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 happens because the graph transitions from two dimensions to higher-dimensional representations. Multivariate normality depends on the normal distribution of all variables at the univariate level. Luckily, for the sake of testing this assumption, understanding what multivariate normality looks like is not very important.
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 help understand differences from a normal distribution. The P-P plot compares to a perfectly diagonal (y=x) line, while the Q-Q plot’s reference line depends on the distribution’s parameters. Both plots compare to the perfect diagonal line, with the Q-Q plot exaggerating differences at the ends and the P-P plot exaggerating 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.