In the table:
SSB = Between Group Sum-of-Squares
SSW = Within Group Sum-of-Squares
k = number of groups
N = n1 + n2 +...+ nk
MSW = SS_W/(N-k)
MSB = SS_B/(k-1)
F = (S_B^2)/(S_W^2 )
SSt = 〖ΣX〗^2-〖ΣX〗^2/N
Where:
Σn(X_1-X_GM) - “sum of squares between groups”, denoted by SSB
Σ(n_1-1)S_1^2 - “sum of squares between groups”, denoted by SSB
If there is no difference from the means:
• the between-group variance estimate will be approximately equal to the within-group variance estimate
• F Test value will be approximately equal to 1
• the null hypothesis will not be rejected
However, if the means differ significantly:
• the between-group variance will be much larger than the within-group variance
• F Test value will be significantly greater than 1
• the null hypothesis will be rejected
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