Advanced ANOVA/Assumptions

Completion status: this resource is ~50% complete.

This page outlines the assumptions for various ANOVA models, including t-tests.

All models

1. Dependent variables must be:
   • Measured at interval or ratio level of measurement.
   • Normally distributed in all groups (of the independent variables).
     • ANOVA is quite robust to violations of this assumption if sample sizes are large and approximately equal (> 15 cases per group)

t-tests, one-way ANOVA and factorial ANOVA

In addition, for between-group designs, it is assumed that:

1. The data in each cell is normally distributed.
   • e.g., for a 2 by 2 factorial ANOVA with age and gender as the IVs, check the distributions of the DV for, say, younger females, older females, younger males, and older males.
2. The data in each cell has homogenous variance:
   • The variance for each cell should be similar - a rule of thumb is that the ratio of the greatest to the smallest SD should be no greater than 2.
   • If violated,
     • the p-values for significance tests are inaccurate.
     • SPSS has tests to adjust for hetereogeneity of variance.
3. Cells are independent - Cases represent random samples from the target populations and the scores of the test variable should be independent of each other (i.e., the scores in one cell are not dependent on the scores in another cell).
   • Inaccurate p-values are produced if the independence assumption is violated.