It is suggested that many analyses of laterality are fundamentally confused in that they fail to distinguish between differences in degree of laterality and differences in direction of laterality, and that direction and degree of laterality have different biological and psychological interpretations. Conventional statistical tests, such as analysis of variance or non-parametric procedures, are unable to differentiate the two measures, and necessarily produce uninterpretable results. A maximum likelihood method is described which can discriminate between direction and degree, and its applications to factorial, test-retest, and repeated measure designs is explained. Two worked examples are also given, one based on hypothetical data, the other on actual data.