Formula for Calculating Quadratic Sum of Squares

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    Kshitij Mehta

    Hello all,

    I am manually trying to calculate the sum of squares in ANOVA. I am familiar with the formula for calculating the sum of squares (SS) of main effects and interaction.

    Can anyone please let me know what would be the formula for calculating Sum of Square of the interaction of the factor A with itself i.e, SS A^2.



    Robert Butler

    I spent some time checking various reference books looking for something that might help and I’m afraid I don’t have much to offer.

    Two thoughts
    1. We are assuming you are running ANOVA on continuous variables. If you are running categorical variables then linear and interaction are all you can expect to compute.
    2. The level of sophistication of modern statistics packages is such that I doubt you will find anything relating to manual calculations in any of the modern statistical texts for anything other than main effects and interactions.

    I did find a reasonable discussion of the problem and what looks like a guide for generating the necessary equations in Statistical Analysis in Chemistry and the Chemical Industry by Bennett and Franklin – Wiley – 5th printing January 1967 under the chapter sub-heading “Analysis of Variance for Polynomial Regression.” The text and discussion are too long to attempt to summarize on a forum of this type but you should be able to get a copy of this book through inter-library loan.

    If you can’t get this book then you might want to do a search on the web for the same topic – Analysis of Variance for Polynomial Regression – and see if anyone has provided the details.

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