# Sample size for 2 groups vs. one large group to measure spread?

I hope this question can simply be answered conceptually, without a specific dataset. I am planning a new study, for which I will be testing the effects of depression on a memory task. I'm currently considering if I should plan to test two groups of high/low depression scores, or test one larger group of varying depression levels to model the effect of the degree of depression on my task.

Without going into specific power calculations on how many subjects I would need specifically for my task, can you already say a priori if either of the two designs requires more subjects than the other?

• You would want a balanced design. – user2974951 Oct 18 '18 at 10:26
• It depends partly on the model and partly on how confident you are that it is correct. As one example, suppose you are extremely confident that within the range of depression scores you will see, the task performance will be a linear function of depression score. Then the optimal solution, in the sense of needing the fewest subjects to achieve any given level of precision in the slope and intercept estimates, is to select half the subjects from the subpopulation with lowest depression scores and the other half from the subpopulation with highest scores. So: what are you assuming? – whuber Oct 18 '18 at 12:15

## 1 Answer

You write:

I'm currently considering if I should plan to test two groups of high/low depression scores, or test one larger group of varying depression levels to model the effect of the degree of depression on my task.

and ask about power calculations, specifically, which would require more subjects. You mention that you don't want to specify the data, but there is a bigger issue: The two studies would test different hypothesis (the first tests if high is different from low; the latter measures across all levels); they would use different statistics (starting points might be a t-test for the first and a regression for the second) and have different effect sizes (difference for the first (measured one way or another) and maybe R^2 for the second.

I think the proper thing is to first figure out what you want to find out and then figure out what sample size is needed.

• I interpret the question, as you have quoted it, somewhat differently. It sounds to me like it is asking how to optimize the design of an experiment in which an ordinary regression between an experimenter-determined variable (depression score) and an observed outcome (task score) will be performed. There is no question of which hypothesis to test, because it's the same in either case: is the slope zero? – whuber Oct 18 '18 at 12:17