Question

For the t-test alone there are three variants based on the independence of the groups and whether we can assume variances the same or variances between the groups as different. The variances issue is easy as we can always assume they are different as the test is robust to accept any variances but the dependent pairs is different. Why is it different and how might you use it?

Answer 1

For two samples we have two types of t test

1) independent t test

2) paired t test

So it is very crucial to determine whether two groups are independent or not . If they are dependent then we take paired data (xi,yi) and then find Di= xi-yi

And then we apply one sample t test to Di's for single mean.

But in Independent groups we apply two sample t test for difference of means .

For paired data it is necessary that sample size is equal in both groups ..but in Independent samples it is not necessary that sample size be equal.