# Paired t-test

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The Student’s t-test or simply, the t-test, is a type of parametric statistical test used to determine if there’s a significant difference between the means or averages of two groups.

And significance is normally defined by a p-value of less than 0.05 or 5%.

Now when doing any parametric test, there are three key assumptions that we have to make about the population.

First, the sample population must have been recruited randomly.

Choosing names randomly ensures that the people included in the study will have similar characteristics to the target population.

This is important because that ensures that the results of the t-test can be applied to the target population - meaning it has good external validity!

The second assumption is that each individual in the sample was recruited independently from other individuals in the sample.

In other words, no individuals influenced whether or not any other individual was included in the study.

For example, if two friends decided to get their blood pressures measured on the same day, and they were both included in the study, these two individuals would not be independent of each other and the second assumption would not be met.

Like random sampling, independent recruitment of individuals is important because it ensures that the sample population approximates the target population.

The third assumption is that the sample size is large enough to approximate the target population, which usually means having more than 20 people.

If it’s impossible to get a large sample size, then the sample population must follow a normal bell-shaped distribution for the characteristic being studied because that’s what we would expect to see in the target population.

Okay, now let’s say you want to figure out if a certain medication lowers systolic blood pressure.

So, you measure 25 people’s systolic blood pressures and find that the mean systolic blood pressure for the whole group is 138 mmHg.

Then, you give them the medication and after six weeks, you find that the mean systolic blood pressure for the group is only 130 mmHg.

Now, to figure out if a decrease in systolic blood pressure from 138 to 130 is significant, we could perform a t-test.

Specifically, since the two means were measured in the same population before and after the treatment, we would use a paired t-test.

This is different than an unpaired t-test, or 2-sample t-test, which is used to compare two groups of individuals.

### Summary

A paired t-test is a type of parametric test used to compare one group of individuals at two different times. It helps to compare the means of the two related groups and determines whether the difference between them is statistically significant. It is based on the t-statistic, which is calculated using the mean difference between the groups and the standard error of the mean difference.

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