Two-sample test + paired/independent samples

Question

This might be an easy question but I got lost in my thinking so thank you for clarifying that for me. So I have some troubles with understanding the ideas of two-sample tests in addition to paired and independent sample tests.

So this is clear for me:

• Two-sample test is used to determine a difference between two independent populations. So an example would be comparing the mean alertness after drinking coffee among men and women.

• Paired and independent samples tests determine the method of collecting results. For example: let's say we want to determine what increases alertness more - energy drinks or coffee. In paired samples test we make each subject drink coffee and then perform a test and the next day we give them energy drink and perform the test again. In independent samples test we divide people into two groups and make the one drink coffee and the other energy drink.

Is it possible to connect these two concepts? From my understanding two-sample tests are independent samples tests because by definition the populations need to be independent. Though I'm not sure if this reasoning is correct. Is there anything like two-sample paired test?

Answer 1

There are possibly some challenges with the wording here. Two-sample test and independent samples test actually refer to the same type of tests: they are used to determine whether the difference between two populations is statistically significant. So, comparing the "mean alertness after drinking coffee among men and women" is the same type of test as comparing the "mean alertness among people drinking coffee and energy drink". In both cases, you work with two random samples, each obtained independently from different populations.

The confusion might come from the interpretation of the paired sample test. They are used to assess dependent samples: the same people are used in both groups (but observations are independent). So, paired test uses already two samples.

Here are some related questions about paired / two- sample tests:

• Paired test or two-sample t-test?
• t-test for partially paired and partially unpaired data