Assumptions Underlying One-Way ANOVA with One Between-Subjects Factor

• Level of measurement. The criterion variable should be assessed on an interval- or ratio-level of measurement. The predictor variable should be a nominal-level variable (a categorical variable) that includes two or more categories.

• Independent observations. A given observation should not be dependent on any other observation in any group. (For a more detailed explanation of this assumption, see Chapter 8.)

• Random sampling. Scores on the criterion variable should represent a random sample drawn from the populations of interest.

• Normal distributions. The distribution of observed values for the criterion variable (all groups) should approximate normal distributions.

• Homogeneity of variance. The populations represented by the various groups should have equal variances on the criterion variable. If the number of participants in the largest group is no more than 1.5 times greater than the number in the smallest group, then the test is robust against violations of the homogeneity assumption (Stevens, 2002).