<P> Comparing model to summaries: μ = m (\ displaystyle \ mu = m) and μ j = m j (\ displaystyle \ mu _ (j) = m_ (j)). The grand mean and grand variance are computed from the grand sums, not from group means and variances . </P> <P> Given the summary statistics, the calculations of the hypothesis test are shown in tabular form . While two columns of SS are shown for their explanatory value, only one column is required to display results . </P> <Table> ANOVA table for fixed model, single factor, fully randomized experiment <Tr> <Th> Source of variation </Th> <Th> Sums of squares </Th> <Th> Sums of squares </Th> <Th> Degrees of freedom </Th> <Th> Mean square </Th> <Th> </Th> </Tr> <Tr> <Th> </Th> <Th> Explanatory SS </Th> <Th> Computational SS </Th> <Th> DF </Th> <Th> MS </Th> <Th> </Th> </Tr> <Tr> <Th> Treatments </Th> <Th> ∑ T r e a t m e n t s I j (m j − m) 2 (\ displaystyle \ sum _ (Treatments) I_ (j) (m_ (j) - m) ^ (2)) </Th> <Th> ∑ j (∑ i y i j) 2 I j − (∑ j ∑ i y i j) 2 I (\ displaystyle \ sum _ (j) (\ frac ((\ sum _ (i) y_ (ij)) ^ (2)) (I_ (j))) - (\ frac ((\ sum _ (j) \ sum _ (i) y_ (ij)) ^ (2)) (I))) </Th> <Th> J − 1 (\ displaystyle J - 1) </Th> <Th> S S T r e a t m e n t D F T r e a t m e n t (\ displaystyle (\ frac (SS_ (Treatment)) (DF_ (Treatment)))) </Th> <Th> M S T r e a t m e n t M S E r r o r (\ displaystyle (\ frac (MS_ (Treatment)) (MS_ (Error)))) </Th> </Tr> <Tr> <Th> Error </Th> <Th> ∑ T r e a t m e n t s (I j − 1) s j 2 (\ displaystyle \ sum _ (Treatments) (I_ (j) - 1) s_ (j) ^ (2)) </Th> <Th> ∑ j ∑ i y i j 2 − ∑ j (∑ i y i j) 2 I j (\ displaystyle \ sum _ (j) \ sum _ (i) y_ (ij) ^ (2) - \ sum _ (j) (\ frac ((\ sum _ (i) y_ (ij)) ^ (2)) (I_ (j)))) </Th> <Th> I − J (\ displaystyle I-J) </Th> <Th> S S E r r o r D F E r r o r (\ displaystyle (\ frac (SS_ (Error)) (DF_ (Error)))) </Th> <Td> </Td> </Tr> <Tr> <Th> Total </Th> <Th> ∑ O b s e r v a t i o n s (y i j − m) 2 (\ displaystyle \ sum _ (Observations) (y_ (ij) - m) ^ (2)) </Th> <Th> ∑ j ∑ i y i j 2 − (∑ j ∑ i y i j) 2 I (\ displaystyle \ sum _ (j) \ sum _ (i) y_ (ij) ^ (2) - (\ frac ((\ sum _ (j) \ sum _ (i) y_ (ij)) ^ (2)) (I))) </Th> <Th> I − 1 (\ displaystyle I - 1) </Th> </Tr> </Table> <Tr> <Th> Source of variation </Th> <Th> Sums of squares </Th> <Th> Sums of squares </Th> <Th> Degrees of freedom </Th> <Th> Mean square </Th> <Th> </Th> </Tr>

The expected value of the error mean square in the single-factor anova is