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

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter11: Data Analysis And Displays
Section11.3: Shapes Of Distributions
Problem 14E
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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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