Suppose that I have a set of certain measurement. There are two factors that can affect the value of the measurement, let's call them the factors A and B. The factor A has 2 levels (levels 1 and 2), and the factor B has 3 levels (levels 1,2,3).

Let xa,b be the value of the measurement which was measured at the level a of the factor A, and the level b of the factor B. For example, x1,2 would be the value of the measurement at the level 1 of factor A and the level 2 of factor B. In that case, the set of all measurements (S) I have is:

S = {x1,1, x1,2, x1,3, x2,1, x2,2, x2,3}.

Suppose that I standardized the measurements xa,b's over the entire set S. Let x*a,b be the standardized value of xa,b. Then,

1. If the sample variance of {x*1,1, x*1,2, x*1,3} is less than the sample variance {x*2,1, x*2,2, x*2,3}, would this indicate that the level 2 of the factor A makes the measurement to vary more than the level 1 of the factor A?

2. Is standardizing the measurements over the set S necessary? For example, if I just compare the sample variance of {x1,1, x1,2, x1,3} and the sample variance of {x2,1, x2,2, x2,3}, would this also indicate whether or not the level 2 of the factor A makes the measurement to vary more than the level 1 of the factor A?

Thank you,