Hello,

You are mistaking two different things for the same : the number of samples in the experiment and the conduct of the experiment itself.

The number of samples will determine the statistical power of the study. It depends on a lot of factors.

The number of replicates you run for each measurement/ test/ experience... only determine if you will have a important variation in your technique. This is called the technical replicate, and it is done in triplicate because it is the minimum number to have a standard deviation. This way you ensure that your technique gives the same result each time you test the same sample.

Only when you have satisfactory technical reproductibility will you look into the statistics of your experiments, and the number of samples required. The triplicate only ensure that you will be able to compare your different samples between them.

I think this is easier to explain with an example:

Let's say I have cells that I want to test drug X on at concentrations of 0, 25, and 50 uM just for toxicity by just counting the cells after 48 hours after exposing them to the drug. Experiment 1: collect 3 samples of each concentration and count. Experiment 2 (repeat): collect 3 samples from each concentration and count. Experiment 3 (repeat): collect 3 samples from each concentration and count.

In total, my n=3 for each concentration, it is not 9 for each concentration, since technical replicates like you said are only to control for variance, they are not biological replicates. N=3 reflects the number of times I

**independently** ran the experiment. Independence is key. Separate experiments in this case produce independent results, replicates within the same experiment do not boost my value of n.

Power of analysis must be done a priori, BEFORE an experiment is done to properly determine sample size (in this case sample size for each concentration reflects how many times I run the experiment). It is possible to do post hoc power of analysis, but it is much less useful. In fact, many statisticians basically claim retrospective power of analysis essentially worthless.

I just don't understand why many fields of science simply assume n=3 is good enough. Why is this so? Should a priori power of analysis determine sample size? Power of analysis is absolutely required in fields like psychology, sociology, medicine, or when one wants to conduct an animal study. Why do other fields of science basically not even use it?