A statistical test of independence in choice data with small samples

This paper develops tests of independence and stationarity in choice data collected with small samples. The method builds on the approach of Smith and Batchelder (2008). The technique is intended to distinguish cases where a person is systematically changing ``true'' preferences (from one group of trials to another) from cases in which a person is following a random preference mixture model with independently and identically distributed sampling in each trial. Preference reversals are counted between all pairs of repetitions. The variance of these preference reversals between all pairs of repetitions is then calculated. The distribution of this statistic is simulated by a Monte Carlo procedure in which the data are randomly permuted and the statistic is recalculated in each simulated sample. A second test computes the correlation between the mean number of preference reversals and the difference between replicates, which is also simulated by Monte Carlo. Data of Regenwetter, Dana, and Davis-Stober (2011) are reanalyzed by this method. Eight of 18 subjects showed significant deviations from the independence assumptions by one or both of these tests, which is significantly more than expected by chance.