Sample size calculation with multiple conditions

Question

I am interested in computing the required sample size for bioreactor yields. The mean yield should be 60% or more with no yield being less than 25% and at-least 60% of runs should have more that 60% yield. the alpha will be 0.05. I plan to use a t-test for the purpose. any suggestions?

Answer 1

The first question is what is the appropriate analysis. This is an analysis of change from baseline, specifically whether a proportion change under one experimental condition is greater than the same change under a different experimental condition, presumably performed in separate units.

The most valid analysis is an ANCOVA where the response is log transformed, the baseline is adjusted as a covariate in the model, and the experimental condition is adjusted as a binary covariate. This will reduce false positive findings when certain assumptions aren't met. However, those assumptions are unexpected and difficult to quantify, so for the purposes of the power calculation, the simplified t-test can be used as the basis for a sample size calculation. The response here is the log of the ratio of post/pre. The one correction we might make is to add one to the final sample size to account for the additional degree-of-freedom for estimating the baseline effect.

To identify the meaningful parameters for a t-test sample size calculation, you've identified the effect, but you must specify the variance of the log-pre-post response. In other words, we don't know what the $\pm$ is for the effect size you've proposed... for experimental condition A, will the 95% CI be 60% (50-70%) or 60% (20-100%)?