Why does the ANOVA use the variance differences, and not use mean differences from the data?

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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  1. Why does the ANOVA use the variance differences, and not use mean differences from the data?

       

    there is no difference whether you use the means or the variance in the numerator

       

    the means are a less accurate descriptive statistic than the variance

       

    none of the answers are correct

       

    calculating the difference of multiple means in the numerator would not make mathematical sense

     

     

    We are testing for the _____ when we are asking how much the independent variable affected the dependent variable.

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