Testing Multivariate Normality in SPSS

Quantitative Results
Statistical Analysis

In a previous blog, we discussed how to test univariate normality in SPSS using charts, skew and kurtosis, and the Kolmogorov Smirnov (KS) test. Today, we will be discussing a second aspect of normality: the multivariate equivalent. While the univariate version of normality is pretty simple to think about, multivariate normality paints a little more of a complex picture. This is because it moves from a graph that can be imagined in two dimensions to higher and higher dimensional graphs. But at its core, multivariate normality really ties back to all of your variables being normally distributed on a univariate level. Luckily, for the sake of testing this assumption, understanding what multivariate normality looks like is not very important.

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One of the quickest ways to look at multivariate normality in SPSS is through a probability plot: either the quantile-quantile (Q-Q) plot, or the probability-probability (P-P) plot. Both plots are useful in understanding differences in your sample data from a perfectly normal distribution, but it may be worth noting that the P-P plot will always be compared to a perfectly diagonal (y=x) line, while a Q-Q plot’s reference line represents a particular distribution and will depend on the parameters of that distribution. In general, both can be compared to the perfect diagonal line, though the Q-Q plot tends to exaggerate differences on the ends of the plot, while the P-P plot tends to exaggerate differences in the middle. Running both can help you get a better idea of the distribution, but only one is typically necessary.

You can run both of these by selecting Analyze -> Descriptive Statistics, and then selecting either the Q-Q or P-P plot. On the following screen, drop in the set of variables that you need to check. In a regression, check all the variables in the model, while a MANOVA’s assumption testing should only include the dependent variables from the model. This same method can be used to test any number of variables for multivariate normality.