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Hypothesis testing is an essential procedure in statistics. A hypothesis test evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data. When we say that a finding is statistically significant, it’s thanks to a hypothesis test. How do these tests really work and what does statistical significance actually mean?
In this series of three posts, I’ll help you intuitively understand how hypothesis tests work by focusing on concepts and graphs rather than equations and numbers. After all, a key reason to use statistical software like Minitab is so you don’t get bogged down in the calculations and can instead focus on understanding your results.
To kick things off in this post, I highlight the rationale for using hypothesis tests with an example.
An economist wants to determine whether the monthly energy cost for families has changed from the previous year, when the mean cost per month was $260. The economist randomly samples 25 families and records their energy costs for the current year. (The data for this example is FamilyEnergyCost and it is just one of the many data set examples that can be found in Minitab’s Data Set Library.)
I’ll use these descriptive statistics to create a probability distribution plot that shows you the importance of hypothesis tests. Read on!
Why do we even need hypothesis tests? After all, we took a random sample and our sample mean of 330.6 is different from 260. That is different, right? Unfortunately, the picture is muddied because we’re looking at a sample rather than the entire population.
Sampling error is the difference between a sample and the entire population. Thanks to sampling error, it’s entirely possible that while our sample mean is 330.6, the population mean could still be 260. Or, to put it another way, if we repeated the experiment, it’s possible that the second sample mean could be close to 260. A hypothesis test helps assess the likelihood of this possibility!
For any given random sample, the mean of the sample almost certainly doesn’t equal the true mean of the population due to sampling error. For our example, it’s unlikely that the mean cost for the entire population is exactly 330.6. In fact, if we took multiple random samples of the same size from the same population, we could plot a distribution of the sample means.
A sampling distribution is the distribution of a statistic, such as the mean, that is obtained by repeatedly drawing a large number of samples from a specific population. This distribution allows you to determine the probability of obtaining the sample statistic.
Fortunately, I can create a plot of sample means without collecting many different random samples! Instead, I’ll create a probability distribution plot using the t-distribution , the sample size, and the variability in our sample to graph the sampling distribution.
Our goal is to determine whether our sample mean is significantly different from the null hypothesis mean. Therefore, we’ll use the graph to see whether our sample mean of 330.6 is unlikely assuming that the population mean is 260. The graph below shows the expected distribution of sample means.
You can see that the most probable sample mean is 260, which makes sense because we’re assuming that the null hypothesis is true. However, there is a reasonable probability of obtaining a sample mean that ranges from 167 to 352, and even beyond! The takeaway from this graph is that while our sample mean of 330.6 is not the most probable, it’s also not outside the realm of possibility.
We’ve placed our sample mean in the context of all possible sample means while assuming that the null hypothesis is true. Are these results statistically significant?
As you can see, there is no magic place on the distribution curve to make this determination. Instead, we have a continual decrease in the probability of obtaining sample means that are further from the null hypothesis value. Where do we draw the line?
This is where hypothesis tests are useful. A hypothesis test allows us quantify the probability that our sample mean is unusual.
For this series of posts, I’ll continue to use this graphical framework and add in the significance level, P value, and confidence interval to show how hypothesis tests work and what statistical significance really means.
If you'd like to see how I made these graphs, please read: How to Create a Graphical Version of the 1-sample t-Test .
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6a.2 - steps for hypothesis tests, the logic of hypothesis testing section .
A hypothesis, in statistics, is a statement about a population parameter, where this statement typically is represented by some specific numerical value. In testing a hypothesis, we use a method where we gather data in an effort to gather evidence about the hypothesis.
How do we decide whether to reject the null hypothesis?
In hypothesis testing, there are certain steps one must follow. Below these are summarized into six such steps to conducting a test of a hypothesis.
We will follow these six steps for the remainder of this Lesson. In the future Lessons, the steps will be followed but may not be explained explicitly.
Step 1 is a very important step to set up correctly. If your hypotheses are incorrect, your conclusion will be incorrect. In this next section, we practice with Step 1 for the one sample situations.
Hypothesis testing is the act of testing a hypothesis or a supposition in relation to a statistical parameter. Analysts implement hypothesis testing in order to test if a hypothesis is plausible or not.
In data science and statistics , hypothesis testing is an important step as it involves the verification of an assumption that could help develop a statistical parameter. For instance, a researcher establishes a hypothesis assuming that the average of all odd numbers is an even number.
In order to find the plausibility of this hypothesis, the researcher will have to test the hypothesis using hypothesis testing methods. Unlike a hypothesis that is ‘supposed’ to stand true on the basis of little or no evidence, hypothesis testing is required to have plausible evidence in order to establish that a statistical hypothesis is true.
Perhaps this is where statistics play an important role. A number of components are involved in this process. But before understanding the process involved in hypothesis testing in research methodology, we shall first understand the types of hypotheses that are involved in the process. Let us get started!
In data sampling, different types of hypothesis are involved in finding whether the tested samples test positive for a hypothesis or not. In this segment, we shall discover the different types of hypotheses and understand the role they play in hypothesis testing.
Alternative Hypothesis (H1) or the research hypothesis states that there is a relationship between two variables (where one variable affects the other). The alternative hypothesis is the main driving force for hypothesis testing.
It implies that the two variables are related to each other and the relationship that exists between them is not due to chance or coincidence.
When the process of hypothesis testing is carried out, the alternative hypothesis is the main subject of the testing process. The analyst intends to test the alternative hypothesis and verifies its plausibility.
The Null Hypothesis (H0) aims to nullify the alternative hypothesis by implying that there exists no relation between two variables in statistics. It states that the effect of one variable on the other is solely due to chance and no empirical cause lies behind it.
The null hypothesis is established alongside the alternative hypothesis and is recognized as important as the latter. In hypothesis testing, the null hypothesis has a major role to play as it influences the testing against the alternative hypothesis.
(Must read: What is ANOVA test? )
The Non-directional hypothesis states that the relation between two variables has no direction.
Simply put, it asserts that there exists a relation between two variables, but does not recognize the direction of effect, whether variable A affects variable B or vice versa.
The Directional hypothesis, on the other hand, asserts the direction of effect of the relationship that exists between two variables.
Herein, the hypothesis clearly states that variable A affects variable B, or vice versa.
A statistical hypothesis is a hypothesis that can be verified to be plausible on the basis of statistics.
By using data sampling and statistical knowledge, one can determine the plausibility of a statistical hypothesis and find out if it stands true or not.
(Related blog: z-test vs t-test )
Now that we have understood the types of hypotheses and the role they play in hypothesis testing, let us now move on to understand the process in a better manner.
In hypothesis testing, a researcher is first required to establish two hypotheses - alternative hypothesis and null hypothesis in order to begin with the procedure.
To establish these two hypotheses, one is required to study data samples, find a plausible pattern among the samples, and pen down a statistical hypothesis that they wish to test.
A random population of samples can be drawn, to begin with hypothesis testing. Among the two hypotheses, alternative and null, only one can be verified to be true. Perhaps the presence of both hypotheses is required to make the process successful.
At the end of the hypothesis testing procedure, either of the hypotheses will be rejected and the other one will be supported. Even though one of the two hypotheses turns out to be true, no hypothesis can ever be verified 100%.
(Read also: Types of data sampling techniques )
Therefore, a hypothesis can only be supported based on the statistical samples and verified data. Here is a step-by-step guide for hypothesis testing.
First things first, one is required to establish two hypotheses - alternative and null, that will set the foundation for hypothesis testing.
These hypotheses initiate the testing process that involves the researcher working on data samples in order to either support the alternative hypothesis or the null hypothesis.
Once the hypotheses have been formulated, it is now time to generate a testing plan. A testing plan or an analysis plan involves the accumulation of data samples, determining which statistic is to be considered and laying out the sample size.
All these factors are very important while one is working on hypothesis testing.
As soon as a testing plan is ready, it is time to move on to the analysis part. Analysis of data samples involves configuring statistical values of samples, drawing them together, and deriving a pattern out of these samples.
While analyzing the data samples, a researcher needs to determine a set of things -
Significance Level - The level of significance in hypothesis testing indicates if a statistical result could have significance if the null hypothesis stands to be true.
Testing Method - The testing method involves a type of sampling-distribution and a test statistic that leads to hypothesis testing. There are a number of testing methods that can assist in the analysis of data samples.
Test statistic - Test statistic is a numerical summary of a data set that can be used to perform hypothesis testing.
P-value - The P-value interpretation is the probability of finding a sample statistic to be as extreme as the test statistic, indicating the plausibility of the null hypothesis.
The analysis of data samples leads to the inference of results that establishes whether the alternative hypothesis stands true or not. When the P-value is less than the significance level, the null hypothesis is rejected and the alternative hypothesis turns out to be plausible.
As we have already looked into different aspects of hypothesis testing, we shall now look into the different methods of hypothesis testing. All in all, there are 2 most common types of hypothesis testing methods. They are as follows -
The frequentist hypothesis or the traditional approach to hypothesis testing is a hypothesis testing method that aims on making assumptions by considering current data.
The supposed truths and assumptions are based on the current data and a set of 2 hypotheses are formulated. A very popular subtype of the frequentist approach is the Null Hypothesis Significance Testing (NHST).
The NHST approach (involving the null and alternative hypothesis) has been one of the most sought-after methods of hypothesis testing in the field of statistics ever since its inception in the mid-1950s.
A much unconventional and modern method of hypothesis testing, the Bayesian Hypothesis Testing claims to test a particular hypothesis in accordance with the past data samples, known as prior probability, and current data that lead to the plausibility of a hypothesis.
The result obtained indicates the posterior probability of the hypothesis. In this method, the researcher relies on ‘prior probability and posterior probability’ to conduct hypothesis testing on hand.
On the basis of this prior probability, the Bayesian approach tests a hypothesis to be true or false. The Bayes factor, a major component of this method, indicates the likelihood ratio among the null hypothesis and the alternative hypothesis.
The Bayes factor is the indicator of the plausibility of either of the two hypotheses that are established for hypothesis testing.
(Also read - Introduction to Bayesian Statistics )
To conclude, hypothesis testing, a way to verify the plausibility of a supposed assumption can be done through different methods - the Bayesian approach or the Frequentist approach.
Although the Bayesian approach relies on the prior probability of data samples, the frequentist approach assumes without a probability. A number of elements involved in hypothesis testing are - significance level, p-level, test statistic, and method of hypothesis testing.
(Also read: Introduction to probability distributions )
A significant way to determine whether a hypothesis stands true or not is to verify the data samples and identify the plausible hypothesis among the null hypothesis and alternative hypothesis.
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Hypothesis testing in statistics involves testing an assumption about a population parameter using sample data. Learners can download Hypothesis Testing PDF to get instant access to all information!
What exactly is hypothesis testing, and how does it work in statistics? Can I find practical examples and understand the different types from this blog?
Hypothesis Testing : Ever wonder how researchers determine if a new medicine actually works or if a new marketing campaign effectively drives sales? They use hypothesis testing! It is at the core of how scientific studies, business experiments and surveys determine if their results are statistically significant or just due to chance.
Hypothesis testing allows us to make evidence-based decisions by quantifying uncertainty and providing a structured process to make data-driven conclusions rather than guessing. In this post, we will discuss hypothesis testing types, examples, and processes!
Table of Contents
Hypothesis testing is a statistical method used to evaluate the validity of a hypothesis using sample data. It involves assessing whether observed data provide enough evidence to reject a specific hypothesis about a population parameter.
Hypothesis testing in data science is a statistical method used to evaluate two mutually exclusive population statements based on sample data. The primary goal is to determine which statement is more supported by the observed data.
Hypothesis testing assists in supporting the certainty of findings in research and data science projects. This statistical inference aids in making decisions about population parameters using sample data. For those who are looking to deepen their knowledge in data science and expand their skillset, we highly recommend checking out Master Generative AI: Data Science Course by Physics Wallah .
Also Read: What is Encapsulation Explain in Details
The hypothesis testing procedure in data science involves a structured approach to evaluating hypotheses using statistical methods. Here’s a step-by-step breakdown of the typical procedure:
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Hypothesis testing is a fundamental concept in statistics that aids analysts in making informed decisions based on sample data about a larger population. The process involves setting up two contrasting hypotheses, the null hypothesis and the alternative hypothesis, and then using statistical methods to determine which hypothesis provides a more plausible explanation for the observed data.
Once these hypotheses are established, analysts gather data from a sample and conduct statistical tests. The objective is to determine whether the observed results are statistically significant enough to reject the null hypothesis in favor of the alternative.
Hypothesis testing is a cornerstone in statistical analysis, providing a framework to evaluate the validity of assumptions or claims made about a population based on sample data. Within this framework, several specific tests are utilized based on the nature of the data and the question at hand. Here’s a closer look at the three fundamental types of hypothesis tests:
The z-test is a statistical method primarily employed when comparing means from two datasets, particularly when the population standard deviation is known. Its main objective is to ascertain if the means are statistically equivalent.
A crucial prerequisite for the z-test is that the sample size should be relatively large, typically 30 data points or more. This test aids researchers and analysts in determining the significance of a relationship or discovery, especially in scenarios where the data’s characteristics align with the assumptions of the z-test.
The t-test is a versatile statistical tool used extensively in research and various fields to compare means between two groups. It’s particularly valuable when the population standard deviation is unknown or when dealing with smaller sample sizes.
By evaluating the means of two groups, the t-test helps ascertain if a particular treatment, intervention, or variable significantly impacts the population under study. Its flexibility and robustness make it a go-to method in scenarios ranging from medical research to business analytics.
The Chi-Square test stands distinct from the previous tests, primarily focusing on categorical data rather than means. This statistical test is instrumental when analyzing categorical variables to determine if observed data aligns with expected outcomes as posited by the null hypothesis.
By assessing the differences between observed and expected frequencies within categorical data, the Chi-Square test offers insights into whether discrepancies are statistically significant. Whether used in social sciences to evaluate survey responses or in quality control to assess product defects, the Chi-Square test remains pivotal for hypothesis testing in diverse scenarios.
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Hypothesis testing is a fundamental concept in statistics used to make decisions or inferences about a population based on a sample of data. The process involves setting up two competing hypotheses, the null hypothesis H 0 and the alternative hypothesis H 1.
Through various statistical tests, such as the t-test, z-test, or Chi-square test, analysts evaluate sample data to determine whether there’s enough evidence to reject the null hypothesis in favor of the alternative. The aim is to draw conclusions about population parameters or to test theories, claims, or hypotheses.
In research, hypothesis testing serves as a structured approach to validate or refute theories or claims. Researchers formulate a clear hypothesis based on existing literature or preliminary observations. They then collect data through experiments, surveys, or observational studies.
Using statistical methods, researchers analyze this data to determine if there’s sufficient evidence to reject the null hypothesis. By doing so, they can draw meaningful conclusions, make predictions, or recommend actions based on empirical evidence rather than mere speculation.
R, a powerful programming language and environment for statistical computing and graphics, offers a wide array of functions and packages specifically designed for hypothesis testing. Here’s how hypothesis testing is conducted in R:
Hypothesis testing is an integral part of statistics and research, offering a systematic approach to validate hypotheses. Leveraging R’s capabilities, researchers and analysts can efficiently conduct and interpret various hypothesis tests, ensuring robust and reliable conclusions from their data.
Yes, data scientists frequently engage in hypothesis testing as part of their analytical toolkit. Hypothesis testing is a foundational statistical technique used to make data-driven decisions, validate assumptions, and draw conclusions from data. Here’s how data scientists utilize hypothesis testing:
Let’s delve into some common examples of hypothesis testing and provide solutions or interpretations for each scenario.
Scenario : A coffee shop owner believes that the average waiting time for customers during peak hours is 5 minutes. To test this, the owner takes a random sample of 30 customer waiting times and wants to determine if the average waiting time is indeed 5 minutes.
Hypotheses :
Solution : Using a t-test (assuming population variance is unknown), calculate the t-statistic based on the sample mean, sample standard deviation, and sample size. Then, determine the p-value and compare it with a significance level (e.g., 0.05) to decide whether to reject the null hypothesis.
Scenario : An e-commerce company wants to determine if changing the color of a “Buy Now” button from blue to green increases the conversion rate.
Solution : Split website visitors into two groups: one sees the blue button (control group), and the other sees the green button (test group). Track the conversion rates for both groups over a specified period. Then, use a chi-square test or z-test (for large sample sizes) to determine if there’s a statistically significant difference in conversion rates between the two groups.
The formula for hypothesis testing typically depends on the type of test (e.g., z-test, t-test, chi-square test) and the nature of the data (e.g., mean, proportion, variance). Below are the basic formulas for some common hypothesis tests:
Z-Test for Population Mean :
Z=(σ/n)(xˉ−μ0)
T-Test for Population Mean :
t= (s/ n ) ( x ˉ −μ 0 )
s = Sample standard deviation
Chi-Square Test for Goodness of Fit :
χ2=∑Ei(Oi−Ei)2
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While you can perform hypothesis testing manually using the above formulas and statistical tables, many online tools and software packages simplify this process. Here’s how you might use a calculator or software:
When using any calculator or software, always ensure you understand the underlying assumptions of the test, interpret the results correctly, and consider the broader context of your research or analysis.
What are the key components of a hypothesis test.
The key components include: Null Hypothesis (H0): A statement of no effect or no difference. Alternative Hypothesis (H1 or Ha): A statement that contradicts the null hypothesis. Test Statistic: A value computed from the sample data to test the null hypothesis. Significance Level (α): The threshold for rejecting the null hypothesis. P-value: The probability of observing the given data, assuming the null hypothesis is true.
The significance level (often denoted as α) is the probability threshold used to determine whether to reject the null hypothesis. Commonly used values for α include 0.05, 0.01, and 0.10, representing a 5%, 1%, or 10% chance of rejecting the null hypothesis when it's actually true.
The choice between one-tailed and two-tailed tests depends on your research question and hypothesis. Use a one-tailed test when you're specifically interested in one direction of an effect (e.g., greater than or less than). Use a two-tailed test when you want to determine if there's a significant difference in either direction.
The p-value is a probability value that helps determine the strength of evidence against the null hypothesis. A low p-value (typically ≤ 0.05) suggests that the observed data is inconsistent with the null hypothesis, leading to its rejection. Conversely, a high p-value suggests that the data is consistent with the null hypothesis, leading to no rejection.
No, hypothesis testing cannot prove a hypothesis true. Instead, it helps assess the likelihood of observing a given set of data under the assumption that the null hypothesis is true. Based on this assessment, you either reject or fail to reject the null hypothesis.
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The bottom line.
Hypothesis testing, sometimes called significance testing, is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis.
Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Such data may come from a larger population or a data-generating process. The word "population" will be used for both of these cases in the following descriptions.
In hypothesis testing, an analyst tests a statistical sample, intending to provide evidence on the plausibility of the null hypothesis. Statistical analysts measure and examine a random sample of the population being analyzed. All analysts use a random population sample to test two different hypotheses: the null hypothesis and the alternative hypothesis.
The null hypothesis is usually a hypothesis of equality between population parameters; e.g., a null hypothesis may state that the population mean return is equal to zero. The alternative hypothesis is effectively the opposite of a null hypothesis. Thus, they are mutually exclusive , and only one can be true. However, one of the two hypotheses will always be true.
The null hypothesis is a statement about a population parameter, such as the population mean, that is assumed to be true.
If an individual wants to test that a penny has exactly a 50% chance of landing on heads, the null hypothesis would be that 50% is correct, and the alternative hypothesis would be that 50% is not correct. Mathematically, the null hypothesis is represented as Ho: P = 0.5. The alternative hypothesis is shown as "Ha" and is identical to the null hypothesis, except with the equal sign struck-through, meaning that it does not equal 50%.
A random sample of 100 coin flips is taken, and the null hypothesis is tested. If it is found that the 100 coin flips were distributed as 40 heads and 60 tails, the analyst would assume that a penny does not have a 50% chance of landing on heads and would reject the null hypothesis and accept the alternative hypothesis.
If there were 48 heads and 52 tails, then it is plausible that the coin could be fair and still produce such a result. In cases such as this where the null hypothesis is "accepted," the analyst states that the difference between the expected results (50 heads and 50 tails) and the observed results (48 heads and 52 tails) is "explainable by chance alone."
Some statisticians attribute the first hypothesis tests to satirical writer John Arbuthnot in 1710, who studied male and female births in England after observing that in nearly every year, male births exceeded female births by a slight proportion. Arbuthnot calculated that the probability of this happening by chance was small, and therefore it was due to “divine providence.”
Hypothesis testing helps assess the accuracy of new ideas or theories by testing them against data. This allows researchers to determine whether the evidence supports their hypothesis, helping to avoid false claims and conclusions. Hypothesis testing also provides a framework for decision-making based on data rather than personal opinions or biases. By relying on statistical analysis, hypothesis testing helps to reduce the effects of chance and confounding variables, providing a robust framework for making informed conclusions.
Hypothesis testing relies exclusively on data and doesn’t provide a comprehensive understanding of the subject being studied. Additionally, the accuracy of the results depends on the quality of the available data and the statistical methods used. Inaccurate data or inappropriate hypothesis formulation may lead to incorrect conclusions or failed tests. Hypothesis testing can also lead to errors, such as analysts either accepting or rejecting a null hypothesis when they shouldn’t have. These errors may result in false conclusions or missed opportunities to identify significant patterns or relationships in the data.
Hypothesis testing refers to a statistical process that helps researchers determine the reliability of a study. By using a well-formulated hypothesis and set of statistical tests, individuals or businesses can make inferences about the population that they are studying and draw conclusions based on the data presented. All hypothesis testing methods have the same four-step process, which includes stating the hypotheses, formulating an analysis plan, analyzing the sample data, and analyzing the result.
Sage. " Introduction to Hypothesis Testing ," Page 4.
Elder Research. " Who Invented the Null Hypothesis? "
Formplus. " Hypothesis Testing: Definition, Uses, Limitations and Examples ."
Published by Alvin Nicolas at August 14th, 2021 , Revised On October 26, 2023
In statistics, hypothesis testing is a critical tool. It allows us to make informed decisions about populations based on sample data. Whether you are a researcher trying to prove a scientific point, a marketer analysing A/B test results, or a manufacturer ensuring quality control, hypothesis testing plays a pivotal role. This guide aims to introduce you to the concept and walk you through real-world examples.
A hypothesis is considered a belief or assumption that has to be accepted, rejected, proved or disproved. In contrast, a research hypothesis is a research question for a researcher that has to be proven correct or incorrect through investigation.
Hypothesis testing is a scientific method used for making a decision and drawing conclusions by using a statistical approach. It is used to suggest new ideas by testing theories to know whether or not the sample data supports research. A research hypothesis is a predictive statement that has to be tested using scientific methods that join an independent variable to a dependent variable.
Example: The academic performance of student A is better than student B
A hypothesis should be:
A null hypothesis is a hypothesis when there is no significant relationship between the dependent and the participants’ independent variables .
In simple words, it’s a hypothesis that has been put forth but hasn’t been proved as yet. A researcher aims to disprove the theory. The abbreviation “Ho” is used to denote a null hypothesis.
If you want to compare two methods and assume that both methods are equally good, this assumption is considered the null hypothesis.
Example: In an automobile trial, you feel that the new vehicle’s mileage is similar to the previous model of the car, on average. You can write it as: Ho: there is no difference between the mileage of both vehicles. If your findings don’t support your hypothesis and you get opposite results, this outcome will be considered an alternative hypothesis.
If you assume that one method is better than another method, then it’s considered an alternative hypothesis. The alternative hypothesis is the theory that a researcher seeks to prove and is typically denoted by H1 or HA.
If you support a null hypothesis, it means you’re not supporting the alternative hypothesis. Similarly, if you reject a null hypothesis, it means you are recommending the alternative hypothesis.
Example: In an automobile trial, you feel that the new vehicle’s mileage is better than the previous model of the vehicle. You can write it as; Ha: the two vehicles have different mileage. On average/ the fuel consumption of the new vehicle model is better than the previous model.
If a null hypothesis is rejected during the hypothesis test, even if it’s true, then it is considered as a type-I error. On the other hand, if you don’t dismiss a hypothesis, even if it’s false because you could not identify its falseness, it’s considered a type-II error.
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Here is a step-by-step guide on how to conduct hypothesis testing.
Once you develop a research hypothesis, it’s important to state it is as a Null hypothesis (Ho) and an Alternative hypothesis (Ha) to test it statistically.
A null hypothesis is a preferred choice as it provides the opportunity to test the theory. In contrast, you can accept the alternative hypothesis when the null hypothesis has been rejected.
Example: You want to identify a relationship between obesity of men and women and the modern living style. You develop a hypothesis that women, on average, gain weight quickly compared to men. Then you write it as: Ho: Women, on average, don’t gain weight quickly compared to men. Ha: Women, on average, gain weight quickly compared to men.
Hypothesis testing follows the statistical method, and statistics are all about data. It’s challenging to gather complete information about a specific population you want to study. You need to gather the data obtained through a large number of samples from a specific population.
Example: Suppose you want to test the difference in the rate of obesity between men and women. You should include an equal number of men and women in your sample. Then investigate various aspects such as their lifestyle, eating patterns and profession, and any other variables that may influence average weight. You should also determine your study’s scope, whether it applies to a specific group of population or worldwide population. You can use available information from various places, countries, and regions.
There are many types of statistical tests , but we discuss the most two common types below, such as One-sided and two-sided tests.
Note: Your choice of the type of test depends on the purpose of your study
In the one-sided test, the values of rejecting a null hypothesis are located in one tail of the probability distribution. The set of values is less or higher than the critical value of the test. It is also called a one-tailed test of significance.
Example: If you want to test that all mangoes in a basket are ripe. You can write it as: Ho: All mangoes in the basket, on average, are ripe. If you find all ripe mangoes in the basket, the null hypothesis you developed will be true.
In the two-sided test, the values of rejecting a null hypothesis are located on both tails of the probability distribution. The set of values is less or higher than the first critical value of the test and higher than the second critical value test. It is also called a two-tailed test of significance.
Example: Nothing can be explicitly said whether all mangoes are ripe in the basket. If you reject the null hypothesis (Ho: All mangoes in the basket, on average, are ripe), then it means all mangoes in the basket are not likely to be ripe. A few mangoes could be raw as well.
When you reject a null hypothesis, even if it’s true during a statistical hypothesis, it is considered the significance level . It is the probability of a type one error. The significance should be as minimum as possible to avoid the type-I error, which is considered severe and should be avoided.
If the significance level is minimum, then it prevents the researchers from false claims.
The significance level is denoted by P, and it has given the value of 0.05 (P=0.05)
If the P-Value is less than 0.05, then the difference will be significant. If the P-value is higher than 0.05, then the difference is non-significant.
Example: Suppose you apply a one-sided test to test whether women gain weight quickly compared to men. You get to know about the average weight between men and women and the factors promoting weight gain.
After conducting a statistical test, you should identify whether your null hypothesis is rejected or accepted based on the test results. It would help if you observed the P-value for this.
Example: If you find the P-value of your test is less than 0.5/5%, then you need to reject your null hypothesis (Ho: Women, on average, don’t gain weight quickly compared to men). On the other hand, if a null hypothesis is rejected, then it means the alternative hypothesis might be true (Ha: Women, on average, gain weight quickly compared to men. If you find your test’s P-value is above 0.5/5%, then it means your null hypothesis is true.
The final step is to present the outcomes of your study . You need to ensure whether you have met the objectives of your research or not.
In the discussion section and conclusion , you can present your findings by using supporting evidence and conclude whether your null hypothesis was rejected or supported.
In the result section, you can summarise your study’s outcomes, including the average difference and P-value of the two groups.
If we talk about the findings, our study your results will be as follows:
Example: In the study of identifying whether women gain weight quickly compared to men, we found the P-value is less than 0.5. Hence, we can reject the null hypothesis (Ho: Women, on average, don’t gain weight quickly than men) and conclude that women may likely gain weight quickly than men.
Did you know in your academic paper you should not mention whether you have accepted or rejected the null hypothesis?
Always remember that you either conclude to reject Ho in favor of Haor do not reject Ho . It would help if you never rejected Ha or even accept Ha .
Suppose your null hypothesis is rejected in the hypothesis testing. If you conclude reject Ho in favor of Haor do not reject Ho, then it doesn’t mean that the null hypothesis is true. It only means that there is a lack of evidence against Ho in favour of Ha. If your null hypothesis is not true, then the alternative hypothesis is likely to be true.
Example: We found that the P-value is less than 0.5. Hence, we can conclude reject Ho in favour of Ha (Ho: Women, on average, don’t gain weight quickly than men) reject Ho in favour of Ha. However, rejected in favour of Ha means (Ha: women may likely to gain weight quickly than men)
What are the 3 types of hypothesis test.
The 3 types of hypothesis tests are:
A hypothesis is a proposed explanation or prediction about a phenomenon, often based on observations. It serves as a starting point for research or experimentation, providing a testable statement that can either be supported or refuted through data and analysis. In essence, it’s an educated guess that drives scientific inquiry.
A null hypothesis (often denoted as H0) suggests that there is no effect or difference in a study or experiment. It represents a default position or status quo. Statistical tests evaluate data to determine if there’s enough evidence to reject this null hypothesis.
The probability value, or p-value, is a measure used in statistics to determine the significance of an observed effect. It indicates the probability of obtaining the observed results, or more extreme, if the null hypothesis were true. A small p-value (typically <0.05) suggests evidence against the null hypothesis, warranting its rejection.
The p-value is a fundamental concept in statistical hypothesis testing. It represents the probability of observing a test statistic as extreme, or more so, than the one calculated from sample data, assuming the null hypothesis is true. A low p-value suggests evidence against the null, possibly justifying its rejection.
A t-test is a statistical test used to compare the means of two groups. It determines if observed differences between the groups are statistically significant or if they likely occurred by chance. Commonly applied in research, there are different t-tests, including independent, paired, and one-sample, tailored to various data scenarios.
Reject the null hypothesis when the test statistic falls into a predefined rejection region or when the p-value is less than the chosen significance level (commonly 0.05). This suggests that the observed data is unlikely under the null hypothesis, indicating evidence for the alternative hypothesis. Always consider the study’s context.
A variable is a characteristic that can change and have more than one value, such as age, height, and weight. But what are the different types of variables?
Experimental research refers to the experiments conducted in the laboratory or under observation in controlled conditions. Here is all you need to know about experimental research.
Ethnography is a type of research where a researcher observes the people in their natural environment. Here is all you need to know about ethnography.
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Hypothesis testing is a tool for making statistical inferences about the population data. It is an analysis tool that tests assumptions and determines how likely something is within a given standard of accuracy. Hypothesis testing provides a way to verify whether the results of an experiment are valid.
A null hypothesis and an alternative hypothesis are set up before performing the hypothesis testing. This helps to arrive at a conclusion regarding the sample obtained from the population. In this article, we will learn more about hypothesis testing, its types, steps to perform the testing, and associated examples.
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Hypothesis testing uses sample data from the population to draw useful conclusions regarding the population probability distribution . It tests an assumption made about the data using different types of hypothesis testing methodologies. The hypothesis testing results in either rejecting or not rejecting the null hypothesis.
Hypothesis testing can be defined as a statistical tool that is used to identify if the results of an experiment are meaningful or not. It involves setting up a null hypothesis and an alternative hypothesis. These two hypotheses will always be mutually exclusive. This means that if the null hypothesis is true then the alternative hypothesis is false and vice versa. An example of hypothesis testing is setting up a test to check if a new medicine works on a disease in a more efficient manner.
The null hypothesis is a concise mathematical statement that is used to indicate that there is no difference between two possibilities. In other words, there is no difference between certain characteristics of data. This hypothesis assumes that the outcomes of an experiment are based on chance alone. It is denoted as \(H_{0}\). Hypothesis testing is used to conclude if the null hypothesis can be rejected or not. Suppose an experiment is conducted to check if girls are shorter than boys at the age of 5. The null hypothesis will say that they are the same height.
The alternative hypothesis is an alternative to the null hypothesis. It is used to show that the observations of an experiment are due to some real effect. It indicates that there is a statistical significance between two possible outcomes and can be denoted as \(H_{1}\) or \(H_{a}\). For the above-mentioned example, the alternative hypothesis would be that girls are shorter than boys at the age of 5.
In hypothesis testing, the p value is used to indicate whether the results obtained after conducting a test are statistically significant or not. It also indicates the probability of making an error in rejecting or not rejecting the null hypothesis.This value is always a number between 0 and 1. The p value is compared to an alpha level, \(\alpha\) or significance level. The alpha level can be defined as the acceptable risk of incorrectly rejecting the null hypothesis. The alpha level is usually chosen between 1% to 5%.
All sets of values that lead to rejecting the null hypothesis lie in the critical region. Furthermore, the value that separates the critical region from the non-critical region is known as the critical value.
Depending upon the type of data available and the size, different types of hypothesis testing are used to determine whether the null hypothesis can be rejected or not. The hypothesis testing formula for some important test statistics are given below:
We will learn more about these test statistics in the upcoming section.
Selecting the correct test for performing hypothesis testing can be confusing. These tests are used to determine a test statistic on the basis of which the null hypothesis can either be rejected or not rejected. Some of the important tests used for hypothesis testing are given below.
A z test is a way of hypothesis testing that is used for a large sample size (n ≥ 30). It is used to determine whether there is a difference between the population mean and the sample mean when the population standard deviation is known. It can also be used to compare the mean of two samples. It is used to compute the z test statistic. The formulas are given as follows:
The t test is another method of hypothesis testing that is used for a small sample size (n < 30). It is also used to compare the sample mean and population mean. However, the population standard deviation is not known. Instead, the sample standard deviation is known. The mean of two samples can also be compared using the t test.
The Chi square test is a hypothesis testing method that is used to check whether the variables in a population are independent or not. It is used when the test statistic is chi-squared distributed.
One tailed hypothesis testing is done when the rejection region is only in one direction. It can also be known as directional hypothesis testing because the effects can be tested in one direction only. This type of testing is further classified into the right tailed test and left tailed test.
Right Tailed Hypothesis Testing
The right tail test is also known as the upper tail test. This test is used to check whether the population parameter is greater than some value. The null and alternative hypotheses for this test are given as follows:
\(H_{0}\): The population parameter is ≤ some value
\(H_{1}\): The population parameter is > some value.
If the test statistic has a greater value than the critical value then the null hypothesis is rejected
Left Tailed Hypothesis Testing
The left tail test is also known as the lower tail test. It is used to check whether the population parameter is less than some value. The hypotheses for this hypothesis testing can be written as follows:
\(H_{0}\): The population parameter is ≥ some value
\(H_{1}\): The population parameter is < some value.
The null hypothesis is rejected if the test statistic has a value lesser than the critical value.
In this hypothesis testing method, the critical region lies on both sides of the sampling distribution. It is also known as a non - directional hypothesis testing method. The two-tailed test is used when it needs to be determined if the population parameter is assumed to be different than some value. The hypotheses can be set up as follows:
\(H_{0}\): the population parameter = some value
\(H_{1}\): the population parameter ≠ some value
The null hypothesis is rejected if the test statistic has a value that is not equal to the critical value.
Hypothesis testing can be easily performed in five simple steps. The most important step is to correctly set up the hypotheses and identify the right method for hypothesis testing. The basic steps to perform hypothesis testing are as follows:
The best way to solve a problem on hypothesis testing is by applying the 5 steps mentioned in the previous section. Suppose a researcher claims that the mean average weight of men is greater than 100kgs with a standard deviation of 15kgs. 30 men are chosen with an average weight of 112.5 Kgs. Using hypothesis testing, check if there is enough evidence to support the researcher's claim. The confidence interval is given as 95%.
Step 1: This is an example of a right-tailed test. Set up the null hypothesis as \(H_{0}\): \(\mu\) = 100.
Step 2: The alternative hypothesis is given by \(H_{1}\): \(\mu\) > 100.
Step 3: As this is a one-tailed test, \(\alpha\) = 100% - 95% = 5%. This can be used to determine the critical value.
1 - \(\alpha\) = 1 - 0.05 = 0.95
0.95 gives the required area under the curve. Now using a normal distribution table, the area 0.95 is at z = 1.645. A similar process can be followed for a t-test. The only additional requirement is to calculate the degrees of freedom given by n - 1.
Step 4: Calculate the z test statistic. This is because the sample size is 30. Furthermore, the sample and population means are known along with the standard deviation.
z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\).
\(\mu\) = 100, \(\overline{x}\) = 112.5, n = 30, \(\sigma\) = 15
z = \(\frac{112.5-100}{\frac{15}{\sqrt{30}}}\) = 4.56
Step 5: Conclusion. As 4.56 > 1.645 thus, the null hypothesis can be rejected.
Confidence intervals form an important part of hypothesis testing. This is because the alpha level can be determined from a given confidence interval. Suppose a confidence interval is given as 95%. Subtract the confidence interval from 100%. This gives 100 - 95 = 5% or 0.05. This is the alpha value of a one-tailed hypothesis testing. To obtain the alpha value for a two-tailed hypothesis testing, divide this value by 2. This gives 0.05 / 2 = 0.025.
Related Articles:
Important Notes on Hypothesis Testing
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What is hypothesis testing.
Hypothesis testing in statistics is a tool that is used to make inferences about the population data. It is also used to check if the results of an experiment are valid.
The z test in hypothesis testing is used to find the z test statistic for normally distributed data . The z test is used when the standard deviation of the population is known and the sample size is greater than or equal to 30.
The t test in hypothesis testing is used when the data follows a student t distribution . It is used when the sample size is less than 30 and standard deviation of the population is not known.
The formula for a one sample z test in hypothesis testing is z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\) and for two samples is z = \(\frac{(\overline{x_{1}}-\overline{x_{2}})-(\mu_{1}-\mu_{2})}{\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}}}\).
The p value helps to determine if the test results are statistically significant or not. In hypothesis testing, the null hypothesis can either be rejected or not rejected based on the comparison between the p value and the alpha level.
When the rejection region is only on one side of the distribution curve then it is known as one tail hypothesis testing. The right tail test and the left tail test are two types of directional hypothesis testing.
To get the alpha level in a two tail hypothesis testing divide \(\alpha\) by 2. This is done as there are two rejection regions in the curve.
Medical terms in lay language.
Please use these descriptions in place of medical jargon in consent documents, recruitment materials and other study documents. Note: These terms are not the only acceptable plain language alternatives for these vocabulary words.
This glossary of terms is derived from a list copyrighted by the University of Kentucky, Office of Research Integrity (1990).
For clinical research-specific definitions, see also the Clinical Research Glossary developed by the Multi-Regional Clinical Trials (MRCT) Center of Brigham and Women’s Hospital and Harvard and the Clinical Data Interchange Standards Consortium (CDISC) .
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
ABDOMEN/ABDOMINAL body cavity below diaphragm that contains stomach, intestines, liver and other organs ABSORB take up fluids, take in ACIDOSIS condition when blood contains more acid than normal ACUITY clearness, keenness, esp. of vision and airways ACUTE new, recent, sudden, urgent ADENOPATHY swollen lymph nodes (glands) ADJUVANT helpful, assisting, aiding, supportive ADJUVANT TREATMENT added treatment (usually to a standard treatment) ANTIBIOTIC drug that kills bacteria and other germs ANTIMICROBIAL drug that kills bacteria and other germs ANTIRETROVIRAL drug that works against the growth of certain viruses ADVERSE EFFECT side effect, bad reaction, unwanted response ALLERGIC REACTION rash, hives, swelling, trouble breathing AMBULATE/AMBULATION/AMBULATORY walk, able to walk ANAPHYLAXIS serious, potentially life-threatening allergic reaction ANEMIA decreased red blood cells; low red cell blood count ANESTHETIC a drug or agent used to decrease the feeling of pain, or eliminate the feeling of pain by putting you to sleep ANGINA pain resulting from not enough blood flowing to the heart ANGINA PECTORIS pain resulting from not enough blood flowing to the heart ANOREXIA disorder in which person will not eat; lack of appetite ANTECUBITAL related to the inner side of the forearm ANTIBODY protein made in the body in response to foreign substance ANTICONVULSANT drug used to prevent seizures ANTILIPEMIC a drug that lowers fat levels in the blood ANTITUSSIVE a drug used to relieve coughing ARRHYTHMIA abnormal heartbeat; any change from the normal heartbeat ASPIRATION fluid entering the lungs, such as after vomiting ASSAY lab test ASSESS to learn about, measure, evaluate, look at ASTHMA lung disease associated with tightening of air passages, making breathing difficult ASYMPTOMATIC without symptoms AXILLA armpit
BENIGN not malignant, without serious consequences BID twice a day BINDING/BOUND carried by, to make stick together, transported BIOAVAILABILITY the extent to which a drug or other substance becomes available to the body BLOOD PROFILE series of blood tests BOLUS a large amount given all at once BONE MASS the amount of calcium and other minerals in a given amount of bone BRADYARRHYTHMIAS slow, irregular heartbeats BRADYCARDIA slow heartbeat BRONCHOSPASM breathing distress caused by narrowing of the airways
CARCINOGENIC cancer-causing CARCINOMA type of cancer CARDIAC related to the heart CARDIOVERSION return to normal heartbeat by electric shock CATHETER a tube for withdrawing or giving fluids CATHETER a tube placed near the spinal cord and used for anesthesia (indwelling epidural) during surgery CENTRAL NERVOUS SYSTEM (CNS) brain and spinal cord CEREBRAL TRAUMA damage to the brain CESSATION stopping CHD coronary heart disease CHEMOTHERAPY treatment of disease, usually cancer, by chemical agents CHRONIC continuing for a long time, ongoing CLINICAL pertaining to medical care CLINICAL TRIAL an experiment involving human subjects COMA unconscious state COMPLETE RESPONSE total disappearance of disease CONGENITAL present before birth CONJUNCTIVITIS redness and irritation of the thin membrane that covers the eye CONSOLIDATION PHASE treatment phase intended to make a remission permanent (follows induction phase) CONTROLLED TRIAL research study in which the experimental treatment or procedure is compared to a standard (control) treatment or procedure COOPERATIVE GROUP association of multiple institutions to perform clinical trials CORONARY related to the blood vessels that supply the heart, or to the heart itself CT SCAN (CAT) computerized series of x-rays (computerized tomography) CULTURE test for infection, or for organisms that could cause infection CUMULATIVE added together from the beginning CUTANEOUS relating to the skin CVA stroke (cerebrovascular accident)
DERMATOLOGIC pertaining to the skin DIASTOLIC lower number in a blood pressure reading DISTAL toward the end, away from the center of the body DIURETIC "water pill" or drug that causes increase in urination DOPPLER device using sound waves to diagnose or test DOUBLE BLIND study in which neither investigators nor subjects know what drug or treatment the subject is receiving DYSFUNCTION state of improper function DYSPLASIA abnormal cells
ECHOCARDIOGRAM sound wave test of the heart EDEMA excess fluid collecting in tissue EEG electric brain wave tracing (electroencephalogram) EFFICACY effectiveness ELECTROCARDIOGRAM electrical tracing of the heartbeat (ECG or EKG) ELECTROLYTE IMBALANCE an imbalance of minerals in the blood EMESIS vomiting EMPIRIC based on experience ENDOSCOPIC EXAMINATION viewing an internal part of the body with a lighted tube ENTERAL by way of the intestines EPIDURAL outside the spinal cord ERADICATE get rid of (such as disease) Page 2 of 7 EVALUATED, ASSESSED examined for a medical condition EXPEDITED REVIEW rapid review of a protocol by the IRB Chair without full committee approval, permitted with certain low-risk research studies EXTERNAL outside the body EXTRAVASATE to leak outside of a planned area, such as out of a blood vessel
FDA U.S. Food and Drug Administration, the branch of federal government that approves new drugs FIBROUS having many fibers, such as scar tissue FIBRILLATION irregular beat of the heart or other muscle
GENERAL ANESTHESIA pain prevention by giving drugs to cause loss of consciousness, as during surgery GESTATIONAL pertaining to pregnancy
HEMATOCRIT amount of red blood cells in the blood HEMATOMA a bruise, a black and blue mark HEMODYNAMIC MEASURING blood flow HEMOLYSIS breakdown in red blood cells HEPARIN LOCK needle placed in the arm with blood thinner to keep the blood from clotting HEPATOMA cancer or tumor of the liver HERITABLE DISEASE can be transmitted to one’s offspring, resulting in damage to future children HISTOPATHOLOGIC pertaining to the disease status of body tissues or cells HOLTER MONITOR a portable machine for recording heart beats HYPERCALCEMIA high blood calcium level HYPERKALEMIA high blood potassium level HYPERNATREMIA high blood sodium level HYPERTENSION high blood pressure HYPOCALCEMIA low blood calcium level HYPOKALEMIA low blood potassium level HYPONATREMIA low blood sodium level HYPOTENSION low blood pressure HYPOXEMIA a decrease of oxygen in the blood HYPOXIA a decrease of oxygen reaching body tissues HYSTERECTOMY surgical removal of the uterus, ovaries (female sex glands), or both uterus and ovaries
IATROGENIC caused by a physician or by treatment IDE investigational device exemption, the license to test an unapproved new medical device IDIOPATHIC of unknown cause IMMUNITY defense against, protection from IMMUNOGLOBIN a protein that makes antibodies IMMUNOSUPPRESSIVE drug which works against the body's immune (protective) response, often used in transplantation and diseases caused by immune system malfunction IMMUNOTHERAPY giving of drugs to help the body's immune (protective) system; usually used to destroy cancer cells IMPAIRED FUNCTION abnormal function IMPLANTED placed in the body IND investigational new drug, the license to test an unapproved new drug INDUCTION PHASE beginning phase or stage of a treatment INDURATION hardening INDWELLING remaining in a given location, such as a catheter INFARCT death of tissue due to lack of blood supply INFECTIOUS DISEASE transmitted from one person to the next INFLAMMATION swelling that is generally painful, red, and warm INFUSION slow injection of a substance into the body, usually into the blood by means of a catheter INGESTION eating; taking by mouth INTERFERON drug which acts against viruses; antiviral agent INTERMITTENT occurring (regularly or irregularly) between two time points; repeatedly stopping, then starting again INTERNAL within the body INTERIOR inside of the body INTRAMUSCULAR into the muscle; within the muscle INTRAPERITONEAL into the abdominal cavity INTRATHECAL into the spinal fluid INTRAVENOUS (IV) through the vein INTRAVESICAL in the bladder INTUBATE the placement of a tube into the airway INVASIVE PROCEDURE puncturing, opening, or cutting the skin INVESTIGATIONAL NEW DRUG (IND) a new drug that has not been approved by the FDA INVESTIGATIONAL METHOD a treatment method which has not been proven to be beneficial or has not been accepted as standard care ISCHEMIA decreased oxygen in a tissue (usually because of decreased blood flow)
LAPAROTOMY surgical procedure in which an incision is made in the abdominal wall to enable a doctor to look at the organs inside LESION wound or injury; a diseased patch of skin LETHARGY sleepiness, tiredness LEUKOPENIA low white blood cell count LIPID fat LIPID CONTENT fat content in the blood LIPID PROFILE (PANEL) fat and cholesterol levels in the blood LOCAL ANESTHESIA creation of insensitivity to pain in a small, local area of the body, usually by injection of numbing drugs LOCALIZED restricted to one area, limited to one area LUMEN the cavity of an organ or tube (e.g., blood vessel) LYMPHANGIOGRAPHY an x-ray of the lymph nodes or tissues after injecting dye into lymph vessels (e.g., in feet) LYMPHOCYTE a type of white blood cell important in immunity (protection) against infection LYMPHOMA a cancer of the lymph nodes (or tissues)
MALAISE a vague feeling of bodily discomfort, feeling badly MALFUNCTION condition in which something is not functioning properly MALIGNANCY cancer or other progressively enlarging and spreading tumor, usually fatal if not successfully treated MEDULLABLASTOMA a type of brain tumor MEGALOBLASTOSIS change in red blood cells METABOLIZE process of breaking down substances in the cells to obtain energy METASTASIS spread of cancer cells from one part of the body to another METRONIDAZOLE drug used to treat infections caused by parasites (invading organisms that take up living in the body) or other causes of anaerobic infection (not requiring oxygen to survive) MI myocardial infarction, heart attack MINIMAL slight MINIMIZE reduce as much as possible Page 4 of 7 MONITOR check on; keep track of; watch carefully MOBILITY ease of movement MORBIDITY undesired result or complication MORTALITY death MOTILITY the ability to move MRI magnetic resonance imaging, diagnostic pictures of the inside of the body, created using magnetic rather than x-ray energy MUCOSA, MUCOUS MEMBRANE moist lining of digestive, respiratory, reproductive, and urinary tracts MYALGIA muscle aches MYOCARDIAL pertaining to the heart muscle MYOCARDIAL INFARCTION heart attack
NASOGASTRIC TUBE placed in the nose, reaching to the stomach NCI the National Cancer Institute NECROSIS death of tissue NEOPLASIA/NEOPLASM tumor, may be benign or malignant NEUROBLASTOMA a cancer of nerve tissue NEUROLOGICAL pertaining to the nervous system NEUTROPENIA decrease in the main part of the white blood cells NIH the National Institutes of Health NONINVASIVE not breaking, cutting, or entering the skin NOSOCOMIAL acquired in the hospital
OCCLUSION closing; blockage; obstruction ONCOLOGY the study of tumors or cancer OPHTHALMIC pertaining to the eye OPTIMAL best, most favorable or desirable ORAL ADMINISTRATION by mouth ORTHOPEDIC pertaining to the bones OSTEOPETROSIS rare bone disorder characterized by dense bone OSTEOPOROSIS softening of the bones OVARIES female sex glands
PARENTERAL given by injection PATENCY condition of being open PATHOGENESIS development of a disease or unhealthy condition PERCUTANEOUS through the skin PERIPHERAL not central PER OS (PO) by mouth PHARMACOKINETICS the study of the way the body absorbs, distributes, and gets rid of a drug PHASE I first phase of study of a new drug in humans to determine action, safety, and proper dosing PHASE II second phase of study of a new drug in humans, intended to gather information about safety and effectiveness of the drug for certain uses PHASE III large-scale studies to confirm and expand information on safety and effectiveness of new drug for certain uses, and to study common side effects PHASE IV studies done after the drug is approved by the FDA, especially to compare it to standard care or to try it for new uses PHLEBITIS irritation or inflammation of the vein PLACEBO an inactive substance; a pill/liquid that contains no medicine PLACEBO EFFECT improvement seen with giving subjects a placebo, though it contains no active drug/treatment PLATELETS small particles in the blood that help with clotting POTENTIAL possible POTENTIATE increase or multiply the effect of a drug or toxin (poison) by giving another drug or toxin at the same time (sometimes an unintentional result) POTENTIATOR an agent that helps another agent work better PRENATAL before birth PROPHYLAXIS a drug given to prevent disease or infection PER OS (PO) by mouth PRN as needed PROGNOSIS outlook, probable outcomes PRONE lying on the stomach PROSPECTIVE STUDY following patients forward in time PROSTHESIS artificial part, most often limbs, such as arms or legs PROTOCOL plan of study PROXIMAL closer to the center of the body, away from the end PULMONARY pertaining to the lungs
QD every day; daily QID four times a day
RADIATION THERAPY x-ray or cobalt treatment RANDOM by chance (like the flip of a coin) RANDOMIZATION chance selection RBC red blood cell RECOMBINANT formation of new combinations of genes RECONSTITUTION putting back together the original parts or elements RECUR happen again REFRACTORY not responding to treatment REGENERATION re-growth of a structure or of lost tissue REGIMEN pattern of giving treatment RELAPSE the return of a disease REMISSION disappearance of evidence of cancer or other disease RENAL pertaining to the kidneys REPLICABLE possible to duplicate RESECT remove or cut out surgically RETROSPECTIVE STUDY looking back over past experience
SARCOMA a type of cancer SEDATIVE a drug to calm or make less anxious SEMINOMA a type of testicular cancer (found in the male sex glands) SEQUENTIALLY in a row, in order SOMNOLENCE sleepiness SPIROMETER an instrument to measure the amount of air taken into and exhaled from the lungs STAGING an evaluation of the extent of the disease STANDARD OF CARE a treatment plan that the majority of the medical community would accept as appropriate STENOSIS narrowing of a duct, tube, or one of the blood vessels in the heart STOMATITIS mouth sores, inflammation of the mouth STRATIFY arrange in groups for analysis of results (e.g., stratify by age, sex, etc.) STUPOR stunned state in which it is difficult to get a response or the attention of the subject SUBCLAVIAN under the collarbone SUBCUTANEOUS under the skin SUPINE lying on the back SUPPORTIVE CARE general medical care aimed at symptoms, not intended to improve or cure underlying disease SYMPTOMATIC having symptoms SYNDROME a condition characterized by a set of symptoms SYSTOLIC top number in blood pressure; pressure during active contraction of the heart
TERATOGENIC capable of causing malformations in a fetus (developing baby still inside the mother’s body) TESTES/TESTICLES male sex glands THROMBOSIS clotting THROMBUS blood clot TID three times a day TITRATION a method for deciding on the strength of a drug or solution; gradually increasing the dose T-LYMPHOCYTES type of white blood cells TOPICAL on the surface TOPICAL ANESTHETIC applied to a certain area of the skin and reducing pain only in the area to which applied TOXICITY side effects or undesirable effects of a drug or treatment TRANSDERMAL through the skin TRANSIENTLY temporarily TRAUMA injury; wound TREADMILL walking machine used to test heart function
UPTAKE absorbing and taking in of a substance by living tissue
VALVULOPLASTY plastic repair of a valve, especially a heart valve VARICES enlarged veins VASOSPASM narrowing of the blood vessels VECTOR a carrier that can transmit disease-causing microorganisms (germs and viruses) VENIPUNCTURE needle stick, blood draw, entering the skin with a needle VERTICAL TRANSMISSION spread of disease
WBC white blood cell
Experts on the subject note that there is no drug that will temporarily mask cognitive decline.
Allies of Donald Trump have painted themselves into a cognitive corner. President Biden is unfit for office, they argue, because he is so old, and his mental abilities have deteriorated markedly. But then Biden will, say, deliver a State of the Union address in which he is energetic and pointed for more than an hour.
So they modify their claim: Biden is addled and wandering, except when he is given some sort of medication, perhaps a stimulant, that reverses that effect. And here we are, with Trump and those seeking his reelection to the White House demanding that Biden submit to some sort of drug test before this week’s first presidential debate, purportedly in effort to sniff out this theoretical drug.
Experts who spoke with The Washington Post, though, confirm that no such medicine exists.
At the outset, we should recognize that this claim is generally not offered seriously. It is, instead, an effort to escape the aforementioned contradiction, a way to hold both that Biden is incapable of serving as president and yet, unquestionably at times, not demonstrating any such impairment. What’s more, the demand that Biden undergo a drug test is itself not serious. It is, instead, meant to create a condition that allows Trump and his allies to continue to claim that any strong performance from Biden is a function of medication. The result is win-win for Trump, who can blame any loss on this wonder drug.
If you haven’t been paying close attention to the debate (such as it is) over this idea, consider a snippet of conversation that aired on Fox Business on Tuesday morning.
Host Maria Bartiromo — no stranger to conspiratorial argumentation — hosted Rep. Eric Burlison (R-Mo.) where she offered an observation made by Rep. Ronny Jackson (R-Tex.).
“Jackson says Biden will have been at Camp David for a full week before the debate,” Bartiromo said , “and that they’re probably experimenting with getting doses right. Giving him medicine ahead of the debate.”
Burlison agreed that this was possible, though he offered that it might be more innocuous than medication. Perhaps, he said, Biden’s team is “jack[ing] him up on Mountain Dew.”
Jackson, you will recall, was Trump’s personal doctor while Trump was in the White House. He is not an expert on cognition or cognition-related illnesses, though he is familiar with drug prescription .
“Nothing like that exists,” Thomas Wisniewski, director of the NYU Langone Alzheimer’s Disease Research Center, told The Washington Post by phone. “There are no medications or stimulants that can reverse a dementing process transiently.”
“All of those sorts of things can perhaps make an individual more alert, but quite often that can just exacerbate their confusion, as well,” he added. “They can be more stimulated, but they are not going to be behaving in a more cogent or normal fashion as a result of being stimulated by anything. Very often it’s the reverse.”
Adam Brickman, professor of neuropsychology at Columbia University Irving Medical Center, concurred with that assessment.
“I’m not aware of any medications that would reverse or mask cognitive decline,” Brickman said. What’s more, he noted that “the association between energy and cognition is a very weak one. In other words, someone could have low energy but totally intact cognition and vice versa.”
Both doctors noted that such a medication would be of enormous benefit. Reversing cognitive decline, after all, would mean turning back the damage done from diseases that impair cognition in the first place. It would be akin not just to treating the pain of a broken bone but, instead, to directly healing the break itself. Sadly, no such drug for cognition exists.
Again, the argument that Biden is or could be receiving targeted treatment to improve his mental state fails multiple logical tests. Why, for example, would he not simply take this medication all the time? Why would he need to retest his dosage for a debate after giving a lengthy State of the Union address? The answer is that there is no good answer, that the intent of the allegations is simply to maintain the political argument that Biden is mentally deficient even in the face of his performing above expectations in a debate.
Not that that argument is itself well-grounded, as Brickman noted.
“It’s not possible to conclude or to determine whether someone has subtle cognitive change without doing a true clinical evaluation,” he said. “So to judge whether there’s an underlying disease or neurodegenerative condition based on public speeches or interactions that are captured by the press is irresponsible.”
Wisniewski offered a more succinct dismissal of the claims being made by Trumpworld.
“It’s spurious,” he said. “It’s nonsensical.”
In other words, if Biden fares better in the debate this week, it’s not because of a secret Camp David drug-dosing regimen that enabled the administration to mask Biden’s physical degeneration. It’s because Biden out-debated the guy who won’t accept that that’s possible.
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President Biden has repeatedly and rightfully described the stakes in this November’s presidential election as nothing less than the future of American democracy.
Donald Trump has proved himself to be a significant jeopardy to that democracy — an erratic and self-interested figure unworthy of the public trust. He systematically attempted to undermine the integrity of elections. His supporters have described, publicly, a 2025 agenda that would give him the power to carry out the most extreme of his promises and threats. If he is returned to office, he has vowed to be a different kind of president, unrestrained by the checks on power built into the American political system.
Mr. Biden has said that he is the candidate with the best chance of taking on this threat of tyranny and defeating it. His argument rests largely on the fact that he beat Mr. Trump in 2020. That is no longer a sufficient rationale for why Mr. Biden should be the Democratic nominee this year.
At Thursday’s debate, the president needed to convince the American public that he was equal to the formidable demands of the office he is seeking to hold for another term. Voters, however, cannot be expected to ignore what was instead plain to see: Mr. Biden is not the man he was four years ago.
The president appeared on Thursday night as the shadow of a great public servant. He struggled to explain what he would accomplish in a second term. He struggled to respond to Mr. Trump’s provocations. He struggled to hold Mr. Trump accountable for his lies, his failures and his chilling plans. More than once, he struggled to make it to the end of a sentence.
Mr. Biden has been an admirable president. Under his leadership, the nation has prospered and begun to address a range of long-term challenges, and the wounds ripped open by Mr. Trump have begun to heal. But the greatest public service Mr. Biden can now perform is to announce that he will not continue to run for re-election.
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Present the findings in your results and discussion section. Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps. Table of contents. Step 1: State your null and alternate hypothesis. Step 2: Collect data. Step 3: Perform a statistical test.
ANOVA and MANOVA tests are used when comparing the means of more than two groups (e.g., the average heights of children, teenagers, and adults). Predictor variable. Outcome variable. Research question example. Paired t-test. Categorical. 1 predictor. Quantitative. groups come from the same population.
Hypothesis testing is a crucial procedure to perform when you want to make inferences about a population using a random sample. These inferences include estimating population properties such as the mean, differences between means, proportions, and the relationships between variables. This post provides an overview of statistical hypothesis testing.
The treatment group's mean is 58.70, compared to the control group's mean of 48.12. The mean difference is 10.67 points. Use the test's p-value and significance level to determine whether this difference is likely a product of random fluctuation in the sample or a genuine population effect.. Because the p-value (0.000) is less than the standard significance level of 0.05, the results are ...
A hypothesis test consists of five steps: 1. State the hypotheses. State the null and alternative hypotheses. These two hypotheses need to be mutually exclusive, so if one is true then the other must be false. 2. Determine a significance level to use for the hypothesis. Decide on a significance level.
Test Statistic: z = ¯ x − μo σ / √n since it is calculated as part of the testing of the hypothesis. Definition 7.1.4. p - value: probability that the test statistic will take on more extreme values than the observed test statistic, given that the null hypothesis is true.
Hypothesis testing is a method of statistical inference that considers the null hypothesis H ₀ vs. the alternative hypothesis H a, where we are typically looking to assess evidence against H ₀. Such a test is used to compare data sets against one another, or compare a data set against some external standard. The former being a two sample ...
In a hypothesis test, sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis, typically denoted with \(H_{0}\). The null is not rejected unless the hypothesis ...
What is Hypothesis Testing? In simple terms, hypothesis testing is a method used to make decisions or inferences about population parameters based on sample data. Imagine being handed a dice and asked if it's biased. By rolling it a few times and analyzing the outcomes, you'd be engaging in the essence of hypothesis testing. Think of ...
Using the p-value to make the decision. The p-value represents how likely we would be to observe such an extreme sample if the null hypothesis were true. The p-value is a probability computed assuming the null hypothesis is true, that the test statistic would take a value as extreme or more extreme than that actually observed. Since it's a probability, it is a number between 0 and 1.
Step 7: Based on Steps 5 and 6, draw a conclusion about H 0. If F calculated is larger than F α, then you are in the rejection region and you can reject the null hypothesis with ( 1 − α) level of confidence. Note that modern statistical software condenses Steps 6 and 7 by providing a p -value. The p -value here is the probability of getting ...
A hypothesis test is a statistical inference method used to test the significance of a proposed (hypothesized) relation between population statistics (parameters) and their corresponding sample estimators. In other words, hypothesis tests are used to determine if there is enough evidence in a sample to prove a hypothesis true for the entire population. The test considers two hypotheses: the ...
Hypothesis Testing is a type of statistical analysis in which you put your assumptions about a population parameter to the test. It is used to estimate the relationship between 2 statistical variables. Let's discuss few examples of statistical hypothesis from real-life -. A teacher assumes that 60% of his college's students come from lower ...
6. Test Statistic: The test statistic measures how close the sample has come to the null hypothesis. Its observed value changes randomly from one random sample to a different sample. A test statistic contains information about the data that is relevant for deciding whether to reject the null hypothesis or not.
This is where hypothesis tests are useful. A hypothesis test allows us quantify the probability that our sample mean is unusual. For this series of posts, I'll continue to use this graphical framework and add in the significance level, P value, and confidence interval to show how hypothesis tests work and what statistical significance really ...
Below these are summarized into six such steps to conducting a test of a hypothesis. Set up the hypotheses and check conditions: Each hypothesis test includes two hypotheses about the population. One is the null hypothesis, notated as H 0, which is a statement of a particular parameter value. This hypothesis is assumed to be true until there is ...
In hypothesis testing, a researcher is first required to establish two hypotheses - alternative hypothesis and null hypothesis in order to begin with the procedure. To establish these two hypotheses, one is required to study data samples, find a plausible pattern among the samples, and pen down a statistical hypothesis that they wish to test.
A statistical hypothesis test is a method of statistical inference used to decide whether the data sufficiently support a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic. Then a decision is made, either by comparing the test statistic to a critical value or equivalently by evaluating a p ...
Here's a closer look at the three fundamental types of hypothesis tests: 1. Z-Test: The z-test is a statistical method primarily employed when comparing means from two datasets, particularly when the population standard deviation is known. Its main objective is to ascertain if the means are statistically equivalent.
Hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used ...
Hypothesis testing is a scientific method used for making a decision and drawing conclusions by using a statistical approach. It is used to suggest new ideas by testing theories to know whether or not the sample data supports research. A research hypothesis is a predictive statement that has to be tested using scientific methods that join an ...
Depending upon the type of data available and the size, different types of hypothesis testing are used to determine whether the null hypothesis can be rejected or not. The hypothesis testing formula for some important test statistics are given below: ... 0.95 gives the required area under the curve. Now using a normal distribution table, the ...
Probability value and types of errors. The probability value, or p value, is the probability of an outcome or research result given the hypothesis.Usually, the probability value is set at 0.05: the null hypothesis will be rejected if the probability value of the statistical test is less than 0.05.
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Both doctors noted that such a medication would be of enormous benefit. Reversing cognitive decline, after all, would mean turning back the damage done from diseases that impair cognition in the ...
The truth Mr. Biden needs to confront now is that he failed his own test. In polls and interviews, voters say they are seeking fresh voices to take on Mr. Trump.