Evaluating order‐constrained hypotheses for circular data using permutation tests

Abstract

Psychological researchers in different fields sometimes encounter circular or directional data. Circular data are data measured in the form of angles or two-dimensional orientations. As an example, experiments investigating the development of spatial memory and the influence of visual experience on haptic orientation perception are presented. Three permutation tests are proposed for the evaluation of ordered hypotheses. The quality of the permutation tests is investigated by means of several simulation studies. The results of these studies show the expected increase in power when the permutation tests for ordered hypotheses are compared to a common non-directional test for circular data. The differences in power between the three tests for ordered alternatives are small.

A Test of Order-Constrained Hypotheses for Circular Data With Applications to Human Movement Science

“…The methods developed in this study generalize the methods by Klugkist et al (2012) and Barragán et al (2011) such that data from a within-subjects design can be evaluated as well. Moreover, the methods do not require the assumption that the data are Von Mises distributed.…”

“…When angles can be seen as values on the interval [0, 2π ], the same kind of ordering that we know from linear data can be used. In this context Klugkist et al (2012) constructed a randomization test for hypotheses containing a simple ordering with regard to a between-subjects design.…”

“…In the specific case of hypotheses concerning a simple ordering in which all angles of interest can be arranged subsequently from small to large (e.g., µ 1 < µ 2 < µ 3 ), Klugkist et al (2012) showed that a randomization method for circular data from a between subjects design can be as much as 20% more powerful than a standard circular ANOVA test (Mardia & Jupp, 2000). The goal of this study was to develop resampling methods for circular data that can be used to test hypotheses involving any kind of ordering.…”

“…To avoid these shortcomings, past research in linear statistics has seen a steady development of methods that can directly test such order-constrained hypotheses (e.g., Barlow, Bartholomew, Bremner, & Brunk, 1972;Robertson, Wright, & Dykstra, 1988;Silvapulle & Sen, 2005). Recently the issue of evaluating order constraints has become increasingly popular in circular statistics (see Barragán, Fernández, Rueda, & Peddada, 2011;Klugkist, Bullens, & Postma, 2012;Rueda, Fernández, & Peddada, 2009). Yet even though more often than not researchers have ordered expectations regarding circular data as well, the methods presently available are still very limited.…”

Bayesian Evaluation of Informative Hypotheses

“…In the frequentist framework, hypothesis testing with inequality constraints has been studied over fifty years starting with (Bartholomew, 1959). Some recent contributions can be found in van de Schoot et al (2010), and Klugkist, Bullens, and Postma (2012). Bayesian evaluation of informative hypotheses by means of the Bayes factor is relatively new.…”