Question

a)Describe what each one of the assumptions of the model consists of in an ANOVA and explain the typical way in which these assumptions are verified.

b)What are the graphical methods to determine the difference of means?

Answer 1

Dear student, please post one question at a time.

a)

• Independence of cases – this is an assumption of the model that simplifies the statistical analysis.

There is no way to test for independence of observations. This assumption can only be satisfied by correctly randomising your experimental design.

• Normality – the distributions of the residuals are normal.

The Shapiro-Wilk test tests the null hypothesis that the samples come from a normal distribution against the alternative hypothesis that the samples do not come from a normal distribution.

• Equality (or "homogeneity") of variances, called homoscedasticity.

Bartlett’s test tests the null hypothesis that the group variances are equal against the alternative hypothesis that the group variances are not equal. Bartlett’s test should be used when the data is normal and Levene’s test should be used when the data is non-normal - where Bartlett’s test is the more powerful of the two.