Question

Which of the following is an assumption of one-way ANOVA comparing samples from three or more experimental treatments?

1) Equal sample sizes
2) Independence of observations
3) Normality of residuals
4) Equal variances

Answer 1

One assumption of one-way ANOVA is that the populations have equal variances.

Step-by-step explanation:

The assumption of one-way ANOVA comparing samples from three or more experimental treatments is that the populations have equal standard deviations (or variances).

Examples:

1. If we are comparing the effects of three different fertilizers on plant growth, we assume that the variance of plant growth is the same for all three fertilizers.
2. If we are comparing the performance of different groups of students under different teaching methods, we assume that the variance of test scores is the same for all groups.

It is important to note that while this assumption is often made in one-way ANOVA, there are alternative tests available that do not require this assumption to be met.