6 wilcoxon - 1 Wilcoxon Rank-Sum Test, also known as the...

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1 Wilcoxon Rank-Sum Test, also known as the Mann-Whitney test Rank the data. That is replace, the data values by their ranks, from smallest to largest. For example, the pH samples are: Group 1: 8.53 8.52 8.01 7.99 7.93 7.89 7.85 7.82 7.80 Group 2: 7.85 7.73 7.58 7.40 7.35 7.30 7.27 7.27 7.23 are replaced by the ranks Group 1: 18 17 16 15 14 13 11.5 10 9 Group 2: 11.5 8 7 6 5 4 3 2 1 The tied values (7.85, 7.85) would have had ranks 11 and 12 were they slightly different. In the case of ties, assign the “mid-rank” [here (11+12)/2] to both values. Calculate W , which is the sum of the ranks in the first group. In this case, W = 123 . 5. Let n 1 be the number of observations in the first group, n 2 the number in the second group, and N = n 1 + n 2 . Here n 1 = n 2 = 9 and N = 18. Under the null hypothesis that the two disbributions are the same, the mean and variance of W are μ W = n 1 ( N +1) / 2 and σ 2 W = n 1 n 2 ( N +1) / 12, the observed value of the test statistic is
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6 wilcoxon - 1 Wilcoxon Rank-Sum Test, also known as the...

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