A Q-Q plot, short for “quantile-quantile” plot, is often used to assess whether or not a variable is normally distributed.
This tutorial explains how to create and interpret a Q-Q plot in SPSS.
Example: Q-Q Plot in SPSS
Suppose we have the following dataset in SPSS that displays the points per game for 25 different basketball players:
We can use the following steps in SPSS to create a Q-Q plot to determine whether or not the variable points is normally distributed.
Step 1: Choose the Explore option.
Click the Analyze tab, then Descriptive Statistics, then Explore:
Step 2: Create the Q-Q plot.
Drag the variable points into the box labelled Dependent List. Then click the button labelled Plots and make sure the box is checked next to Normality plots with tests. Then click Continue. Then click OK.
Step 3: Interpret the Q-Q plot.
Once you click OK, the following Q-Q plot will be displayed:
The idea behind a Q-Q plot is simple: if the residuals fall along a roughly straight line at a 45-degree angle, then the residuals are roughly normally distributed.
We can see in our Q-Q plot above that the residuals tend to deviate from the 45-degree line quite a bit, especially on the tail ends, which could be an indication that they’re not normally distributed.
Although a Q-Q plot isn’t a formal statistical test, it offers an easy way to visually check whether or not the residuals are normally distributed.
For two formal statistical tests, refer to the p-values from the Kolmogorov-Smirnov Test and the Shapiro-Wilk Test displayed above the Q-Q plot:
- P-value of Kolmogorov-Smirnov Normality Test: .086
- P-value of Shapiro-Wilk Normality Test: .042
Since both of these values are close to .05, this is an indication that the variable points may not be normally distributed.
