# Should you bootstrap when doing F-test on small sample

I want to conduct an F-test on a linear model with 5 groups each with around 20-25 samples. I know I could perform an anova() in R, but the residuals aren't quite normally distributed.

If I perform a bootstrap to have around 10K samples can I now safely use an F-test? Or do I have to check some assumptions?

Does the central limit theorem make the residuals normally distributed for large n and therefore make the F-statistic follow an F-distribution?

• Boostrapping is not a magic wand that creates information that was not already there. You only have the data points you started with. Large samples do not make for normally distributed residuals; if you're worried about potential non-normality with a small sample, you might perhaps consider a permutation test - or likely better still, try to think about a more suitable distributional model for the kinds of variable you're dealing with (and then maybe base a permutation test off that). Jan 19 at 2:56

Bootstrapping does not increase the sample size. You usually use bootstrapping (drawing from the data with replacement) to create multiple bootstrap samples of the same size as your original data in order to calculate e.g. a standard error or confidence interval for something you calculate on your original data. E.g. you have $$n$$ patients in two groups (of size $$n_1$$ and $$n_2$$), and want a confidence interval for the difference between the group means (that you simply calculate on the original data), in which case you could draw repeatedly (e.g. a few thousand times) $$n$$ patients from your data, calculate the difference between the groups and take the 2.5th and 97.5th percentile of the calculated differences as a (quantile bootstrap) confidence interval.