Wilcoxon signed ranks test

Because age is not normally distributed here, the Wilcoxon signed rank test is used to calculate the p-value and is placed into a data set called pvalue. (Inferential statistics are discussed further in Chapter 7.)... 

The p-value for the sign test or Wilcoxon signed rank test can be found in the pValue variable in the pvalue data set. If the variable is from a symmetric distribution, you can get the p-value from the Wilcoxon signed rank test, where the Test variable in the pvalue data set is Signed Rank. If the variable is from a skewed distribution, you can get the p-value from the sign test, where the Test variable in the pvalue data set is Sign. ... 

Statistical analyses were performed with SPSS 8.0. We used a Wilcoxon signed ranks test to test for seasonality. To test for individuality we used a general linear model (GLM) with either individual or colony as a fixed factor. All tests were... 

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)...

To compare between days and locations I standardised visitation rates for each species by calculating visits to each odour type as a proportion of mean visits to the blank stations by that species, on that night, and at that location. By making the data proportional I removed effects of differing population size and density, as well as variation between nights, for example in moon phase. These data were checked for normality and symmetry, and subsequently analysed with a two-tailed Wilcoxon signed ranks test (Zar 1999) to determine whether visitation rate differed from a value of one (indicating no difference between visitation rate to an odour source... 

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

Having calculated the level of significance can be obtained from appropriate tables. The Wilcoxon signed rank test is the non-parametric equivalent of the paired t-test. The Kruskal-Wallis test is another rank sums test that is used to test the null hypothesis that k independent samples come from identical populations against the alternative that the means of the populations are unequal. It provides a non-parametric alternative to the one-way analysis of variance. 

Analysis of allergic mediators in nasal fluid before and immediately after the NAC showed that prostaglandin D2 concentration changes were significantly different from zero in the loratadine (two-tailed Wilcoxon signed rank test P = 0.006) and... 

The Wilcoxon signed rank test (two-tailed) is used to compare baseline recordings and recordings after substance administration. 

W - Significant differences between weekly and derived concentrations, based on Wilcoxon signed-ranks test, t - Significant differences between weekly and derived concentrations, based on paired t-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. 

HC-healthy controls (n = 20), MA-mild asthmatics (n = 20), NL nasal lavage, BW bronchial wash, BAL bronchoalveolar lavage. Data represented as medians, with interquartile and full ranges. Comparison of concentrations was performed using Wilcoxons-Signed-Rank-Test. p < 0.05, p < 0.01, p < 0.005. Plasma concentrations are illustrated for comparison. Based on data published by Kelly et al., 1999 [41]. 

The alpha spectrometry results were also significantly different at a 99% confidence level from the assigned NPL values (which deviations are 0% by definition). Application of the non-parametric Wilcoxon Signed Rank test, which, like the Rank Sum test, does not assume a normal distribution and does not require the removal of outliers, also resulted in a significant difference at a 99% confidence level between the alpha spectrometry results and the assigned NPL values (the absolute z-value being 3.72). 

The gamma spectrometry results were not significantly different from the assigned NPL values (Table 2), which was supported by Wilcoxon Signed Rank test (the z-value being 2.24). 

Wilcoxon signed rank test (paired or matched pairs)... 

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... 

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... 

While the results shown in Table 6.1 assume that the data resemble a normal probability distribution, some may argue the credibility of this assumption. Hence, a nonparametric hypothesis testing method (the Wilcoxon signed-rank test) was employed to confirm the significance of the results, assuming the distribution of data is not necessarily normal. The results for the nonparametric test as shown in Table 6.2 confirm that the results are statistically significant to the 0.01 level. 

Table 6.2 Nonparametric hypothesis test using Wilcoxon signed-rank test for the difference of group activity means before and after partieipating in the simulation exercises...

Mole rats groom significantly more in the presence of a conspecific than when they are caged alone (p<0.05, Wilcoxon sign rank test). 

Figure 4. The average number of events (grooming, scratching, and genital licking) during a 3-h exposure to room temperature , heat stress (cross hatched), and cold stress (shaded), in the summer (a) and in the winter (b). p< 0.05, Wilcoxon sign-ranked test.

The physiological and behavioral responses to heat stress in the winter were similar to those of the summer. However, the cold stress during the winter did not affect the animals body temperature, but was followed by a significant increase in grooming behavior (p<0.05, Wilcoxon sign ranked test Figure 4b). 

Figure 6. Mean ( SE) rate of attacks of test males and females towards either intact (a) males and (b) females before they groom , and after they groom , or towards Harderianectomized (Harx) (a) males and (b) females before they groom (diagonal lines) and after they groom (hatched bar) p< 0.05, Wilcoxon sign-ranked test.

Indicates p<.001. paired, within-subjects % test. Indicates p<.005, Wilcoxon signed-ranks test. 

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