How do we calculate the between groups sum of squares for the interaction?
How do we calculate the between groups sum of squares for the interaction?
The Mean Sum of Squares between the groups, denoted MSB, is calculated by dividing the Sum of Squares between the groups by the between group degrees of freedom. That is, MSB = SS(Between)/(m−1).
How do you calculate the SSE in two-way Anova?
SS (AB) = SS Total − SS Error − SS (A) − SS(B) SS Error = S iΣ jΣ k (y ijk − y̅ ij. ) SS Total = Σ iΣ jΣ k (y ijk − y̅…)…Adj SS.
| Term | Description |
|---|---|
| y… | overall mean of all observations |
| y .j. | mean of the j th factor level of factor B |
| y ij. | mean of observations at the i th level of factor A and the j th level of factor B |
What is AXB interaction?
There is an interaction between two factors if the effect of one factor depends on the levels of the second factor. When the two factors are identified as A and B, the interaction is identified as the A X B interaction. Often the best way of interpreting and understanding an interaction is by a graph.
Is the sums of squares of AXB interaction statistically significant?
This might be a good time to check and make sure that those calculations are accurate. As we can see, the sums of squares for the interaction between A x B has a very small value. It is highly unlikely that the interaction between these two factors is statistically significant.
How to calculate sums of squares between groups?
This is a very simple calculation that is obtained by taking the sums of squares for between groups (which was calculated from the squared deviations of each cell total from the grand mean estimate) and removing the main effects estimates.
How to calculate the corrected sum of squares?
Random actors will be discussed later. When an \\(a imes b\\) factorial experiment is conducted with an equal number of observations per treatment combination, the total (corrected) sum of squares is partitioned as: $$ SS(total) = SS(A) + SS(B) + SS(AB) + SSE \\, , $$ where \\(AB\\) represents the interaction between \\(A\\) and \\(B\\).
How to calculate the interaction between factors a x b?
Now we are ready to calculate the interaction between Factors A x B. This is a very simple calculation that is obtained by taking the sums of squares for between groups (which was calculated from the squared deviations of each cell total from the grand mean estimate) and removing the main effects estimates.