I am having difficulty understanding how the Mean Square Treatments should be approximately the same as the Mean Square Error if the null hypothesis is true.
For example:
Ho: mean 1 = mean 2 = .... = mean n
Ha: at least one mean is not equal
Based on the equation for SST and Mean Square Treatments, any time all the treatment means are equal to the grand mean then the Mean Square Treatment will be equal to 0. However, there can situations where the Mean Square Treatment is 0, but the Mean Square Error is not equal to 0.
The following dataset illustrates the point:
X1 Y
1 4
1 4
2 1
2 7
3 2
3 6
4 3
4 5
5 4
5 4
6 5
6 3
The data shows that the Mean Square Treatments = 0, but the Mean Square Error = 5.
Mean Square Treatments !~ Mean Square Error; even though, the degrees of freedom numerator and denominator are about the same.
Granted, the unequal variance assumption is probably broken.
Is there a visual or logical way to understand that the Mean Square Treatments is a variance estimate of both the treatments and the error?
Thank you,
negodfre
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