A0197
Title: A non-parametric approach to detect patterns in binary sequences
Authors: Anushka De - Indian Statistical Instiute (India) [presenting]
Abstract: In many circumstances, given an ordered sequence of one or more types of elements/ symbols, the objective is to determine any existence of randomness in the occurrence of one of the elements, say type 1 element. Such a method can be useful in determining the existence of any non-random pattern in the wins or losses of a player in a series of games played. Existing methods of tests based on a total number of runs or tests based on the length of the longest run can be used for testing the null hypothesis of randomness in the entire sequence and not a specific type of element. Additionally, the Runs Test tends to show results that are contradictory to the intuition visualised by the graphs of, say, win proportions over time due to the method used in the computation of runs. A test approach is developed to address this problem by computing the gaps between two consecutive type 1 elements and thereafter following the idea of pattern in occurrence and directional trend (increasing, decreasing or constant), employing the use of exact Binomial test, Kendall's Tau and Siegel-Tukey test for scale problem. Further modifications have been applied in the Siegel Tukey test to adjust for tied ranks and achieve more accurate results. This approach is distribution-free and suitable for small sizes. Also, comparisons with the conventional runs test show the superiority of the proposed approach under the null hypothesis of randomness in the occurrence of type 1 elements.
