Question

One assumption needed for ANOVA is that the k populations involved are normally distributed, with equal variances.

T OR F ??

Answer 1

True

Assumptions for ANOVA

To use the ANOVA test we made the following assumptions:

• Each group sample is drawn from a normally distributed population
• All populations have a common variance
• All samples are drawn independently of each other
• Within each sample, the observations are sampled randomly and independently of each other
• Factor effects are additive

The presence of outliers can also cause problems. In addition, we need to make sure that the F statistic is well behaved. In particular, the F statistic is relatively robust to violations of normality provided:

• The populations are symmetrical and uni-modal.
• The sample sizes for the groups are equal and greater than 10

In general, as long as the sample sizes are equal and sufficiently large, the normality assumption can be violated provided the samples are symmetrical or at least similar in shape