Question

1. When conducting an analysis of variance, you are comparing two components of variation. What two components are you comparing? In order for you to reject the null hypothesis, which component has to be statistically larger?

Answer 1

Solution:

In Analysis of Variance ( ANOVA) , we compare two components of variation , that are:

i) Variation Between groups ( Treatments)

ii) Variation Within groups ( Treatments)

Variation Between groups is given by Mean squares between groups ( Treatments) and Variation Within groups is given by Mean square Error.

We use F test statistic for testing the null hypothesis of equality of population means of groups and it is given by:

We reject null hypothesis H0, when ratio of F test statistic fall in rejection area which is in right tail of F distribution.

Thus in order to fall F test statistic in rejection region it should be Large ratio.
Thus in order to get large F test statistic numerator should be large and thus MSTR = Mean squares between Treatments should be large. That is component "Variation Between Groups" should be large.