Mann-Whitney U-test

Fig. 19.3. Analysis of (A) lgG1 and (B) lgG2a titres in BALB/c mice exposed to either ES-62, or ES-62 manufactured in the presence of HC-3. Specific lgG2a titres were significantly higher in mice inoculated with ES-62 synthesized in the presence of HC-3 (P< 0.05 Mann Whitney U test). Results are expressed as mean reciprocal endpoint dilutions sem (n = 4).

Fig. 17.2 Pasting rates of male and female spotted hyenas by age. Male cubs pasted more frequently than female cubs (Mann-Whitney U test, U = 42, P = 0.03), however, no sex difference was apparent when the hyenas were subadults (U = 76, P = 0.71)...

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). 

The Mann-Whitney U test is employed for the count data, but which test should be employed for the percentage variables should be decided on the same grounds as described later under reproduction studies. 

When we find a significant difference, we do not know which groups are different. It is not correct to then perform a Mann-Whitney U Test on all possible combinations rather, a multiple comparison method must be used, such as the distribution-free multiple comparisons. 

Mann-Whitneys U test (Z reported) was used to examine sex differences in carotenoid pigmentation. Means S.D. are provided for each group. 

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. 

The distribution of number of new lesions (count data) is clearly not normal within each of the treatment groups. There is a peak at zero in each of the groups with then fewer and fewer patients as the number of lesions increases. A log transformation would not work here because of the presence of the zero values for the endpoint. The authors used the Mann-Whitney U-test to compare each of the natalizumab dose groups with placebo obtaining p < 0.001 in each case. Each dose level is significantly better than placebo in reducing the number of new enhancing lesions. 

It may seem strange to see the normal distribution play a part in the p-value calculations in Section 11.5.1 and 11.5.2. The appearance of this distribution is in no sense related to the underlying distribution of the data. For the Mann-Whitney U-test for example it relates to the behaviour of the average of the ranks within each of the individual groups under the assumption of equal treatments where the ranks in those groups of sizes and 2 simply a random split of the numbers 1 through to Hi -b 2-... 

C4,p-0.005 (Mann-Whitney U test). Result was compared with timolol release from unbuffered matrices containing c 50... 

Mann-Whitney Rank Sum Test, Sigmastat v 2.0 1 PERE = Potential Effluent Related Effect 3 NF (Nearfield) significantly greater than both Tunnel Bay and Santoy Bay reference areas, 4 t-tests, Mann-Whitney U-tests, Mann-Whitney rank sum tests, a = 0.05,5 National EEM database, unpublished data 6 significantly less at Santoy Bay reference area, Significant difference at Tunnel Bay. 

Behavioral data may be analyzed with the Mann-Whitney U test for comparing two groups (parametric Student s t test may be used only if data are normally distributed), or analysis of variance (ANOVA) for multiple groups, followed by an appropriate post hoc test. 

Figure 14.1b Bioessays using various synthetic blends show = mixture of all 12 EAD-active hydrocarbons (HCs) and mixture of (Z)-7 alkenes induced similar number of attractions and contacts (Mann-Whitney U test with P < 0.005, different letters indicate significant differences between groups). Behavioral responses to the all-alkene mixture are not different for the (Z)-7 alkene mixture all alkanes with dummy control show similar response with low approach and contact behaviors (from Mant et al., 2005a with approximate number of responses).

The principal measure taken is the animal s latency to cross to the dark compartment at T2. This score provides an estimate of the animal s retention of the shock received at Tl. The latencies measured at T2 have a 180 second cut-off. The scores in the control group are therefore abnormally distributed because of the presence of numerous ceiling scores. It is therefore essential to apply non-parametric statistics, for example the Mann-Whitney U-test, to analyze the data. 

Parametric data were presented as mean SD. To determine differences in glutamate concentrations, a repeated-measures analysis of variance was performed. The cutaneous sensation, hind-limb motor function, and morphological changes of the spinal cord were analyzed with a non-parametric method (Kruskal-Wallis test) followed by the Mann-Whitney U-test. 

The nonparametric Mann-Whitney U-test for the comparison of two independent sets of data, without accepting normal distributions, uses the ranks of all the observations, previously arranged from the lowest to the highest value, to test Ho = mediani = median2 (Massart et al. 1990 O Mahony 1986). If P < a, Ho is rejected. 

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. ... 

Percent aphids settled on control (C) and treated (T) disks. Significant difference, p<0.05, Mann-Whitney U-Test. 

The Mann-Whitney U-test was used to test for differences between two samples that might represent different populations. The frequency distribution of the variables was examined by applying the Kolmogorov-Smimov test. The 95% confidence interval of the median was calculated according to the equation... 

Fig. 26.6 The time between contact and the cradle-carrying behavior in male shore crabs (red or green color morphs) exposed to copper chloride (CuCl2) (0.1 or 0.5 mg L 1 Cu) and in control males. The male stands guard over the female and this guarding behavior is induced by pheromones in the female urine. Kruskal-Wallis nonparametric variance analysis followed by Mann Whitney U-test, demonstrated that the latency between contact and cradle-carrying was longer in copper exposed male compare to the unexposed controls (figure from Krang and Ekerholm 2006 photo by K. Reise). Figure reprinted with permission from Elsevier...

By employing a statistical test method, e.g. f-test or Mann-Whitney U test [25], a P value can be computed for strictly assessing whether the mean of D is significantly different from zero (P<0.05) or not (P>0.05). If P<0.05, the sign of the mean of D is then used to compare which model (variable set) is of better predictive performance. If P>0.05, we say two models have the same predictive ability. 

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