A note on the runs test

摘要

After the idea was conveyed by Swed and Eisenhart [5], the runs test has been used in many areas for checking the randomness of a sequence containing two kinds of items. A special application of the runs test is to check whether or not a serial correlation exists among the residuals in a regression analysis model. Because of its simplicity, the runs test is used by many statistics users, and is covered by many statistics textbooks. The purpose of this short note is to propose an alternative way for conducting the runs test. Instead of looking at the number of runs, the proposed method pays more attention to the number of shifts in the sequence. Compared with the runs test, the proposed method is easier to use for the statistics users. Since the distribution of the number of shifts is a binomial distribution with success probability 0.5, the expression of the critical values and the p-values of the statistical tests are of closed forms. No special tables are needed for the test. Finally, power study is conducted to evaluate the performance of the proposed method. It is found that the proposed test statistic possesses comparable power to the runs test.