Adapting the Robust Effect Size Cliff's Delta to Compare Behaviour Profiles

Abstract

Cliff’s Delta is a non-parametric effect size that is based on data observations. In this paper, we introduce an adaptation of Cliff’s Delta in order to compare behaviour profiles. Behaviour profiles are density distributions in which survey answer behaviour is summarized for specific groups of respondents or items. Such profiles are useful, as they take into account the varying number of survey items that is filled out per respondent due to filter questions. By the adapted Cliff’s Delta, two subgroups of respondents (for instance higher and lower educated respondents) can be compared on the occurrence of specific answer behaviour (for instance giving ‘don’t know’-answers). By means of simulations, we show that the adapted profile-based Cliff’s Delta converges towards the original observation-based Cliff’s Delta as the number of items that is filled out by respondents increases. We conclude that the profile-based Cliff’s Delta is a solid and conservative statistic that is both useful and advantageous to compare behaviour profiles. We close with various data examples to illustrate its broad usefulness and by discussing potential difficulty in using the profile-based Cliff’s Delta.