Question

Difference between a paired t-test (hypothesis test) and an unpaired t-test (hypothesis test)?

Answer 1

Can someone please explain the difference between a paired and an unpaired test and how this affects the null and alternative hypothesis?

Answer 2

I'm not positive but I'll give it a shot...

First, both types of tests (paired and unpaired) are used when you're trying to determine whether or not two population means are equal. The unpaired test does this directly by taking two samples, using a "pooled" estimate of the variance (Note: you are assuming the variances of the two populations are equal), and testing the null hypothesis that Mean#1 = Mean#2 (the alternative being that they are not equal), etc.

With paired two-sample test, you're still trying to see whether or not the two populations have the same population means, but this time, for each pair you take the difference of their values and then that difference becomes your observation. So, if your 3rd pair equals (58, 43), then your 3rd observation is "15".

Thus, you're testing the null hypothesis that their difference is zero versus the alternative hypothesis that their difference is NOT zero.

The benefit, I believe, is that you end up with smaller standard errors, and, hence, greater precision.

Apologies if this appears rushed....