# Three-Way ANOVA

#### herbemd

##### New Member
Hi all,

I am so confused. I have gone through my book over and over to figure this out. Ok, I understand how to perform an ANOVA, T-test or Z test with raw data. However I cannot grasp the idea of performing an ANOVA on Data that contains a Table of Means and a Table of Variances and just the basic info on the study itself (i.e. # of subjects, etc).

HERBEMD

#### JohnM

##### TS Contributor
You can work "backward" from the variances and sample sizes to get the sums of squares needed to fill in the ANOVA table....

Sum of Squares = variance * (n-1)

#### herbemd

##### New Member
Three way anova

ok, john

WHen you say backward in my table of means I have two rows and four columns. If the mean of row one column one is 54 how can I figure out the SS. For instance, I have 80 subjects but I have 10 in each condition. Would I multiply by 10 in order to obtain the SS? Because in order to obtain the mean I would have had to add the sum of all the scores for column one row one and dive them by ten in order to obtain 54 correct? Melinda

#### JohnM

##### TS Contributor
2 rows by 4 columns is actually a 2-way ANOVA

Does your text have a table that shows the formulas for determining the row and/or column SS and the interaction SS?

I can work on an example done in Excel, but it may take a while....

#### herbemd

##### New Member
yes you are right it is a two-way ANOVA. However we are working on this problem via calculator. Melinda

#### JohnM

##### TS Contributor
I'll try to attach the file to this thread so you can see the calculations...

Here it is: