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If ANOVA tests the homogeneity of means then why the test statistics involves the standard deviation ... F=MSSE/MSST only involves variance ... is there anyone who knows the logic behind it?

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    $\begingroup$ As you move the means further apart but keeping the distribution within the groups the same you will increase the between groups variance. $\endgroup$
    – mdewey
    Commented Dec 20, 2016 at 14:47
  • $\begingroup$ Mdewey could u explain please $\endgroup$ Commented Dec 20, 2016 at 14:52
  • $\begingroup$ You are dividing the between by the within to get F (I do not know what your symbols mean). So if you hold within constant and increase between then F increases. $\endgroup$
    – mdewey
    Commented Dec 20, 2016 at 17:22

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