Assumption Checks Cheat Sheet (Printable)

① t-tests & ANOVA · comparing means

Assumption (how to check)	If it's violated	§
Normality · Q–Q plot; Shapiro–Wilk at small n	Non-parametric (Mann–Whitney / Kruskal–Wallis), or transform. Robust when n is large.	2.5
Equal variances · Levene's test; compare boxplot spreads	Use Welch's t / Welch's ANOVA — don't pool the variances.	1.12
Independence · by design; no hidden clustering	Model the structure: paired / RM-ANOVA / mixed model.	4.5
Sphericity · RM-ANOVA only; Mauchly's test	Greenhouse–Geisser / Huynh–Feldt correction, or a mixed model.	2.4

② Correlation & regression

Assumption (how to check)	If it's violated	§
Linearity · scatterplot; residuals-vs-fitted	Transform, add a polynomial term, or use Spearman ρ.	2.10
Normal residuals · Q–Q plot of the residuals	Usually fine at large n; transform y; bootstrap the CIs.	3.8
Constant variance · residuals-vs-fitted; a funnel = bad	Robust (HC) SEs, transform y, or weighted least squares.	2.10
No influential points · Cook's distance; leverage	Investigate it; report with & without; robust regression.	2.10
Low multicollinearity · VIF (worry > 10)	Drop or combine predictors; ridge / lasso.	3.2

③ Chi-square · counts

Assumption (how to check)	If it's violated	§
Expected counts ≥ 5 · read the expected-count table (~80% of cells)	Fisher's exact test (small / 2×2), or merge sparse categories.	2.7
Independence · each case in exactly one cell	McNemar's test for paired / repeated data.	2.7

The order of operations

Look before you test. A Q–Q plot, a residual plot and a boxplot tell you more than a p-value for the assumption ever will.
Sample size flips the risk. Assumption tests are themselves too weak at small n and too twitchy at large n. And by the CLT, mean-comparison tests are robust to non-normality when n is large — it's the small samples where violations bite.
A violation is a fork, not a wall. It tells you which method to switch to — never a reason to look away and report the broken test anyway.