One-sided paired t-test vs two-sided paired t-test

Question

I am writing a grant, where we have a prospective cohort study and 4 hypotheses. Our hypotheses are directional, that is, we expect significantly increased values in hypothesis #1,2,3; and significantly decreased value on hypothesis #4 (compared with baseline at 3-month follow up post-intervention). We will be performing a pre-intervention measurement and 3 months after the intervention, the same measurements will be repeated.

Inherently, the intervention we will be performing is a routine procedure to alleviate symptoms (hypotheses 1-2-3-4). Therefore, unidirectional changes in our respective hypotheses are I believe justified. The preliminary data also indicate that the changes will be unidirectional. Since the hypotheses are not "significantly different values compared to baseline", but rather "significantly increased" for hypotheses #1-2-3, and "significantly decreased" for the hypothesis #4 following the intervention at 3-months, I am thinking that one-sided paired t-test is justified.

I use STATA to run the sample size calculations for the grant, and I will be using STATA for the stats analysis.

Am I right?

Many thanks in advance.

Answer 1

From what you say, paired t tests seem appropriate, provided that the differences between pre-intervention 'baseline' measurements and the 3-month post-intervention measurements on the same $n$ subjects are approximately normally distributed.

Because you expect changes in one direction according to he "preliminary data" (which will not be included in the four final paired t tests), it seems reasonable to do one-sided tests. However, if it should happen that final results are in the opposite direction, it would not be appropriate to change the directions of test post hoc.

STATA should be able to do the appropriate one-sided paired t tests. However, if this is your first time doing such tests in STATA, you should verify results for one of the four tests by manual computation according to the textbook formula to make sure that you are using the software correctly.

Finally, doing a power and sample size computation in advance was a fine idea. [Because you did not share the input or output for this procedure I will not comment on the resulting sample size(s).]