I have a somewhat unusual study design where I need some advice on power calculation.
Between subjects, I have:
Exposure A
Exposure B
Exposure A+B
And I have measures obtained before and after exposure.
Now, this could be treated as a 3x2 design which gives a numerator df = 2. But that seems inefficient and I need to answer my research question with as few participants as possible. One could instead see it as two between subjects factors - exposure A (yes/no) and exposure B (yes/no) - which gives a numerator df = 1 and hence should allow inference based on a smaller sample. As I understand it, this option will essentially equal an approach where the effect of each between subjects factor is tested controlling for the effect of the other. I'm only interested in the main effects of the between subjects factors and the two-way between x within interactions. When I run preliminary analyses (RM ANOVA in SPSS) on the small set of data I have so far, these seem to yield the same test statistics for the effects of concern regardless of whether I enter Exposure B as a second between subjects factor or as a covariate.
I use G*Power for power calculations but there I can only specify the between subjects design in terms of the number of groups, as with the 3(between)x2(within) option. To get a power estimate for a 1df between subjects design I have to enter that I have 2 groups, corresponding to the case where Exposure B is treated as a covariate in a 2(between)x2(within) design. But then I have no way to consider the impact on power of the "covariate"? Is there a more appropriate way to estimate power for this analytic approach?
I will be very grateful for any thoughts on this!
Dear Freddie Lymeus
It seems like you have a complex study design with multiple exposures and measures before and after exposure. Given your interest in efficiency and needing to answer your research question with as few participants as possible, it's crucial to optimize your power calculation appropriately.
while G*Power may not directly support your design, you can still estimate power using simulation-based approaches or consulting with a statistician to ensure your power calculation is appropriate for your study's unique characteristics.
Your approach of treating Exposure A and Exposure B as two between-subjects factors rather than a 3x2 design is sensible, especially if you're primarily interested in the main effects and two-way interactions. This simplification should indeed allow you to infer based on a smaller sample size.
you could consider consulting with a statistician who can perform a power analysis tailored to your specific design using statistical software like R or Python. They can help you set up the analysis to properly account for the complexities of your design, including treating Exposure B as a between-subjects factor rather than a covariate.
Thanks for you advice Imad-Addin Almasri ! Good to hear someone else agree that the approach sounds reasonable. Perhaps I will need to look at simulation based power analyses to get a more precise estimate, although I expect the 2x2 specification in G*Power at least comes close to what I would find there.
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