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    In a one-way ANOVA, why does reducing the standard deviation of subjects to zero decrease the F-Value and make the test insignificant?
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    Because when the sum of the squares is smaller, the alternative hypothesis tends to be false.
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    F = MS(model)/MS(residual)

    where MS = SS/df for each type of class variability. If variability = 0, then both types of MS = 0.

    e.g., if the sum of squares for your model is 0 for the 3 group scenario, then df = N-1 = 2.

    Therefore 0/2 = 0.

    Similarly, if the df for the residual = 12, then for no variability, SS = 0 and MS = 0/12 = 0.

    Thus, F = 0/0 = 0

    In essence, if SD = 0, then all the data is the same score - of course they can't be derived from different populations. It's the perfect nil hypothesis.
 
 
 

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