= How do I work out degrees of freedom for terms in an ANOVA? =

For N subjects and g group variables (factors) with respective levels L1, L2, ... , Lg and a within subjects factors, W, the table below gives the degrees of freedom for various types of sources variation in an analysis of variance.

|||| '''Source of variation'''|| '''df''' ||
|||| Factor || L1-1 ||
|||| 2-way interaction || (L1-1)(L2-1) ||
|||| K-way interaction of factors || $$\prod_text{k} (L_text{k}-1)$$ ||
|||| ''Between subjects error terms'' || ||
|||| Error (one-way anova between subjects) || N - L1 ||
|||| Error (between subjects) || N - df of terms involving between subjects factors - 1 ||
|||| ''Within subjects error terms'' || ||
|||| Error (subjects x W1), no between subjects factor || (N-1)(L1-1) ||
|||| Error (subjects x W1 x W2, no between subjects factor ) || (N-1)(L1-1)(L2-1) ||
|||| Error (subjects x W1 x W2, 1 between subjects factor) || (N-L1)(L2-1)(L3-1) ||
|||| Error (subjects x Within subjects interaction) || df of Error (between subjects) x df(Within subjects interaction term) ||

__Reference__

Boniface DR (1995) Experiment design and statistical methods for behavioural and social research. Chapman and Hall:London. (This book contains further details about computing degrees of freedom and also SS in balanced designs for terms in an ANOVA).