744 APPENDIX A Tables and Formulas TABLE A-10 Runs Test for Randomness: Critical Values for Number of Runs G Value of n2 Value of n1 2 3 4 5 6 7 8 91011121314151617181920 2 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 3 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 6 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 1 1 1 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 6 8 9 9 91010101010101010101010101010 5 1 1 2 2 3 3 3 3 3 4 4 4 4 4 4 4 5 5 5 6 8 910101111121212121212121212121212 6 1 2 2 3 3 3 3 4 4 4 4 5 5 5 5 5 5 6 6 6 8 910111212131313131414141414141414 7 1 2 2 3 3 3 4 4 5 5 5 5 5 6 6 6 6 6 6 6 8 10 11 12 13 13 14 14 14 14 15 15 15 16 16 16 16 16 8 1 2 3 3 3 4 4 5 5 5 6 6 6 6 6 7 7 7 7 6 8 10 11 12 13 14 14 15 15 16 16 16 16 17 17 17 17 17 9 1 2 3 3 4 4 5 5 5 6 6 6 7 7 7 7 8 8 8 6 8 10 12 13 14 14 15 16 16 16 17 17 18 18 18 18 18 18 10 1 2 3 3 4 5 5 5 6 6 7 7 7 7 8 8 8 8 9 6 8 10 12 13 14 15 16 16 17 17 18 18 18 19 19 19 20 20 11 1 2 3 4 4 5 5 6 6 7 7 7 8 8 8 9 9 9 9 6 8 10 12 13 14 15 16 17 17 18 19 19 19 20 20 20 21 21 12 2 2 3 4 4 5 6 6 7 7 7 8 8 8 9 9 91010 6 8 10 12 13 14 16 16 17 18 19 19 20 20 21 21 21 22 22 13 2 2 3 4 5 5 6 6 7 7 8 8 9 9 910101010 6 8 10 12 14 15 16 17 18 19 19 20 20 21 21 22 22 23 23 14 2 2 3 4 5 5 6 7 7 8 8 9 9 91010101111 6 8 10 12 14 15 16 17 18 19 20 20 21 22 22 23 23 23 24 15 2 3 3 4 5 6 6 7 7 8 8 9 9101011111112 6 8 10 12 14 15 16 18 18 19 20 21 22 22 23 23 24 24 25 16 2 3 4 4 5 6 6 7 8 8 9 910101111111212 6 8 10 12 14 16 17 18 19 20 21 21 22 23 23 24 25 25 25 17 2 3 4 4 5 6 7 7 8 9 91010111111121213 6 8 10 12 14 16 17 18 19 20 21 22 23 23 24 25 25 26 26 18 2 3 4 5 5 6 7 8 8 9 91010111112121313 6 8 10 12 14 16 17 18 19 20 21 22 23 24 25 25 26 26 27 19 2 3 4 5 6 6 7 8 8 9101011111212131313 6 8 10 12 14 16 17 18 20 21 22 23 23 24 25 26 26 27 27 20 2 3 4 5 6 6 7 8 9 9101011121213131314 6 8 10 12 14 16 17 18 20 21 22 23 24 25 25 26 27 27 28 NOTES: 1. The entries in this table are the critical G values, assuming a two-tailed test with a significance level of a = 0.05. 2. Reject the null hypothesis of randomness if either of these conditions is satisfied: • The number of runs G is less than or equal to the smaller entry in the table. • The number of runs G is greater than or equal to the larger entry in the table. From “Tables for Testing Randomness of Groupings in a Sequence of Alternatives,” The Annals of Mathematical Statistics, Vol. 14, No. 1. Reprinted with permission of the Institute of Mathematical Statistics.
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