How to Perform a Shapiro-Wilk Test in SPSS


The Shapiro-Wilk test is a statistical that is used to determine whether or not given dataset follows a normal distribution.

The Shapiro-Wilk test uses the following hypotheses:

  • H0: The data is normally distributed.
  • HA: The data is not normally distributed.

If the p-value that results from the test is less than your chosen significance level (e.g. 0.05) then you can reject the null hypothesis and conclude that the data is not normally distributed.

To perform a Shapiro-Wilk test in SPSS, you can use Analyze > Descriptive Statistics > Explore.

The following example shows how to perform this test in practice.

Example: How to Perform a Shapiro-Wilk Test in SPSS

Suppose we have the following dataset in SPSS that contains information about the final exam scores received by 25 different students in some class:

Suppose that we would like to perform a Shapiro-Wilk test to determine if the exam scores are normally distributed.

To do so, click the Analyze tab, then click Descriptive Statistics, then click Explore:

In the new window that appears, drag the Score variable into the Dependent List panel: 

Then click the Plots button.

Check the box next to Histogram and Normality plots with tests:

Then click Continue. Then click OK.

The following output will be generated that shows the results of the Shapiro-Wilk test along with a histogram that displays the distribution of exam scores:

Shapiro-wilk test in SPSS

From the output we can see that the p-value of the Shapiro-Wilk test is .006.

Recall that the Shapiro-Wilk test uses the following hypotheses:

  • H0: The data is normally distributed.
  • HA: The data is not normally distributed.

Since the p-value of the test is less than .05, we have sufficient evidence to reject the null hypothesis.

Thus, we would conclude that the distribution of exam scores is not normally distributed.

From looking at the histogram, it’s also clear that this distribution of exam scores does not follow a typical “bell curve” that is associated with a normal distribution.

The distribution of exam scores appear to be left-skewed, with the “tail” of the distribution extending towards the left side of the graph.

Additional Resources

The following tutorials explain how to perform other common operations in SPSS:

How to Perform a Correlation Test in SPSS
How to Calculate Spearman Rank Correlation in SPSS
How to Calculate Percentiles in SPSS

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