Question

Given the sums of squares of several models from a hierarchical regression, one where the interaction was entered first, how do select the sums of squares for A and B to calculate a 2-way ANOVA and complete an ANOVA summary and F test?

Answer 1

Refer the sample output of 2 Way Anova given below:

Here, sum of squares are given for the interaction as:

For Sample, SS is 99.73324

Columns. SS is 1150.432

Interaction, SS is 1577.52 and so on...

df is the Degree of Freedom

SS: Sum of Squares

Calculation of F test statistic:

MS = SS/df

So for Sample, MS = 99.73/1 = 99.73

For Column, MS = 1150.432/2 = 575.21 and so on...

In this way all the respective Mean Sum of Squares can be calculated...

F is calculated by dividing all the MS for sample, column and interaction by MS within the groups...

Here, MS (within) is 18.99083

So, F₁ = 99.73324/18.99083 = 5.251652

Similarly,

F₂ = 575.2161/18.99083 = 30.28914

and, F₃ = 788.7629/18.99083 = 41.53387

Finally, from these F values, the P values can be calculated and then further analysis can be done...

If you can provide us with a sample data set, then we can show you the full analysis with calculations so that you can be more clear in this regard.

End of the Solution...