# ANOVA or multiple t-tests when comparing pre-existing group means?

I understand that Anova is preferred over multiple t-tests, but what exact is multiple t-tests?

Examples involving taking groups from the population (with the same population mean):

• We have groups taken from a population, then tested with different treatment per group, then comparing the effect of the treatment between each pair of groups. E.g. students from a school are randomly split into 3 groups, each takes a different vitamin pill and we compare the fitness level between group 1 & 2, 2 & 3, 3 & 1.
• You have two or more groups, and you are comparing multiple parameters. E.g. the you have two groups of students, one taken a vitamin pill and the other a placebo but we are comparing the fitness level, height, weight, fat content etc between the groups. This also require multiple t-tests and would be best to use Anova with some post-test correct method.

A different example involving comparing existing groups:

• We take 5 different species of animals, subject them with the same treatment, and compare their response with each other. E.g. Sheep, cows, horses, chicken and mice were given a chemical injection and we recorded their change in fitness level (in the same manner).

If I want to compare the result in pairs (e.g. sheep and cows, cows and horses, horse and chicken, chicken and mice, etc) using t-test, is this still "multiple t-tests" (they don't have a common population mean...). Do I still have to use Anova?

• When would it be useful to test for differences between the responses of different species? Wouldn't the thing of interest be whether each of the species responded? The latter question would not require any inter-species comparison. Commented Sep 4, 2021 at 21:58