APA Dictionary of Psychology

(symbol: F) in an analysis of variance or a multivariate analysis of variance, the amount of explained variance divided by the amount of the error variance; that is, the ratio of between-groups variance to within-group variance. Its value determines whether to accept the null hypothesis stating that there is no difference between the treatment and control conditions, with a large value indicating the presence of a significant effect. Ideally, a researcher prefers to have rather small variation within each group and maximal variation between the groups in order to demonstrate significant group differences. Also called F statistic; F value.