Friday, May 17, 2013
Data Assumption: Normality of error term distribution
We often come across requirements in procedures such as General Linear Models (GLM) used for ANOVA's, ANCOVA's, etc, which state "normality of error term distribution", "normally distributed errors" or "normality of residuals".
These all mean the same thing: Residuals (error) must be random, normally distributed with a mean of zero, so the difference between our model and the observed data should be close to zero. Not only do residuals have to be normally distributed, but they should be normally distributed at every value of the dependent variable, while predictors themselves do not have to be normally distributed.
Tests are the same as for Univariate normality
though you should plot the model's "Standadized Residuals". Most common tests are:
1. Histogram of the regression standardized residuals.
2. PP and QQ plots of the standardized residuals.
3. Kolmogorov-Smirnoff / Shapiro Wilke tests on the standardized residuals.
Note that in SPSS you can select to plot residuals on an Y / X axis within the Regression procedure and also can select "histogram" and "normal probability plot" (PP). Normality is indicated by errors falling along the diagonal._________________________________________________