Table 3. ANOVA Table Resulted from the Example.

	Sum of squares	Freedom	Mean sum of squares	F	Significance probability
Intergroup	273.875	2	136.937	3.629	0.031
	$$\sum _{\mathit{i}=1}^{\mathit{K}}{\mathit{n}}_{\mathit{i}}{\left({\stackrel{-}{\mathit{Y}}}_{\mathit{i}}-\stackrel{-}{\mathit{Y}}\right)}^2$$	(K − 1)	$$\sum _{\mathit{i}=1}^{\mathit{K}}{\mathit{n}}_{\mathit{i}}{\left({\stackrel{-}{\mathit{Y}}}_{\mathit{i}}-\stackrel{-}{\mathit{Y}}\right)}^2/\left(\mathit{K}-\mathrm{1}\right)$$
Intragroup	3282.843	87	37.734
	$$\sum _{\mathit{\text{ij}}=1}^{\mathit{n}}{\left({\mathit{Y}}_{\mathit{\text{ij}}}-{\stackrel{-}{\mathit{Y}}}_{\mathit{i}}\right)}^2$$	(N − K)	$$\sum _{\mathit{\text{ij}}=1}^{\mathit{n}}{\left({\mathit{Y}}_{\mathit{\text{ij}}}-{\stackrel{-}{\mathit{Y}}}_{\mathit{i}}\right)}^2/\left(\mathit{N}-\mathit{K}\right)$$
Overall	3556.718	89

Ȳⁱ is the mean of the group i; n_i is the number of observations of the group i; Ȳ is the overall mean; K is the number of groups; Y_ij is the j^th observational value of group i; and N is the number of all observational values. The F statistic is the ratio of intergroup mean sum of squares to intragroup mean sum of squares.