To determine any pattern in an ordered binary sequence of wins and losses of a player over a period of time, the Runs Test may show results contradictory to the intuition visualised by scatter plots of win proportions over time. We design a test suitable for this purpose by computing the gaps between two consecutive wins and then using exact binomial tests and non-parametric tests like Kendall's Tau and Siegel-Tukey's test for scale problem for determination of heteroscedastic patterns and direction of the occurrence of wins. Further modifications suggested by Jan Vegelius(1982) have been applied in the Siegel Tukey test to adjust for tied ranks.
翻译:为确定玩家在一段时间内胜负有序二元序列中是否存在任何模式,游程检验可能会得出与随时间变化的胜率散点图所直观呈现的结果相矛盾的结论。我们通过计算连续两次获胜之间的间隔,并采用精确二项检验及肯德尔τ系数(Kendall's Tau)和西格尔-图基检验(Siegel-Tukey's test)等非参数检验方法,来解决异方差模式及获胜方向判定中的尺度问题。针对西格尔-图基检验中存在的并列秩次调整问题,我们进一步采纳了Jan Vegelius(1982)提出的改进方案。