Assumption Checks & Diagnostics
Before you trust a p value, confirm the model's assumptions hold. Here are the checks that matter and what to do when they fail.
What it is
Every parametric model — regression, ANOVA, structural equation model — rests on a set of assumptions. If those assumptions are violated, the standard errors, p values, and confidence intervals can all be wrong, even when the point estimates look plausible. Assumption checks and diagnostics are the set of tests and plots you run before you interpret a model's output. The good news is that most of these checks are quick and the remedies are well-established. The key is to run them routinely, not only when results look suspicious. Reviewers and editors increasingly expect a sentence in the methods section confirming that assumptions were checked.
When to use it
- Before interpreting any parametric model — regression, ANOVA or SEM — to confirm its assumptions hold.
- Routinely, as a standard step, not only when results look suspicious.
- When a reviewer or editor expects a statement that assumptions were checked.
- When the point estimates look plausible but you need to trust the standard errors, p values and confidence intervals.
Assumptions
- Normality of residuals — the model's errors are approximately normal (the raw outcome need not be).
- Homoscedasticity — residual variance is roughly constant across fitted values.
- Linearity — each predictor relates to the outcome in a straight line.
- No unduly influential outliers — no single case pulls the estimates substantially.
- No severe multicollinearity — predictors are not too strongly correlated (VIF below 5).
Thresholds & cutoffs
| Criterion | Rule of thumb | Source |
|---|---|---|
| Normality | Shapiro–Wilk, Q–Q plot — SW p < .05 (small n); curved Q–Q | Remedy: Log/sqrt transform; nonparametric alternative |
| Homoscedasticity | Residual-vs-fitted; Levene's — Fan pattern; Levene's p < .05 | Remedy: Robust SEs (HC correction); Welch's ANOVA |
| Linearity | Partial regression plot — Clear curve in plot | Remedy: Polynomial term; log transform |
| Outliers | Standardized residuals; Cook's D — |z| > 3; Cook's D > 4/n | Remedy: Inspect; report with and without outlier |
| Multicollinearity | VIF / Tolerance — VIF > 5 (warning), > 10 (serious) | Remedy: Remove a predictor; center variables; PCA |
How to report it in APA
Prior to the main analysis, assumptions were checked. Residuals were approximately normally distributed (Shapiro–Wilk W = .98, p = .23). Homoscedasticity was supported by visual inspection of residual-vs-fitted plots. No influential cases were identified (all Cook's D < .08). Variance inflation factors ranged from 1.12 to 2.34, indicating no multicollinearity concerns.
How Explonia runs it
Explonia surfaces assumption diagnostics alongside the relevant analysis. When you run a regression or an ANOVA in the platform, it automatically checks and displays normality (Shapiro–Wilk), Levene's test for group comparisons, and VIF for regression models. The results appear in the same output panel as the main analysis, so you do not have to run a separate tool. Where a check fails, the output flags it so you can take action before reporting. In a group comparison set to Auto, a failed normality check switches the test to Mann-Whitney or Kruskal-Wallis; with large groups you can choose ANOVA or Welch's ANOVA instead, and say why in your report.
Frequently asked questions
Does my data need to be normally distributed?
The normality assumption applies to the residuals of your model, not the raw data. With large samples (n > 30 per group), the central limit theorem makes most tests robust to non-normality. Shapiro-Wilk is sensitive with large samples and will flag trivial deviations. Use Q–Q plots alongside the test.
What VIF value is too high?
VIF > 5 is a common warning threshold; VIF > 10 is widely treated as a serious concern. Tolerance (= 1/VIF) below .10 is the equivalent signal. When multicollinearity is high, coefficient estimates become unstable, though the overall model fit may still look good.
What should I do if an assumption is violated?
It depends on the assumption. For non-normality with small samples: apply a log or square-root transform, or use a nonparametric alternative (Mann-Whitney, Kruskal-Wallis). With large groups, ANOVA or Welch's ANOVA is usually robust, so justify the choice either way. For heteroscedasticity: use robust standard errors (HC correction). For outliers: report with and without the outlier so readers can see the impact. Never simply delete outliers without explanation.
How do I report assumption checks in APA?
A brief statement in the Methods section is enough when assumptions are met. If a violation required action (e.g., a transform or a robust estimator), explain what you did and why. Readers should be able to evaluate whether your choice was reasonable.
Last updated: September 2026
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