I have three treatments (Wild type, Mutant1 and Mutant2); I request inputs on how to decide the sample size that would be statistically significant (alpha <0.05) with high statistical power (1-beta=0.8).
Questions
I understand that we need the information of effect size. We approach this problem if we don't know the expected effect size prior; a trial experiment to estimate the effect size. In such case if we want to estimate the effect size with trial experiment; what could be the sample size to start with; a high (n=10) or as low as n=3? Can n=3 among treatments provide a good estimate of effect size or n=10 is better to get this estimate. Let's be specific; if we have resource for n=10 max. and we are given option to choose between n=3 or n=10 for this trial
This question is better asked in https://stats.stackexchange.com.
I would discourage you from trying to estimate effects sizes from pilot experiments with low n. Your estimates will be quite noisy and this is rarely done (at least in my field of neuroscience). Instead, I would suggest you estimate your effect size from the literature. Have other people measured something similar to what you are planning to do? What are the sample sizes they use? What kind of effect sizes do they report.
If you were going to go ahead with the plan to run a pilot study, I would recommend pre-registering your experimental design (https://www.cos.io/initiatives/prereg). Something like:
We will test the effects of mutation 1 and mutation 2 on XXXX (compared to wild type) in a cohort of 30 mice (10 in each group). Based on the results of this study, we will then conduct a power analysis and reproduce the experiments in a sample size required to have a power of 0.8 at p=0.05.
Our criteria for excluding animals from the power analysis will be .....
The statistical test for estimating effect size will be......"
etc.