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If I have a drug purported to lower heart rate and I give it to a group of volunteers, I would conduct a paired t-test to determine if their HR before is lower than their HR after taking the drug.

I find significant results, so now I accept the premise that the drug lowers HR.

Now, what if I conduct the same experiment, except I have two groups to whom I give the drug. One of these groups is different in one way (say, overweight) and the other group is not. Otherwise, they are completely controlled.

If I want to test that the decrease in heart rate is more significant in group A compared to the decrease in heart rate in group B (i.e. group A's HR dropped more than group B), I would use an unpaired t-test. Is that correct the correct usage of a paired vs. unpaired t-test?

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  • $\begingroup$ You do the same experiment, measuring HR pre- and post-treatment, yes? To compare the effect in both groups, you can measure and compare effect sizes $\endgroup$ – kjetil b halvorsen Nov 5 '18 at 18:47
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Let's write down explicitly what the groups are.

V1a: Before group

V1b: After group

V2a: Regular weight group, before treatment

V2b: Regular weight group, after treatment

V3a: Overweight group, before treatment

V3b: Overweight group, after treatment

In situation #1, you are comparing V1a and V1b. These groups contain the same people, so a paired test, such as the paired t-test, would be appropriate.

In situation #2, you are comparing V2b-V2a and V3b-V3a. Let's call these V4 and V5, respectively. Then you have a basket of data, V4, on subjects of regular weight, and a basket of data, V5, on subjects who are overweight. This is a situation to do two-sample testing, such as the unpaired t-test.

If you're doing situation #2, a technique worth reading about is called difference in differences.

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