# How can I estimate the optimal number of experiments? [closed]

I have a list of 20 experiments, each have a certain numerical value as a result. I would like to run many more experiments of this type (for different conditions, and so on), but 20 experiments are too expensive.

What's the best way to estimate the optimal number of experiments, for which additional experiments change the mean only slightly?

I have tried randomly sampling a subset (2,3,...18 and so on) of the experiments, calculating the standard deviation for each (for a number of iterations), trying to see from which number of experiments the std change only slightly, this is what I got after averaging all the STD per number of samples: (y-axis is the mean STD, x-axis is the number of experiment sampled from the total 20) However, I'm not sure this is the optimal way to do such a thing.

## closed as unclear what you're asking by mkt - Reinstate Monica, kjetil b halvorsen, user158565, Reinstate Monica, Michael R. ChernickJun 20 at 17:04

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• What do you mean by an experiment? Are there multiple measurements involved? – mkt - Reinstate Monica Jun 19 at 11:17
• Example of an experiment - Estimating the expression level of a gene (how many copies of a gene are present in a cell). Measurements are noisy, so we conduct the experiment multiple times. – Protostome Jun 19 at 11:26
• So each 'experiment' here has a single measurement? – mkt - Reinstate Monica Jun 19 at 11:36
• @mkt That is correct – Protostome Jun 20 at 6:28
• This is useful to know; I would say that calling these 'measurements' rather than experiments is likely to make the question clearer to most readers. One more thing: your initial question is about how many measurements are needed for the mean to not change much with additional data, but you subsequently talk about the stability of the standard deviation. It's still not entirely clear what you are interested in. – mkt - Reinstate Monica Jun 20 at 8:06