Measuring the relationship between scores on two questionnaires

Characterising the relationship between participants’ scores on two different questionnaires is a common problem in educational research. The complement of the statistic known as Wilks’ Λ (lambda) measures the amount of variance shared between the scores obtained by the same group of participants on two sets of variables. (1 − Λ) is symmetric, in that it yields the same outcome whichever of the two sets is defined as the dependent variables. Other measures of shared variance have been proposed, but they are systematically conservative in comparison with (1 − Λ). In particular, measures of redundancy underestimate the proportion of shared variance because they fail to take into account the multivariate properties of the data. In short, (1 − Λ) can be commended for use as a measure of the strength of the association between the scores obtained on two questionnaires.