688 CHAPTER 13 Nonparametric Tests Yes No No Yes Yes No Start The test statistic is G. Use Table A-10 to get the critical values. Does a5 0.05? Is n2 > 20? Determine the critical values of z from Table A-2 as usual. (If a5 0.05, the critical values are 21.96 and 1.96.) Calculate the test statistic Is n1 > 20? Identify a sequence of two different characteristics. Determine the value of n1, the number of elements of the first type. Determine the value of n2, the number of elements of the second type. Reject randomness if the test statistic is less than or equal to the smaller critical value or greater than or equal to the larger critical value. Otherwise, fail to reject the null hypothesis of randomness. Determine the value of G, the number of runs. z 5 G2mG sG Calculate mG5 1 1 2n1n2 n1 1n2 Calculate sG5 2n1n2(2n1n2 2n1 2n2) (n1 1n2) 2(n 1 1n2 2 1) Î FIGURE 13-5 Procedure for Runs Test for Randomness Sports Hot Streaks It is a common belief that athletes often have “hot streaks”— that is, brief periods of extraordinary success. Stanford University psychologist Amos Tversky and other researchers used statistics to analyze the thousands of shots taken by the Philadelphia 76ers for one full season and half of another. They found that the number of “hot streaks” was no different than you would expect from random trials with the outcome of each trial independent of any preceding results. That is, the probability of making a basket doesn’t depend on the preceding make or miss. I b a h s t p
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