The decision tree: every question, every answer, every test
Questions run from left to right; the path lights up as you answer, and each leaf on the right is a test. On a phone, the tree scrolls sideways in its box.
The questions
What kind of outcome did you measure? A number: a measurement such as days, millilitres or euros
How many groups are you comparing? Three or more groups
The test
One-way ANOVA, then Tukey's HSD
Assumes
Independent observations; roughly normal residuals; similar variances across groups.
How to check
Levene's test; a plot of the residuals.
If it fails
Welch's ANOVA, or Kruskal–Wallis with pairwise Mann–Whitney and Holm (chapter 14).
Which test fits depends on what you measured, how many groups you compare, whether the groups are independent or paired, and whether σ is known. Answer one question at a time: the path lights up in the tree, and the leaf names the test with its assumptions, what to do if they fail, and the code. Or switch to the drill and name the test for a scenario yourself.