Detecting Patterns by One-Sample Runs Test: Paradox, Explanation, and a New Omnibus Procedure.

Abstract The standard nonparametric 1-sample runs test, which is based on the total number of runs, has recently been found to give anomalous results in the case of data consisting solely of runs of length 2. Furthermore, tests based on the total number of runs provide little information as to the length of the individual runs. An explanation for that anomaly is provided, and tests based on the length of runs are described. Such tests can be successfully applied to runs of length 2 but usually use asymptotic methods of assessing statistical significance. In addition, such tests generally impose arbitrary limits as to the maximum run length. A new procedure that allows the maximum run length to be empirically determined is described. In that procedure, one uses a Monte Carlo permutation test to ascertain statistical significance. The new Monte Carlo omnibus length-of-runs procedure is illustrated with examples from suicide research and from psycholinguistics.