Question

how do you decide whether to use an independent groups t test or a correlated t test ?

Answer 1

If you have two groups of data and you find that the two groups are completely independent of each other that means the participants of each groups are different then you will use the independent groups t test .

For example if group 1 has the marks of boys of a school and group 2 has marks of girls of the school. Then this two groups are completely independent of each other.

But if you are testing the means of two groups which are dependent on each another that means if the two groups has same participants and we are comparing two different characteristics of same participants then we will use correlated t test.

For example group 1 containing marks of students of a class after taking a course and group 2 containing the marks of these students before taking the course. Clearly this two groups are dependent and each have the same participants.