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MASH : Maths and Stats Help

Shapiro-Wilk Test of Normality


Normality tests are one way to assess whether a data set is approximately distributed along a normal distribution curve. These tests check if normality is violated, therefore significant results in a Shapiro-Wilk test (demonstrated below) would indicate that the distribution of that data is not normal.

Interpret the results with caution and consider them in conjunction with other ways of assessing the distribution of your data such as histograms, P-P or Q-Q plots, and values of skewness and kurtosis. Another common normality test is the  Kolmogorov-Smirnov test. An example of the Shapiro-Wilk test is provided below.

Normality is one of the assumptions of parametric tests. 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 (20) = .824, p = .002.