When Your Data Violates Assumptions: What to Do Next

You've run your assumption checks and something failed. Maybe Shapiro-Wilk was significant, Levene's test flagged unequal variances, or your residual plots look like modern art. Your first instinct might be panic. Don't.

Violated assumptions are one of the most common issues in dissertation research, and there are clear steps you can take.

Why Assumptions Matter

Every parametric test (t-tests, ANOVA, regression) comes with assumptions — conditions your data must reasonably meet for the results to be trustworthy. The most common assumptions are:

• Normality — the data (or residuals) follow a roughly normal distribution
• Homogeneity of variance — groups have similar spread
• Independence — observations don't influence each other
• Linearity — the relationship between variables is approximately linear

When these assumptions are violated, your p-values and confidence intervals may be inaccurate, leading to incorrect conclusions. But "violated" doesn't always mean "abandon ship."

Step 1: Assess the Severity

Not all violations are equal. Ask yourself:

Is the violation mild or severe? Many parametric tests are robust to mild violations, especially with larger samples. A slightly non-normal distribution with 100+ participants? Your t-test is probably fine. A severely skewed distribution with 15 participants? That's a problem.

Check visually. Histograms, Q-Q plots, and boxplots often tell you more than formal tests. Formal normality tests like Shapiro-Wilk are very sensitive with large samples — they'll flag trivial departures that don't actually matter. Read more in our guide on the assumption of normality.

Step 2: Know Your Options

When a violation is serious enough to address, you have several strategies:

Option A: Transform Your Data

Applying a mathematical transformation can sometimes fix non-normality or heteroscedasticity:

• Log transformation — good for right-skewed data
• Square root transformation — good for count data
• Inverse transformation — good for severely skewed data

The downside: transformed data can be harder to interpret. You're now reporting results in log-units, not the original scale.

Option B: Use a Non-Parametric Alternative

Non-parametric tests don't assume normality. Common substitutions:

These tests work on ranks rather than raw values, so they're less affected by outliers and non-normality.

Option C: Use Robust Methods

Modern statistics offers robust alternatives that handle violations gracefully. Welch's t-test (which doesn't assume equal variances) is now recommended as the default over the classic Student's t-test. Bootstrapped confidence intervals work regardless of distribution shape.

Option D: Proceed With Justification

If the violation is mild and your sample is large, you can proceed with the parametric test and note the violation. Many researchers do this, citing the robustness of the test. Just be transparent.

Step 3: Document Everything

Whatever you decide, your methods section should describe:

1. Which assumptions you tested and how
2. Which assumptions were violated
3. What you did about it and why
4. Any references supporting your decision

The Most Common Mistake

The biggest mistake isn't having violated assumptions — it's not checking them at all. Many dissertation drafts report results from parametric tests with zero mention of assumption checking. Committees notice, and they will ask. Stay ahead of it by testing assumptions before you run your main analysis.

For more on the most common assumption issue, see our guide on testing for normality.