Question

1) If a test is robust, what does this allow us to do? Be as detailed as possible (although we are not looking for a long answer).

2) When we state that there is homogeneity of variance, precisely which variances are homogeneous? Use words, not symbols.

Answer 1

(1)

If a test is robust against a particular assumtion, this allows us to relax that assumption in the statistical modeling. For example, t test is robust against the assumption of normality condition of population, it is valid for comparing approximately normally distributed groups. F test is not robust against the assumption of normality condition of population, because F test is very sensitive to non-normality and therefore invalid for approximat normality.

(2)

When we state that there is homogeneity of variance, precisely the population variances of all comparison groups are homogeneous. The Levene's test uses an F test to test the null hypothesis that the variance is equal across groups. In ANOVA, when the homogeneity of variance is violated, there is greater probability offasely rejecting the null hypothesis.