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 Anovo 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?