Normality Test in SPSS: Shapiro-Wilk, K-S Test, and Q-Q Plot

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Why Test for Normality?

Parametric tests (t-test, ANOVA, Pearson correlation, regression) rest on the assumption that data are approximately normally distributed. Applying parametric tests when this assumption is severely violated can produce misleading results. Normality testing is therefore the mandatory first step in any analysis pipeline.

Running Normality Tests in SPSS

Go to Analyze → Descriptive Academy → Explore.

1. Move the variable(s) to Dependent List.
2. If testing by group, move the grouping variable to Factor List.
3. Click Plots and check Normality plots with tests.
4. Click OK.

Shapiro-Wilk vs. Kolmogorov-Smirnov

• Shapiro-Wilk: Preferred for small to moderate samples (n≤50). More powerful and sensitive than K-S for detecting non-normality.
• Kolmogorov-Smirnov (with Lilliefors correction): Used for larger samples (n>50); however, it becomes extremely sensitive in large samples and may flag trivial deviations.

Interpretation: p>0.05 → normality assumption is not rejected. p<0.05 → significant departure from normality detected.

Visual Assessment: Q-Q Plot

In a Normal Q-Q Plot, data points that closely follow the diagonal reference line indicate normality. Systematic deviations — S-shaped curves or heavy tails — signal non-normality. Always examine the Q-Q plot alongside the statistical test, especially in large samples.

Skewness and Kurtosis

Skewness values within ±2.0 and kurtosis values within ±7.0 indicate a sufficiently normal distribution (Hair et al., 2019). This rule is especially useful as a supplement to formal tests in larger samples.

What to Do When Normality Is Violated

• Try data transformations: log10, square root, or inverse transformation.
• Switch to non-parametric tests: Mann-Whitney U, Kruskal-Wallis, Spearman rho.
• For n>30 per group, the Central Limit Theorem provides some justification for parametric tests even with mild non-normality.

APA Reporting

Normality of the data was assessed using the Shapiro-Wilk test. Results indicated that the data were approximately normally distributed (p>.05); therefore, parametric tests were employed in subsequent analyses.

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