The Most Important Rule
Perhaps the most important lesson in this entire unit:
You must follow the assumptions for statistical tests.
The most common way people misuse statistics isn't picking the wrong test on purpose — it's picking a reasonable-looking test and ignoring the assumptions it requires. The test will run. It will give you a p-value. The p-value will be wrong, possibly badly, and you won't know.
A Real Consequence
A data scientist at a pharmaceutical company is comparing two drugs for reducing blood pressure. Two groups of patients, one on each drug. She uses a t-test.
The t-test assumes approximately normally distributed data. When she looks at the actual blood pressure measurements, they're skewed with outliers. She proceeds anyway. The test returns a statistically significant result: Drug A is better than Drug B.
A teammate catches the error before the results ship. Because she violated the normality assumption, the t-test result was unreliable. The outliers distorted the result. She could have shipped the wrong conclusion about patient care.
That's why this chapter starts with assumptions. Parametric tests have requirements. Checking those requirements is part of the job.