Normality Test

Check whether your data follows a normal distribution.

Definition

Before applying most parametric tests (t-test, ANOVA, Pearson correlation), it is essential to verify the normality of the data. StatsLab offers Shapiro-Wilk and Kolmogorov-Smirnov tests, plus a Q-Q plot for visual inspection.

When to use it

• Before a t-test, ANOVA, or Pearson correlation
• To validate assumptions of a regression model
• To choose between parametric and non-parametric tests

Requirements

• Continuous variables
• Shapiro-Wilk recommended for n < 50
• Kolmogorov-Smirnov for large samples

What StatsLab computes

• W statistic (Shapiro-Wilk) and p-value
• D statistic (Kolmogorov-Smirnov) and p-value
• Q-Q plot with 95% CI
• Histogram with theoretical normal curve
• Skewness and kurtosis

Worked example

Context : Normality test on exam scores (out of 20) for 30 students.

Result : Shapiro-Wilk W = 0.971, p = 0.563

Interpretation : p > 0.05: we fail to reject the normality hypothesis. The data are consistent with a normal distribution — parametric tests are justified.

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