Two-way Analysis of Variance
Hint & Reminder
Always check the interaction first when you do a two-way Analysis of Variance
Partitioning Variance in a two-way Design:
So What F-ratio Do We Calculate?
When we have data we can calculate using fancy formulas (see your books), the following terms:
MS A, MS B, MS AB; & MS Within Groups
MS
A estimates
sa
MS B estimates s2b
MS AB estimates s2ab
MS Within Groups estimates s2e
Focus On the MS AB and F AB!
Because:
They tell you if there is an interaction!
Thus, you usually use a computer program to calculate the Mean Squares and the F-ratios.
The F-ratios must be bigger than 1.0 for significance.
In fact, they must not only be bigger than 1.0, it must be bigger than the F-table value for significance.
The larger your sample size the smaller the F-ratio you need (still has to be bigger than 1.0).
The smaller your sample, the larger F has to be - even much greater than the region of 1.0
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