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MASH : Maths and Stats Help

Shapiro-Wilk Test of Normality


A Shapiro-Wilk Test compares if your data is normally distributed, one of the underlying assumptions for determining if your data is parametric. For more details on determining if your data is parametric see our detailed Parametric or Not Guide (PDF).


Test Procedure

  1. Click Analyze > Descriptive Statistics > Explore

  2. Within the 'Explore' window, select the variable you wish to analyse and move it to the 'Dependent List' Box, then select 'Plots.

  3. Select 'Normality plots with tests' (optionally select 'Histogram' and deselect 'Stem-and-leaf')

  4. Click 'Continue' then click 'OK'



SPSS will generate many tables and graphs, for this test we only need one table the Tests of Normality.

Tests of Normality

This table shows the specific test results including the Shapiro-Wilk Test Statistic (Statistic), the degrees of freedom (df) the two-tailed significance or p-value (Sig.)

The normality of test scores was assessed. A Shapiro-Wilk test indicated that the test scores were not normally distributed W(20) = .824, p = .002.