Nonparametric and Resampling Statistics. Wilcoxon Rank-Sum Test . To compare two independent samples Null is that the two populations are identical The test statistic is W s , Table of Critical Vals . For large samples, there is a normal approx. Is equivalent to the Mann-Whitney test.
A Wilcoxon rank-sum test indicated that babies whose mothers started prenatal care in the first trimester weighed significantly more (N = 8, M = 3259 g, Mdn = 3015 g, s = 692 g) than did those whose mothers started prenatal care in the third trimester (N = 10, M = 2576 g, Mdn = 2769 g, s = 757 g), W = 52, p = .034.
A Wilcoxon signed-ranks test indicated that participants who were injected with glucose had significantly better recall (M = 7.62, Mdn = 8.5, s = 3.69) than did subjects who were injected with saccharine (M = 5.81, Mdn = 6, s = 2.86), T(N = 16) = 14.5, p = .004.
Kruskal-Wallis ANOVA indicated that type of drug significantly affected the number of problems solved, H(2, N = 19) = 10.36, p = .006. Pairwise comparisons made with Wilcoxon’s rank-sum test revealed that .........
Friedman’s ANOVA indicated that judgments of the quality of the lectures were significantly affected by the number of visual aids employed, (2, n = 17) = 10.94, p = .004. Pairwise comparisons with Wilcoxon signed-ranks tests indicated that .......................
We repeat this process, obtaining a second sample of 20 scores and computing and recording a second median.
We continue until we have obtained a large number (10,000 or more) of resample medians. We obtain the probability distribution of these medians and treat it like a sampling distribution.
From the obtained resampling distribution, we find the .025 and the .975 percentiles. These define the confidence limits.
From the resulting resampling distribution of values of r, we obtain the .025 and .975 percentiles. This is the confidence interval for our sample r.
We continue this until we have assigned 49 scores to the success group. The remaining 17 scores are assigned to the fail group.
We compute the medians of the resulting groups and then the difference between those medians. We record the difference in medians.
We put the 67 scores back in the pot and repeat the process, obtaining and recording a second difference in medians for the resulting sample of 49 scores assigned to one group, 17 to the other group.
We repeat this procedure a large number of times. The resulting set of differences in medians is our resampling distribution under the null of no difference in population medians.
We map out the nonrejection region (typically the middle 95% of the resampling distribution.
If the observed difference in sample medians falls outside of the nonrejection region, then the difference is significant.
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We take the 19 difference scores, strip them of their signs, and then randomly assign signs to them.
From the resulting sampling distribution under the null hypothesis of no difference in population means (that is, a mean difference score of 0), we compute our p value by finding what proportion of the resampled t values differ from 0 by at least as much as did the t from our actual samples.