. Without adequate knowledge about the subject matter, you will not be able to decide whether to write a hypothesis for correlation or causation. Read the findings of similar experiments before writing your own hypothesis.

Identify the independent variable and dependent variable. Your hypothesis will be concerned with what happens to the dependent variable when a change is made in the independent variable. In a correlation, the two variables undergo changes at the same time in a significant number of cases. However, this does not mean that the change in the independent variable causes the change in the dependent variable.

Construct an experiment to test your hypothesis. In a correlative experiment, you must be able to measure the exact relationship between two variables. This means you will need to find out how often a change occurs in both variables in terms of a specific percentage.

Establish the requirements of the experiment with regard to statistical significance. Instruct readers exactly how often the variables must correlate to reach a high enough level of statistical significance. This number will vary considerably depending on the field. In a highly technical scientific study, for instance, the variables may need to correlate 98 percent of the time; but in a sociological study, 90 percent correlation may suffice. Look at other studies in your particular field to determine the requirements for statistical significance.

State the null hypothesis. The null hypothesis gives an exact value that implies there is no correlation between the two variables. If the results show a percentage equal to or lower than the value of the null hypothesis, then the variables are not proven to correlate.

Record and summarize the results of your experiment. State whether or not the experiment met the minimum requirements of your hypothesis in terms of both percentage and significance.

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• University of New England; Steps in Hypothesis Testing for Correlation; 2000
• Research Methods Knowledge Base; Correlation; William M.K. Trochim; 2006
• Science Buddies; Hypothesis

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Brian Gabriel has been a writer and blogger since 2009, contributing to various online publications. He earned his Bachelor of Arts in history from Whitworth University.

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Understanding the Null Hypothesis for Linear Regression

Linear regression is a technique we can use to understand the relationship between one or more predictor variables and a response variable .

If we only have one predictor variable and one response variable, we can use simple linear regression , which uses the following formula to estimate the relationship between the variables:

ŷ = β 0 + β 1 x

• ŷ: The estimated response value.
• β 0 : The average value of y when x is zero.
• β 1 : The average change in y associated with a one unit increase in x.
• x: The value of the predictor variable.

Simple linear regression uses the following null and alternative hypotheses:

• H 0 : β 1 = 0
• H A : β 1 ≠ 0

The null hypothesis states that the coefficient β 1 is equal to zero. In other words, there is no statistically significant relationship between the predictor variable, x, and the response variable, y.

The alternative hypothesis states that β 1 is not equal to zero. In other words, there is a statistically significant relationship between x and y.

If we have multiple predictor variables and one response variable, we can use multiple linear regression , which uses the following formula to estimate the relationship between the variables:

ŷ = β 0 + β 1 x 1 + β 2 x 2 + … + β k x k

• β 0 : The average value of y when all predictor variables are equal to zero.
• β i : The average change in y associated with a one unit increase in x i .
• x i : The value of the predictor variable x i .

Multiple linear regression uses the following null and alternative hypotheses:

• H 0 : β 1 = β 2 = … = β k = 0
• H A : β 1 = β 2 = … = β k ≠ 0

The null hypothesis states that all coefficients in the model are equal to zero. In other words, none of the predictor variables have a statistically significant relationship with the response variable, y.

The alternative hypothesis states that not every coefficient is simultaneously equal to zero.

The following examples show how to decide to reject or fail to reject the null hypothesis in both simple linear regression and multiple linear regression models.

Example 1: Simple Linear Regression

Suppose a professor would like to use the number of hours studied to predict the exam score that students will receive in his class. He collects data for 20 students and fits a simple linear regression model.

The following screenshot shows the output of the regression model:

The fitted simple linear regression model is:

Exam Score = 67.1617 + 5.2503*(hours studied)

To determine if there is a statistically significant relationship between hours studied and exam score, we need to analyze the overall F value of the model and the corresponding p-value:

• Overall F-Value:  47.9952
• P-value:  0.000

Since this p-value is less than .05, we can reject the null hypothesis. In other words, there is a statistically significant relationship between hours studied and exam score received.

Example 2: Multiple Linear Regression

Suppose a professor would like to use the number of hours studied and the number of prep exams taken to predict the exam score that students will receive in his class. He collects data for 20 students and fits a multiple linear regression model.

The fitted multiple linear regression model is:

Exam Score = 67.67 + 5.56*(hours studied) – 0.60*(prep exams taken)

To determine if there is a jointly statistically significant relationship between the two predictor variables and the response variable, we need to analyze the overall F value of the model and the corresponding p-value:

• Overall F-Value:  23.46
• P-value:  0.00

Since this p-value is less than .05, we can reject the null hypothesis. In other words, hours studied and prep exams taken have a jointly statistically significant relationship with exam score.

Note: Although the p-value for prep exams taken (p = 0.52) is not significant, prep exams combined with hours studied has a significant relationship with exam score.

Additional Resources

Understanding the F-Test of Overall Significance in Regression How to Read and Interpret a Regression Table How to Report Regression Results How to Perform Simple Linear Regression in Excel How to Perform Multiple Linear Regression in Excel

Hey there. My name is Zach Bobbitt. I have a Master of Science degree in Applied Statistics and I’ve worked on machine learning algorithms for professional businesses in both healthcare and retail. I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike.  My goal with this site is to help you learn statistics through using simple terms, plenty of real-world examples, and helpful illustrations.

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How To Write A Hypothesis Guide And Detailed Instructions

Whether you’re studying for a college degree, MBA, or Ph.D., developing a hypothesis for your research is mandatory. You must know how to write a good hypothesis to impress your professors. Now, how should a hypothesis be written?

This is where some students get confused and exhausted. You already know that you’re to formulate a hypothesis around something testable. But you don’t know how to create hypotheses based on previous observations that you would later explain in your paper or journal.

In this article, you’ll learn what a hypothesis is, how to make a hypothesis, examples of how to write hypothesis statement, and how to go about yours.

What Is A Hypothesis?

A hypothesis is a statement that is not proven, and it’s an assumption that you’ll base your research on. They must be testable: they must have answers that can be checked with experiments and evidence.

The theory around your hypothesis becomes valid when it’s proven to be true through experiments. Scientists have rules for writing that make their chemistry, physics, and biology research reproducible.

An essential part is that they must understand the experiments of others so that they can build on them and improve them. These rules define how scientists write about science. This rule applies to hypotheses, too.

Why Do You Need A Hypothesis?

Writing a good hypothesis is a key part of any scientific exploration. It allows a broad and open-ended question that compels you to investigate. There are many other reasons, including:

It’s different from a theory because a theory is something like:

“The earth orbits around the sun.”

This is not testable because we know that it’s true. A theory is more like an explanation for why something happens, while a hypothesis is a guess about what will happen and why it would.

A hypothesis is a statement of the relationship you’ve observed in a pair of variables. The easiest way to think about it is that the hypothesis is your testable statement for your research project.

You would typically use your background knowledge and experience as a researcher to come up with this statement before you set out to collect data. A good hypothesis will give you insight into what kind of data you need to collect to answer the question (or provide evidence).

For example:

“People who live in cities have higher stress levels than those who live in rural areas because there are more people around them all day long!”

This hypothesis would then lead us to ask questions like “How do we measure stress?” or “What factors contribute to stress?” You’ll provide answers to these questions with the paper.

A hypothesis can be proven or disproven throughout an experiment. The most common way to disprove a hypothesis is through statistical significance testing. This entails using probability and data analysis to show that there’s no practical difference between the two compared groups.

The hypothesis is a testable statement about how the world works. It’s also a way to properly arrange and structure your data. Without a hypothesis, you won’t even know what to set your scientific experiment on. A hypothesis is what you’ll use to predict what will happen in the future, and the data you collect during the research will help validate or disprove this.

In science, you’re always trying to figure out why things happen the way they do and what factors affect them. When you know how something works, “why do some people get sick while others don’t?” You might make up a hypothesis to test your idea: “People who are exposed to germs get flu symptoms.” Here’s how to start a hypothesis as the answer lets you determine whether your idea is right or wrong; an experiment then validates (or disproves) it.

Now that you know why you need to formulate a testable hypothesis, learn how to write a research hypothesis with tangible examples.

How To Write A Hypothesis

Before you start your experiments in the lab, it’s important to take some time to think about what you’re trying to achieve. After all, you can’t know your research destination until you plan it beforehand. This is why mastering how to state a hypothesis gives room for healthy predictions. Here’s how you formulate hypothesis:

Your first step is to determine what you want to investigate. You can start with a question you’d like to answer or a problem that needs solving.For example, if you’re a teacher trying to improve your students’ reading skills, you might ask:

“What techniques can I use for my students to boost reading comprehension scores on their standardized tests?”

This could also be stated as “Do test-taking strategies lead to improved standardized test scores?”

Once your question pops in your mind, especially while reflecting on a scientific paper you’ve read or a documentary you saw, write it down and commence research.

You need some facts to state a hypothesis and prove it. It might be tricky to get these facts, and you’ll want to look for relevant and irrelevant information.

Relevant information is directly related to your hypothesis. For example, your relevant sources would be academic, examination, and psychology journals, quantitative data or news outlets for the above statement.

Irrelevant information is any other kind of data, and this could be random news outlets or interviews that could help bolster what your assumptions are.

Use the word “because” to indicate that your variable causes or explains another variable. For example: If we are testing whether exercise leads to weight loss, our sentence might look like this:

“Consistent gym practice causes weight loss because it burns calories and gets the body in shape.”

You need to identify if your hypothesis is testable or if it’s an opinion you can’t prove. You can’t test what you don’t know or can’t prove. So you’d need to rewrite your hypothesis if you think it’s not testable.

Your hypothesis should be clear, concise, testable, specific, and relevant. The best way to do this is to write a brief summary of your hypothesis in the form: “If X happens, then Y will happen.”

Here’s a sample hypothesis:

“If I add 15 minutes to my sitting time everyday, then my body mass index (BMI) will reduce by 5 points in three months.”

Now that you’ve defined your idea, it’s time for the actual experiment to determine whether it’ll work.

How To Write A Hypothesis Statement: Example Of A Hypothesis

There are numerous examples of a hypothesis statement you can take a clue from. A scientific hypothesis examines two variables that need evidence-based research to be considered valid. For example:

“If I increase the amount of water applied to a plant garden, then it will make it grow faster.”

You have identified the independent and dependent variables in this statement. The independent variable is “amount of water applied,” and the dependent variable is “grow faster.” You also included a control group, which is important in scientific experiments to eliminate bias from other factors that could influence your results.

In this case, you are comparing how much growth there would be if you increase the amount of water versus how much growth there would be if you do not increase it.

You then need to research the topic in detail and design an experiment before you can write your report. The first step is to decide what you’re going to measure, how you’ll measure it, and how many times you’ll do this so that it’s accurate.

Once you’ve measured your experiment, interpreting the results can be challenging. You should look at graphs or charts of your data to see if any patterns or trends might indicate a cause-and-effect relationship between two things (like applying more water to the plant garden and faster growth).

After looking at the results of your experiment and deciding whether or not they support your original hypothesis, use this new knowledge in your conclusion. Write up something like:

“Based on my findings, it’s clear that applying more water to any plant garden would make the plant garden grow faster and greener.”

Then, write an introduction section where you can explain why this project interests/matters/is relevant to your reader. At this point, your hypothesis is no longer an educated guess. It started as one (with the observation or thoughts/idea) and ended as verifiable.

Format For Hypothesis: How Should A Hypothesis Be Written?

The usual format of a hypothesis is If – (then) – because.

Because we have the idea that if a hypothesis is formatted as an if-then statement, it’s clear what the hypothesis is about. This can be helpful for your readers and yourself if you ever need to come back and look at your work.

So, now that you know how to format it correctly (and why) let’s look at some hypothesis examples.

“If snow falls, then I’ll catch a cold when I get outside because cold can be a result of heavy snow.”

“If anyone in my family eats cake, then we will feel sick because the cake contains ingredients we are allergic to.”

“Some grasses never grow because they’re stumped every day.”

All these show that two variables must come together in the sentence. The variables must also be a probability the research attempts to solve to make them valid statements.

How To Know Your Hypothesis Is Good

Now that you know how to create a hypothesis, you need to know if it’s good through these pointers:

State a Hypothesis as Clearly as Possible You can choose precise words that are neither ambiguous nor too technical. You should also avoid jargon and words with multiple meanings to keep your language simple and clear. Don’t use fancy or pretentious words unless they’re absolutely necessary for the meaning you want to convey, and make sure you’ve used them in their correct context. In addition, use a tone of voice appropriate to the audience. A scientific paper may need more formal language than an article for popular consumption. A Good Hypothesis Should Explain the Bond Between Multiple Variables The main purpose of forming a hypothesis is to explain the relationship between multiple variables clearly. The relationship should be testable for it to be proven. This is, why if X leads to Y, what is in between that connects X and Y? This must reflect in the hypothesis as it’s the factor that’ll be experimented. A Hypothesis should Be Testable This means that your hypothesis should be a statement that can be proven or disproven with an experiment. You want to make sure your hypothesis is specific enough to guide you towards the right experiment but not so specific that it eliminates any other possible outcomes of your experiment. Also, a hypothesis should not make claims about unobservable things (like feelings or thoughts). Instead, focus on observable results (things we can see) like measurements and observations from experiments conducted by scientists over time.If your hypothesis isn’t testable, then it needs to be reformulated.

What Should You Do If Your Hypothesis Is Incorrect?

You need to reformulate your thesis if it’s incorrect. You may have to reevaluate the problem or look at it differently. It’s also possible that you need to test your hypothesis with a different method of experimentation.

Here are some ideas from the best scientific thesis writing help experts:

Try Another Approach: Try looking at your hypothesis from a different angle, or consider changing up your methods entirely (for example, instead of asking people what they think will happen in the future and then testing their opinions against reality, you could run an experiment where participants predict events and then actually follow up on those predictions). Share Your Idea with a Third Party: Your hypothesis can be tested by allowing a third party to observe the results of your attempt to prove or disprove the statement. For example, if you’re testing whether peanuts can be made into peanut butter using only as few steps as possible, have someone else make it for you or observe them make it.

Document how you made your product and recorded any necessary changes along the way. This will help you know what works and doesn’t so that you’ll make changes to the whole idea.

Get Hypothesis Writing Help

Writing a hypothesis is smart work. You need professionals who know how to write a scientific hypothesis and journal that reflect the experiment supporting the hypothesis. You need professionals who are also expert writers and can offer writing help online.

We offer some of the best writing helpers online, with fast with turnovers. Our writers create the best hypothesis scenario with the possibility to ace any experiment at a cheap price. They will offer writing help if you need these professionals to help write a good hypothesis for you. After all, you need to complete your degrees stronger than you started. A great paper by professionals can seal that deal, and our master thesis writing service is here to help.

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