Wilcoxon’s tests

All quantitative, continuously distributed data are expressed as mean SEM. Significance of differences between groups is determined using Wilcoxon s test. Statistical evaluation of severity grades to determine differences between treatment groups is inappropriate. 

Statistical evaluation. Student s t-test (two-tailed) was used for weight of rats and food intake. Differences in plasma lipids, lipoproteins and lipoprotein lipase activities were evaluated with Wilcoxon s test (two-tailed). 

The Wilcoxon s Rank-Sum Test (WRST) is a non-parametric alternative. The WRST is robust to the normal distribution assumption, but not to the assumption of equal variance. Furthermore, this test requires that the two groups of data under comparison have similarly shaped distributions. Non-parametric tests typically suffer from having less statistical power than their parametric counterparts. Similar to the /-test, the WRST will exhibit false positive rate inflation across a microarray dataset. It is possible to use the Wilcoxon test statistic as the single filtering mechanism however calculation of the false positive rate is challenging (48). 

Fig. 7. Effects of L-PDMP on spatial cognition deficit induced by repeated cerebral ischemia. (A) Protocol for behavioral experiments to evaluate the efficacy of L-PDMP against spatial cognition deficit in rats with cerebral ischemia. (B) Sham (sham-operated rats, n — 11), Group 1-vehicle, l-PDMP (i.p. injections of vehicle or 40 mg/kg L-PDMP twice a day for 6 days from 24 h after ischemia, n = 13), Group 2-vehicle, L-PDMP (i.p. injection of vehicle or 40 mg/kg L-PDMP twice a day for 4 days from 3 days after ischemia, n — 9 and n — 10, respectively). P < 0.001 versus sham-operated rats, P < 0.05 and P < 0.01 versus vehicle-treated rats (Wilcoxon s rank sum test).

Test for significance among the different treatments, using Friedman s test for related samples. The days are blocks for this test. If significant overall, examine differences between pairs of treatments by the Wilcoxon signed ranks test. Remember, the main question is whether predator odor reduces feeding. 

Suitable non-parametric comparisons of location for paired quantitative data (sample size > 6) include Wilcoxon s signed rank test, which assumes that the distributions have similar shape. 

There are times when the required assumptions for ANOVA, a parametric test, are not met. One example would be if the underlying distributions are non-normal. In these cases, nonparametric tests are very useful and informative. For example, we saw in Section 11.3 that a nonparametric analog to the two-sample ttest, Wilcoxon s rank sum test, makes use of the ranks of observations rather than the scores themselves. When a one-factor ANOVA is not appropriate in a particular case a corresponding nonparametric approach called the Kruskal-Wallis test can be used. This test is a hypothesis test of the location of (more than) two distributions. 

In the Kruskal-Wallis test the original scores are first ranked and an ANOVA analysis is then carried out on the ranks. As with Wilcoxon s rank sum test, ranking of the observations must deal with ties. The sums of squares are based on... 

For each estimation/measurement, the mean of the values obtained from six control and/or experimental animals was taken into consideration. Standard deviations were calculated and Wilcoxon s r-test was employed to derive the level of significance between the means of controls and experimentals. The level at 5% or below was considered significant. 

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... 

Nonparametrical statistical test (Wilcoxon matched pairs test) were applied for two-choice experiments because data were characterized by a high level of variability. The sexual activation experiment was analyzed by Student s test. 

Statistical analysis was formed by using a commercially available computer programme (Analyse-It, Andyse-It Software Ltd, Leeds, UK). Differences between various pressures and LD blood flow values over one cycle were analysed using Student s t-test or the Wilcoxon s signed rank test depending on whether or not data were normally distributed. A difference was considered significant when p<0.05. 

P-values Age = Wilcoxon rank-sum, Gender = Pearson s chi-square, Race = Fisher s exact 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). 

Statistical Analysis. Analysis of variance (ANOVA) of toxicity data was conducted using SAS/STAT software (version 8.2 SAS Institute, Cary, NC). All toxicity data were transformed (square root, log, or rank) before ANOVA. Comparisons among multiple treatment means were made by Fisher s LSD procedure, and differences between individual treatments and controls were determined by one-tailed Dunnett s or Wilcoxon tests. Statements of statistical significance refer to a probability of type 1 error of 5% or less (p s 0.05). Median lethal concentrations (LCjq) were determined by the Trimmed Spearman-Karber method using TOXSTAT software (version 3.5 Lincoln Software Associates, Bisbee, AZ). 

Verapamil and its active metabolite norverapamil were assayed from serum (frozen at -18°C) using a gas chromatographic-mass spectrometric method [5]. The detection limit of the method was 1 ng/ml. The areas under the concentration-time curves (AUC 0-32 h) were calculated by the trapezoidal method. Statistical evaluation was carried out using the paired Wilcoxon test and paired Student s t test. 

Figure 3. The effect of fluence rate and light fractionation on BPD-mediated PDT. BPD-MA was administered to rats with NBT II tumors implanted into the bladder wall. One hour later tumors were exposed to a total fluence of 30 J/cm of 690 nm irradiation under the following conditions 100 mWcm"- continuous 100 mW/cm - fractionated 15 s on/15 s off 100 mWcm 2 30 s on/30 s off 100 mWcm" 60 s on/60 s off. Tumors were disaggregated 24 h later and tumor cells were plated for colony formation assay. Colonies (50 cells or more) were counted 9 days later after fixing with methanol and staining with crystal violet. The Wilcoxon rank sum test was used to compare the number of clonogenic cells with data at 100 mWcm - and continuous wave irradiations. NS not significant. (Source linuma et al. [32]. Reproduced with permission.)...

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). 

Fig. 20.5 Using bioassay-guided fractionation to identify the molecular size of female sex pheromone. The dependent measure is the number of male blue crabs out of 72 tested that performed courtship stationary paddling. Stimuli were male or female urine fractionated into the indicated molecular sizes (S small <500 Da, M medium 500-1,000 Da, L large >1,000 Da, a mixture of S+M+L Mix) and positive control (unprocessed pubertal female urine = Urine) and a negative control (.SW sea water). Friedman ANOVA shows an overall difference in the responsiveness to these stimuli (P < 0.0001, n = 10). An asterisk marks stimuli that elicit significantly more males to respond compared to the sea water control (Wilcoxon post hoc tests, P < 0.05)...

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