In a balanced design (i.e. a design in which all cells have the same number of observations), if the effects in the linear model are random and normally distributed, the distribution of the ratio of any sum of squares (s.s.) in the ANOVA to the expected value of its mean square (m.s.) has a [chi][superscript 2]-distribution. In this note, we investigate the conditions under which this ratio is a [chi][superscript 2] if the design is not balanced.