Can the Committee Meet? A Markov Chain Analysis

Abstract

If the 5-digit numbers have been generated at random, the test statistic is the value of an approximate chi-squared random variable having expected value 3. Values significantly greater than 3 indicate systematic departures from randomness. Our value of 1.837 shows a better than expected agreement. (A statistician would not consider rejecting the hypothesis of randomness unless the test statistic exceeded 6.25, the critical value for a level .10 test.) Thus the MINITAB data pass our test with flying colors. (Notes on this test: (a) The degrees of freedom are one fewer than the number of categories, which in our case is 4 1. (b) Not all authors agree on how large a sample is required for the chi-squared test to be appropriate. There is general agreement that all Eis should be at least one. Cochran [1] suggests that at least 80% of the expected cell frequencies should be 5 or greater. Moore [5] says this is too conservative.)