Paired t test

What is Paired t test?

The paired t test is a statistical test used to compare the means of two related or paired samples. It is used when you have two sets of measurements on the same subject or unit, such as before-and-after measurements, matched-pair samples, or repeated measures.

The paired t-test determines whether there is a significant difference between the means of the two samples by comparing the difference between each pair of observations with the expected difference under the null hypothesis (i.e., no difference between the two means).

The test assumes that the differences between the pairs are normally distributed and that the variances of the two samples are equal. If these assumptions are met, the paired t-test is a powerful and robust statistical test for comparing the means of two related samples.

When to use Paired t test?

A paired t test is a statistical test used to compare the means of two related groups or samples. It is used when the two samples being compared are related or paired, such as in a before-and-after study, where the same individuals are measured twice, or in a matched-pairs study, where individuals are matched on important characteristics and then assigned to different treatments.

Here are some specific situations where a paired t-test might be appropriate:

  • Before-and-after studies: When you want to test if an intervention or treatment has had a significant effect on an individual or group, a paired t-test can be used to compare the mean scores of the same group before and after the intervention.
  • Matched-pairs studies: In studies where individuals are paired based on similar characteristics, such as age, sex, or health status, and then assigned to different treatments, a paired t-test can be used to compare the means of the two groups.
  • Repeated-measures studies: When a study involves measuring the same variable multiple times on the same individual or group, a paired t-test can be used to compare the means of the measurements at different time points.

Overall, a paired t-test is useful when you want to compare two related groups or samples and control for individual differences between the groups.

Guidelines for correct usage of Paired t test

  • Collect continuous data with an infinite number of values between any two values.
  • Avoid severely skewed data and ensure sample sizes are greater than 20.
  • Use paired observations for the same item under different conditions, or use 2-Sample t for independent observations.
  • Collect data randomly to make generalizations about the population.
  • Determine an appropriate sample size that provides enough precision and protection against errors.

Alternatives: When not to use Paired t test

  • In case you have two sets of independent observations, it is recommended to use the 2-Sample t-test instead.

Example of Paired t test?

In order to investigate the impact of a specific running program on resting heart rate, a physiologist selects a group of 15 individuals and measures their heart rates. After one year, the same individuals undergo the running program again and their heart rates are measured once more. As a result, the physiologist has a pair of observations (before and after) for each individual. A paired t-test is then carried out to assess whether there is a statistically significant difference in heart rates before and after the running program. She has performed the test in following steps:

  1. She worked all day and gathered the necessary data.

  1. Now, she analyzes the data with the help of https://qtools.zometric.com/
  2. Inside the tool, she feeds the data. Also, she puts 95 as the confidence level and hypothesized difference as 0.
  3. After using the above mentioned tool, she fetches the output as follows:

How to do Paired t test

The guide is as follows:

  1. Login in to QTools account with the help of https://qtools.zometric.com/
  2. On the home page, you can see Paired t test under Hypothesis Tests.
  3. Click on Paired t test and reach the dashboard.
  4. Next, update the data manually or can completely copy (Ctrl+C) the data from excel sheet and paste (Ctrl+V) it here.
  5. Next, you need to put the values of confidence level, and hypothesized difference.
  6. Finally, click on calculate at the bottom of the page and you will get desired results.

On the dashboard of Paired t test, the window is separated into two parts.

On the left part, Data Pane is present. In the Data Pane, each row makes one subgroup. Data can be fed manually or the one can completely copy (Ctrl+C) the data from excel sheet and paste (Ctrl+V) it here.

On the right part, there are many options present as follows:

  • Confidence level:In hypothesis testing, the confidence level represents the degree of certainty or level of confidence that we have in our statistical analysis. It is a probability value that indicates the likelihood that the true population parameter falls within the specified range of values.Typically, the confidence level is expressed as a percentage and is denoted by (1 - α), where α is the level of significance or the probability of rejecting a true null hypothesis. For example, if we have a confidence level of 95%, then we are saying that we are 95% confident that the true population parameter lies within our interval estimate, and there is a 5% chance of making a type I error (rejecting a true null hypothesis).In practical terms, a higher confidence level means that we are more confident in our statistical analysis and results. However, increasing the confidence level also increases the width of the confidence interval, making it more difficult to detect small effects. Therefore, the choice of the confidence level depends on the context of the study and the goals of the researcher.
  • Hypothesized difference: The hypothesized difference refers to the difference in the population parameters between the null hypothesis and the alternative hypothesis. For example, if we want to test whether the mean score on a test is significantly different between two groups (e.g., males and females), the hypothesized difference would be the difference between the mean score of males and the mean score of females.
  • Alternative hypothesis: In hypothesis testing, the alternative hypothesis (also called the research hypothesis) is a statement that represents a different conclusion than the null hypothesis. The null hypothesis typically represents the status quo or the assumption that there is no significant difference or relationship between two or more groups or variables. The alternative hypothesis is the statement that is being tested, and it proposes that there is a significant difference or relationship between the groups or variables being studied.
  • Histogram of difference:The histogram of differences is a graphical representation of the distribution of differences between two sets of data. In the context of hypothesis testing, it can be used to visually assess the difference between the means of two groups.The process typically involves collecting data from two groups, calculating the mean and variance for each group, and then calculating the difference between the means. This difference is often referred to as the "effect size".
  • Individual value plot of difference:An individual value plot of difference is a graphical representation of the differences between two groups in a hypothesis test. In a hypothesis test, researchers want to determine if there is a statistically significant difference between two groups, such as a treatment group and a control group.An individual value plot can be used to display the differences between the two groups on a single plot. The plot typically shows the individual data points for each group, as well as the mean and standard deviation for each group.
  • Box Plot of difference: In the context of hypothesis testing, a box plot of difference can be used to display the distribution of the differences between two groups being compared. For example, if we are comparing the mean values of two groups, we can calculate the difference between the means and then create a box plot of the differences.