# Power calculation; determine required difference in means

I want to perform a power analysis for a 2 sample t-test for the difference in means. However, instead of computing the required sample size, I would like to compute the required difference in the means given the sample size.

The sample size is fixed at $n=34$ (i.e. 17 per group). Due to different reasons, it is not possible to increase the sample size. Therefore, I was asked to perform a power analysis to determine the required difference in means. The investigator wants to determine if it would be worthwhile to even do the study or if the required difference is just too big and unrealistic to achieve.

For a given type I error and power I can compute the required effect size. If I further assume the standard deviations in both groups (from prior studies) I can easily compute the required difference. However, I'm wondering if this is reasonable or whether there are problems that I'm missing with this approach.

• Seems perfectly reasonable to me. Alternatively you could specify a largest difference in means that would be realistic and then compute the power for that difference. Jul 3, 2014 at 15:43

## 1 Answer

It is perfectly reasonable. As you've noted it is also mathematically feasible... the formulas involved can be translated to leave any of the necessary inputs undefined provided the levels of all of the other inputs.

Along the lines of a recommendation, I'd mention that you might find it useful to plot power x effect size for your fixed N. This might help you avoid getting caught up on what effect size is needed for an arbitrary level of power and help you visualize how steep the drop in power is as the effect size diminishes.