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[Rank Transformations as a Bridge Between Parametric and Nonparametric Statistics]: Rejoinder

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Abstract

Many of the more useful and powerful nonparametric procedures may be presented in a unified manner by treating them as rank transformation procedures. Rank transformation procedures are ones in which the usual parametric procedure is applied to the ranks of the data instead of to the data themselves. This technique should be viewed as a useful tool for developing nonparametric procedures to solve new problems.
... For multiple comparisons, we apply a two-stage procedure, which starts with a Friedman test [8]. If the result of that test is significant, we continue with a Conover post-hoc pairwise comparison procedure [2,3] to determine the location of the significant differences. ...
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... To study factors associated with selfreported exercise, we adopted univariate and multivariate logistic regression analysis with the stepwise forward criterion for the selection of variables. To study the factors related to the WHOQOL-BREF Qol scores, linear, simple, and multiple regression analysis was used (with stepwise criterion for selection of variables), with variables without normal distribution transformed into ranks (Conover and Iman 1981). The software used to perform the statistical analysis was the SAS (Statistical Analysis System) version 9.2 for Windows (SAS Institute Inc., 2002-2008. ...
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... In general, this test aims to detect significant differences between two sample means, where the two sample data represent the behavior of two algorithms. The underlying idea of this test is not just making a count of the wins of each compared algorithm but ranking the differences between the performance and developing the statistic over them (Conover and Iman 1981). In our statistical comparison, the samples related to the two compared algorithms, HGQGA and HQGA, used in the statistical comparison are composed of the average fitness values obtained for the different benchmark functions (i.e., the values contained in Table 4). ...
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