Mann-Whitney-Wilcoxon test

Rank test. A statistical test, such as the Mann-Whitney-Wilcoxon test, carried out on the ranks of the data rather than on the original data. Thus, the statistic used in the test, the rank statistic, is calculated from ranks of the data. Usually such tests are associated with randomization. Given knowledge of the randomization procedure, the distribution of the rank statistic is perfectly general under the null h5q)othesis. The rank is but the guinea stamp. The Mann s the gowd for a that (Burns). 

The Wilcoxon rank-sum test is a nonparametric test for assessing whether two samples of measurements come from the same distribution. That is, as an alternative to the two-sample f-test, this test can be used to discover differentially expressed candidates under two conditions. For example, again consider the measurements of the probe set used for the two-sample t-test. The gene expression values are 12.79, 12.53, and 12.46 for the naive condition and 11.12, 10.77, and 11.38 for the 48-h activated condition. Measurement 12.79 has rank 6, measurement 12.53 has 5, and measurement 12.46 has rank 4. The rank sum of the naive condition is 6 -I- 5 -I-4=15. Then after the sum is subtracted by ni(ni-I-l)/2 = 3 x 4/2 = 6, the Wilcoxon rank-sum test statistic becomes 9. Considering all of the combinations of the three measurements, we can compute the probability that the rank sum happens more extremely than 9. The probability becomes its p-value. This is the most extreme among the 20 combinations thus the p-value is 2 x Pr( W > 9) = 2 x = 0.1 for the two-sided test. It is hard to say that the probe set is differentially expressed since the p-value 0.1 > 0.05. This test is also called the Mann - Whitney- Wilcoxon test because this test was proposed initially by Wilcoxon for equal sample sizes and extended to arbitrary sample sizes by Mann and Whitney. As a nonparametric alternative to the paired t-test for the two related samples, the Wilcoxon signed-rank test can be used. The statistic is computed by ordering absolute values of differences of paired samples. For example, consider a peptide in the platelet study data. Their differences for each... 

Mann-Whitney U Test n Also known as the Wilcoxon-Mann-Whitney test, the Mann-Whitney-Wilcoxon test, the MWW test, or the Wilcoxon rank-sum test is a nonparametric test used to test whether two samples of different sizes come the same population or populations with the same distribution. The samples must be independent. 

MWW Test n short for the Mann-Whitney-Wilcoxon Test, and alternate name for the Mann-Whitney U Test. 

Fig. 17.3 Proportion of spotted hyena pastings that were overmarks by age and sex. Males increased their overmarking activity with age (Wilcoxon signed-rank test, S = 32.5, P = 0.04), however, females did not (cub vs. subadult S = — 15.5, P = 0.24 across subadult periods N = 6, Friedman ANOVA x2 = 3.5, P = 0.17). Although male and female cubs did not differ in their frequency of overmarking (Mann-Whitney U test, U = 75, P = 0.67), a sex difference was apparent among subadults (U = 37, P = 0.02)...

The analysis of rank data, what is generally called nonparametric statistical analysis, is an exact parallel of the more traditional (and familiar) parametric methods. There are methods for the single comparison case (just as Student s t-test is used) and for the multiple comparison case (just as analysis of variance is used) with appropriate post hoc tests for exact identification of the significance with a set of groups. Four tests are presented for evaluating statistical significance in rank data the Wilcoxon Rank Sum Test, distribution-free multiple comparisons, Mann-Whitney U Test, and the Kruskall-Wallis nonparametric analysis of variance. For each of these tests, tables of distribution values for the evaluations of results can be found in any of a number of reference volumes (Gad, 1998). 

Ordinal or numerical Mann-Whitney U test Wilcoxon signed rank test Kruskal-Wallis Friedman... 

The Mann-Whitney U-test is equivalent to an alternative test called the Wilcoxon rank sum test. These tests were developed independently, but subsequently shown to be mathematically the same. We will develop the test using the Wilcoxon rank sum methodology. 

It has been advocated that the area under the ROC curve is a relative measure of a tesfs performance. A Wilcoxon statistic (or equivalently the Mann-Whitney U-Test) statists cally determines which ROC curve has more area under it. Less computationally intensive alternatives, which are no longer necessary, have been described. These methods are particularly helpful when the curves do not intersect. When the ROC curves of two laboratory tests for the same disease intersect, they may offer quite different performances even though the areas under their curves are identical. The performance depends on the region of the curve (i.e., high sensitivity versus high specificity) chosen. Details on how to compare statistically individual points on two curves have been developed elsewhere. ... 

The choice of an appropriate statistical method is important, and a method suitable for the comparison of two groups in terms of an ordinal outcome measurement is the Mann-Whitney/Wilcoxon rank-sum test (not to be confused with the Wilcoxon matched-pairs signed ranks test, which is appropriate for paired data - see later). It is both inefficient and inappropriate to use a qualitative data test (such as a simple chi-square) for such a measurement, and the application of quantitative data tests (such as one of the f-tests) is also invalid. 

Chi-.square. binomial test, runs test, one-sample Kolmogorov Smirnov test. Mann-Whitney U test. Moses test. Wald-Wolfowitz test. Kruskal Wallis te.st, Wilcoxon signed rank test. Friedman s test. Kendall s W test, Cochran s Q test... 

Data distribution was examined by One-Sample Kolmogorov-Smimov test, and transformed by square root to fit the normal distribution (Sokal and Rohlf, 1995). The behavioral comparisons between the control and experiment were analyzed by Wilcoxon Rank test, and comparisons between sexual experience and odor effects on pandas behavioral responsiveness were analyzed by two-way ANOVA. Finally, the mating duration of familiar mates and strange mates were analyzed by Mann-Whitney U test. Significance level was 0.05. 

Comparisons between the sexes with respect to the size of the sternal gland indicate that it is longer, wider, and thicker in males than in females (P < 0.05 for each measure, Mann-Whitney U test Table 1). The active surface areas compared in 22 heterosexual pairs by the Wilcoxon matched-pairs sign rank test show that the gland is also more active... 

The tests which we can use to assess lifetime are Wilcoxon Rank Sum Test or Mann-Whitney U Test, Wilcoxon Signed Rank Test and Kruskal-Wallis test. 

Wilcoxon Rank Sum Test or Mann-Whitney U Test is the technique tests whether the medians of two populations are the same, when the two samples are independent of each other. This test is comparable to the parametric t-test on the difference between two means that we considered previously. Technique is followed merge and rank the observations and find the sum of the ranks Rj and... 

Ordinal Mann-Whitney U-test Wilcoxon Sign... 

The test statistics from a Mann-Whitney are linearly related to those of Wilcoxon. The two tests will always yield the same result. The Mann-Whitney is presented here for historical completeness, as it has been much favored in reproductive and developmental toxicology studies. However, it should be noted that the author does not include it in the decision tree for method selection (Figure 22.2). 

Non-parametric Mann-Whitney test Wilcoxon paired samples test Kruskal-Wallis test Spearman correlation... 

In case that both data sets to be compared are normally distributed the F-test is applied. The hypothesis of homogeneity of variance of both test series is eliminated when the significance level for homogeneity of variance is 5 %. The t-test for paired and non-paired data is performed when homogeneity of variance is present. In any case, a paired difference test (for paired data) or the U-test (for non-paired data) is likewise carried out (paired of difference test = Wilcoxon test U-test = Wilcoxon-Mann-Whitney or Mann-Whitney test, respectively). 

Feltovich, N. Nonparametric tests of differences in medians comparison of the wilcoxon-mann-whitney and robust rank-order tests. Exp. Econ. 6, 273-297 (2003)... 

Table 1. Mass (g diy weight m-2) of remaining and percent (%) of initial mass of exposed natural plant (NPL) and polypropylene (PP) litter during the course of the experiment. Significance of differences between treatments are assessed by non-parametric Wilcoxon Sum-of-Ranks (Mann-Whitney) test. AH data from five natural litter treatments (I Dactylis glomerata II Festuca rubra and III Trijblium pratense), IV mixture of three species I, II and III V mixture of twelve species, IV and nine other meadow plants) were analyzed with the exception of month where only data of treatments I and HI were used. Standard errors in parentheses.

The amounts of time spent investigating male vs. female odors and left vs. right screens (in the clean condition) as well as the number of entries into each arm in both conditions were compared by 1-tailed Wilcoxon tests. The total number of arm entries in both conditions were compared between groups (Mann-Whitney test) to determine if any differences existed in locomotor behavior. 

Friedman s repeated measures ANOVA. Differences in vaginal marking across estrous cycle days (D2 vs. PE) were analyzed within each odor condition and on combined scores with Wilcoxon tests. Mann-Whitney tests were used to compare the marking scores of LOT and sham females within each odor condition and cycle day as well as on scores collapsed across estrous days and odor conditions. Flank marking scores were only analyzed (Mann-Whitney test) between groups as LOT females almost never marked in any of the conditions. 

As the results were not distributed normally, median values were used for the descriptive statistics, while parameter-free test procedures were used for the analytical statistics (Wilcoxon test for paired differences by Wilcoxon/Mann and Whitney) (ClauC and Ebner 1992). 

A "comparison between groups," performed by the U test of Wilcoxon-Mann-Whitney. Only P values lower than 1% were considered statistically significant. 

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