Wiggles and Curves: The Analysis of Ordinal Patterns

Abstract

Almost all social science data are analysed with variants of the General Linear Model (GLM): regression analyses, analyses of variance, factor analyses, path analyses and the like. However, many interesting and important social phenomena cannot be addressed with the GLM. Ordinal Pattern Analysis (OPA) was developed to examine such excluded phenomena. OPA is a goodness-of-fit procedure for calculating indices of how well a researcher's ordinal predictions match the ordinal properties of data at hand. While the GLM requires raw data to be aggregated across individuals or groups first before being analysed, OPA permits the reverse: Raw data from each individual or group can first be analysed, then aggregated. The reversal reveals what occurs "in general" rather than "on average" – two revelations that often diverge. We illustrate some uses of OPA with simple examples, and provide a computer programme for expediting OPA calculations.

Keywords

• statistics
• inference
• goodness-of-fit
• ordinal
• pattern