Inferential Statistics

Question

How is a t-test for correlated groups and the t-test for single samples alike and different? Is there a current example of this?

Answer 1

When doing a t-test for correlated groups (also called matched pairs), you're considering the difference between each group/pair; your Null Hypothesis is (usually, at least in Intro Stats) that these differences are drawn from a population (of groups/pairs) whose mean difference is zero. This will function just like a single sample t-test when the Null Hypothesis is that the population mean is zero. You can even use the same formulas; the sample mean is the mean of the group/pair differences in the sample, similar for the sample standard deviation. The sample size is the number of groups/pairs.

As for an example...when I taught Intro Stats, student performance on Exam 2 was usually worse than Exam 1. Using matched pairs, I would compute the difference (Exam 1 - Exam 2) for each student and test:

* Null Hypothesis: mu = 0

* Alternative Hypothesis: mu > 0

since a given student's Exam 1 score is expected to be higher than that student's Exam 2 score.

There is an issue with the results here since I'm not really using a Simple Random Sample, but it's good enough to illustrate the concept.