One of the most poorly understood concepts in the use of statistics is the idea of assumptions. You’ve probably encountered many of these assumptions, such as “data normality is an assumption of the one-sample t-test.” But if you read that statement and believe normality is a requirement of the one-sample t-test, then you have missed a subtle and important characteristic of assumptions and need to read on.

An “assumption” is not necessarily a “requirement”

To understand where this idea of assumptions comes from, let’s forget about statistics for a minute and imagine we sell bikes online. We can’t ship our bikes whole, so we ship each bike separated into the frame, handlebar, seat, and wheels, and must provide assembly instructions. We, of course, want simple and effective instructions.

 …