Assumption Checking Checklist

Before running any parametric test, verify its assumptions. This checklist tells you what to check, how to check it, and what to do when an assumption is violated.

Independent-Samples t-Test

Assumption How to Test If Violated
Independence of observations Study design — each participant contributes one data point; no clustering or repeated measures. Use a paired test, multilevel model, or GEE to account for dependency.
Normality (of DV in each group) Shapiro-Wilk test (p > .05 = normal). Also inspect Q-Q plots and histograms. Skewness and kurtosis within +/- 2. If n > 30 per group, the t-test is robust via CLT. Otherwise use Mann-Whitney U or apply a log/square-root transformation.
Homogeneity of variance Levene's test (p > .05 = equal variances). Compare group SDs — ratio > 2:1 is a concern. Use Welch's t-test (does not assume equal variances). Most software offers this as the default option.
No significant outliers Boxplots. Values beyond 1.5 * IQR flagged. Check if outlier is a data-entry error. Winsorize, trim, or use a robust test (e.g., bootstrapped t-test). Report results with and without the outlier.

Paired-Samples t-Test

Assumption How to Test If Violated
Related pairs Study design — same participants measured at two time points, or matched pairs. If observations are independent, use an independent-samples t-test instead.
Normality of difference scores Compute difference scores (post − pre). Run Shapiro-Wilk on the differences. Inspect Q-Q plot of differences. Use Wilcoxon signed-rank test or bootstrapping. Robust with n > 30.
No extreme outliers in differences Boxplot of difference scores. Investigate outlier. Winsorize or use a robust method. Report sensitivity analysis.

One-Way ANOVA

Assumption How to Test If Violated
Independence of observations Study design. No participant appears in more than one group. Use repeated-measures ANOVA or mixed-effects model.
Normality (DV within each group) Shapiro-Wilk per group. Q-Q plots. ANOVA is robust when n ≥ 15 per group and groups are roughly equal in size. Use Kruskal-Wallis H test. Or transform the DV (log, square root, Box-Cox).
Homogeneity of variance Levene's test (p > .05). Compare largest and smallest group SDs. Use Welch's ANOVA (oneway.test() in R) with Games-Howell post hoc. Do not use Tukey HSD.
No significant outliers Boxplots per group. Studentized residuals > |3| are extreme. Remove only with justification. Use robust ANOVA (trimmed means) or report with and without.

Pearson Correlation

Assumption How to Test If Violated
Both variables continuous Verify measurement scale. Interval or ratio data required. For ordinal data, use Spearman's ρ or Kendall's τ. For one dichotomous variable, use point-biserial r.
Linearity Scatterplot of X vs. Y. Look for a straight-line pattern (not a curve). Transform one or both variables. Or use Spearman ρ (which only requires a monotonic relationship).
Bivariate normality Shapiro-Wilk on each variable individually. Joint normality is hard to test — if both are univariate-normal and the scatterplot is elliptical, you're fine. Use Spearman ρ or bootstrapped Pearson r.
No significant outliers Scatterplot — look for points far from the cloud. A single outlier can dramatically inflate or deflate r. Winsorize or remove with justification. Report r with and without the outlier.
Independence of observations Study design. Each pair of scores comes from a different participant. Use multilevel modeling or repeated-measures correlation if data are nested.

Linear Regression (Simple & Multiple)

Assumption How to Test If Violated
Linearity Scatterplot of predicted vs. residuals — should show no pattern (random cloud around zero). Add polynomial terms, transform predictors, or use non-linear regression.
Independence of residuals Durbin-Watson test (value near 2.0 = independent). Values < 1.5 or > 2.5 are concerning. Use generalized least squares, add a lagged DV, or use a time-series model.
Normality of residuals Q-Q plot of standardized residuals. Shapiro-Wilk on residuals. Histogram of residuals. Transform the DV (log, Box-Cox). Use bootstrapped regression for inference. Robust with large n.
Homoscedasticity (constant variance of residuals) Plot residuals vs. predicted values — spread should be constant (no funnel shape). Breusch-Pagan test (p > .05 = homoscedastic). Use robust (HC3) standard errors. Or transform the DV. Weighted least squares for severe cases.
No multicollinearity (multiple regression only) VIF (Variance Inflation Factor) for each predictor. VIF > 5 is problematic; VIF > 10 is severe. Tolerance < 0.2 is a concern. Remove or combine correlated predictors. Use ridge regression or PCA to reduce dimensionality.
No influential outliers Cook's distance (> 1 is influential, some use > 4/n). Leverage values, studentized residuals > |3|. Investigate the case. Report results with and without influential points. Use robust regression.

At-a-Glance Decision Table

Assumption Test It With Rule of Thumb
Normality Shapiro-Wilk + Q-Q plot p > .05 = normal. Visual check is often more useful than the test.
Equal variances Levene's test p > .05 = equal. Largest SD / smallest SD < 2.
Linearity Scatterplot / residual plot No curved pattern in the residual plot.
Homoscedasticity Residuals vs. fitted plot, Breusch-Pagan Even spread of residuals. No fan/funnel shape.
No multicollinearity VIF / Tolerance VIF < 5. Tolerance > 0.2.
Independence Study design / Durbin-Watson DW near 2.0. No clustering in the data.