Signed rank 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. 

If a normal distribution is not assumed, the Wilcoxon matched-pairs signed-ranks test can be used to test Ho = p,d = 0. 

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. 

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). 

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. 

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

Significantly different from controls (P< 0. 05), Wilcoxon one-tailed Matched-pairs signed ranks test. 

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