Performing Normality in PASW (SPSS)

When do we do normality test?
A lot of statistical tests (e.g. t-test) require that our data are normally distributed and therefore we should always check if this assumption is violated.

Example Scenario
Given a set of data, we would like to check if its distribution is normal.

In this example, the null hypothesis is that the data is normally distributed and the alternative hypothesis is that the data is not normally distributed. The dataset can be obtained here.

The data to be tested in stored in the first column.

Step 1
Select "Analyze -> Descriptive Statistics -> Explore".

A new window pops out.

Step 2
From the list on the left, select the variable "Data" to the "Dependent List".

Click "Plots" on the right. A new window pops out. Check "None" for boxplot, uncheck everything for descriptive and make sure the box "Normality plots with tests" is checked.

Step 3
The results now pop out in the "Output" window.

Step 4
We can now interpret the result.

The test statistics are shown in the third table. Here two tests for normality are run. For dataset small than 2000 elements, we use the Shapiro-Wilk test, otherwise, the Kolmogorov-Smirnov test is used. In our case, since we have only 20 elements, the Shapiro-Wilk test is used. From A, the p-value is 0.316. We can reject the alternative hypothesis and conclude that the data comes from a normal distribution.

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