Question

Which of the following is not an assumption of the one-way ANOVA?

A. Group means are equal

B. Group variances are equal

C. data between and within groups are independent

D. Observations are normally distributed within groups.

Answer 1

Analysis of variance test (sometimes shorthand ANOVA) is a way to find out whether the survey or experiment results are significant. In other words, they help us to figure out if we need to reject the null hypothesis or accept the alternate hypothesis. Basically, we are testing groups to see if there’s a difference between them.
One-way or two-way refers to the number of independent variables in our Analysis of Variance test.
So One-way ANOVA between groups is essentially used when we want to test two groups to see if there’s a difference between them.

In order to use the ANOVA test we made the following assumptions:

• Each group sample is more or less drawn from a normally distributed population i.e., Observations are normally distributed within groups.
• All populations have a common variance i.e., group variances are equal.
• All samples are drawn independently of each other, moreover within each sample, the observations are sampled randomly and independently of each other i.e., Data between and within groups are independent.
• Factor effects are additive.

So group means not necessary to be equal to use ANOVA test.
Hence from the given options the correct option is option A. Group means are equal which is not an assumption for the one-way ANOVA test.