Expected Results when the Independent Variable is NOT effectiveThese are the kind of results we expect when the Independent Variable is NOT effective

Expected Results when the Independent Variable IS EffectiveThese are the kind of results we expect when the Independent Variable is Effective

Variance is Standard Deviation Squared Another name for Variance is "Mean Square" Variance is "Sum of Squares" divided by "Degrees of Freedom" "Mean Square" is the "average Sum of Squares" 


Source 





Numerator of F 
Between Groups 
2 
90013.3423 
45006.6712 
4.5235 
Denominator of F 
Within Groups 
12 
119393.6000 
9949.4667 

Total 
14 
209406.9423 
Denominator of the FRatio. This is always an estimate of population variance


Error Variance 
An estimate of population variable that does not depend upon whether or not the indpendent variable was effective.

Within Groups SS 
Calculate the Sum of Squares for each group of subjects. The degrees of freedom for each of these sums is one less than the number of scores in that group. Add together the sum of squares for the groups to get the Within Groups Sum of Squares. 
Error Variance aka Mean Square Within Groups 
Divide "Within Groups SS" by the DF 
Numerator of the Fratio. Its meaning depends upon whether or not the Ho is True or False.


Between Groups Variance 
If the independent variable was NOT effective then this number estimates population variance If the independent variable WAS effective, then this number is larger than population variance. 


Between Groups SS  For its calculation, see below. 
Between Groups Mean Square  Divide the Between Groups SS by (the number of groups less 1). 
Here is a less obvious situation. Was the independent variable effective? 


Source 





Between Groups 
2 
33157.2022 
16578.6011 
1.2471 

Within Groups 
12 
159518 
13293.20000 

Total 
14 
192675.6022 


Source 





Between Groups 
2 
90013.3423 
180545.6712 
4.5235 

Within Groups 
12 
119393.6000 
9949.4667 

Total 
14 
209406.9423 


Source 





Between Groups 
2 
68824.9385 
34412.4692 
2.5486 

Within Groups 
12 
162028.400 
13502.3667 

Total 
14 
230853.3385 