[mikorym]

On the other side of the thought process, if you are interested in ways to completely ignore p-values, multivariate stats is a good candidate, and is rather pedagogically well suited, too.

For example, if you have a friend who hates chi-squared tests, instead teach them correspondence analysis.

A year later you can tell them they already know how to do a chi-squared test. To be fair, this latter comment depends a bit on how the library is implemented, and possibly it only does correspondence analysis while not giving you direct access to a way to generate p-values. Some libraries will have a function that you can call that runs simulations and then provides the p-values.

Many of these statistical techniques are an obligation only if you have to sample from a space and you have to somehow determine whether the sample is representative. If you presuppose that your sample is representative, then you move into a parallel world of statistics. An example would be a thermometer. If you sample it at 10:00 00 and again at 10:00 01, certainly you would expect both to be the same? If it's not the same or a close value I would rather say that the thermometer is broken, not that your within group variation for the minute 10:00 is high...