1. Hypotheses for ANOVA

In a hypothesis test for ANOVA, you are interested in the significance of the difference between . You assume that you have samples from populations that are distributed with variances. The test is designed to be used with -level dependent variables.

What is the null hypothesis in an ANOVA?

H0: All population means are different.

H0: The population variances are equal.

H0: Not all population means are equal.

H0: All population means are equal.

What is the alternative hypothesis in an ANOVA?

H1: The population variances are not equal.

H1: At least one of the population means is different.

H1: All population means are equal.

H1: All population means are different.

The F-test statistic is formed by taking the of two separate estimates of , where the estimate in the numerator is derived from the and the estimate in the denominator is derived from the . The sampling distribution is the distribution with degrees of freedom within categories and degrees of freedom between categories.

Once you compute the F(obtained) statistic for your data, you compare its value with F( ) determined by the given alpha level and the degrees of freedom. If the test statistic is in the critical region, you the null hypothesis and conclude that there a significant difference between the means.