mrjiaruiwang
commented
9 years ago t-tests/f-tests/their derivatives such as ANOVA all have assumptions about the distributions from which the data was sampled. At the base of all these tests is they're trying to maximize the likelihood "odds" ratio. In order for a convenient analytical solution to be obtained, we have to assume gaussian distributions at the asymptotic limit as the number of samples goes to very large. The problem arises in that the gaussian distribution assumption does not always hold, and rarely in biology do we get as many samples as we may need for the asymptotic assumption to hold.
People nowadays are using non-parametric tests like the Wilcoxon rank-sum statistic to remove the gaussian assumption, and monte-carlo simulation for "permutation testing" to remove the asymptotic assumption.
When you do not assume asymptotic limit or gaussian distribution, you are able to conclude with much higher confidence, but with greater power comes greater responsibility. It is usually the case that using these simpler more rigorous methods will make previously significant results not significant.
yaxigeigei
We mentioned in class that the results for ANOVA and for t-test are asymptotic and, therefore, not great for finite data. What do people use instead of these? What are the pros and cons about using these other methods instead?