Question

In a paired samples t test, explain the logic of difference scores (why do you need to find them to make conclusions about your research) and why do you compare it to a population mean often designated as zero (µ = 0)?

Answer 1

In a paired samples t-test we compare two dependent samples. It's usually the scores of the same person (Eg Say we consider test scores of students before and after going through a special training, and we want to check if training has improved the mean scores)

So for a dependent samples test, we find the difference between scores and then we try to see whether there's a change in the scores in the appropriate direction or whether it's the same.

This is why we check it against u= 0

Here we would have wanted the alternative hypothesis as u> 0 (if D= After training scores- Before training) to check if scores have improved.