Ordinal Pattern Analysis: A Tutorial on Assessing the Fit of Hypotheses to Individual Repeated Measures Data


 
 This article provides a tutorial introduction to ordinal pattern analysis, a statistical analysis method designed to quantify the extent to which hypotheses of relative change across experimental conditions match observed data at the level of individuals. This method may be a useful addition to familiar parametric statistical methods including repeated measures analysis of variance and generalized linear mixed-effects models, particularly when analyzing inherently individual characteristics, such as perceptual processes, and where experimental effects are usefully modeled in relative rather than absolute terms.
 
 
 
 Three analyses of increasing complexity are demonstrated using ordinal pattern analysis. An initial analysis of a very small data set is designed to explicate the simple mathematical calculations that make up ordinal pattern analysis, which can be performed without the aid of a computer. Analyses of slightly larger data sets are used to demonstrate familiar concepts, including comparison of competing hypotheses, handling missing data, group comparisons, and pairwise tests. All analyses can be reproduced using provided code and data.
 
 
 
 Ordinal pattern analysis results are presented, along with an analogous linear mixed-effects analysis, to illustrate the similarities and differences in information provided by ordinal pattern analysis in comparison to familiar parametric methods.
 
 
 
 Although ordinal pattern analysis does not produce familiar numerical effect sizes, it does provide highly interpretable results in terms of the proportion of individuals whose results are consistent with a hypothesis, along with individual and group-level statistics, which quantify hypothesis performance.
