A Generalized Rank-Order Method for Nonparametric Analysis of Data from Exercise Science: A Tutorial

Abstract

Frequent violations of the assumption that data are normally distributed occur in exercise science and other life and behavioral sciences. When this assumption is violated, parametric statistical analyses may be inappropriate for data analysis. We provide a rationale for using a generalized form of nonparametric analyses based on the Puri and Sen (1985) L treated as a chi 2 approximation. If data do not meet the assumption of normality, this nonparametric approach has substantial power and is easy to use. An advantage of this generalized technique is that ranked data may be used in standard parametric statistical programs widely available on desktop and mainframe computers, for example, regression, analysis of variance (ANOVA), multivariate analysis of variance (MANOVA) within BioMed, SAS, SPSS. Once the data are ranked and analyzed with these programs, the only adjustment required is to use a standard formula to calculate the nonparametric test statistic, L, instead of the parametric test statistic (e.g., F). Thus, rank-order nonparametric models become parallel with their parametric counterparts allowing the researcher to select between them based on characteristics of the data distribution. Examples of this approach are provided using data from exercise science for regression, ANOVA (including repeated measures) and MANOVA techniques from SPSSPC. Using these procedures, researchers can easily examine data distributions and make an appropriate decision about parametric or nonparametric analyses while continuing to use their regular statistical packages.

Amplitude-Integrated EEG in Preterm Infants: Maturation of Background Pattern and Amplitude Voltage with Postmenstrual Age and Gestational Age

“…Specifically, Puri and Sen's L statistics, treated as a w 2 approximation, were calculated by multiplying Pillai's Trace by the degree of freedom (i.e., number of subjects minus one). 26 …”

The relationship of asymmetric weight-bearing with postural sway and visual reliance in stroke

“…Due to the non-normality of the dependent variables, data was rank transformed before entering the MANOVAs [18]. Subsequently, Pillai's Trace value was used to calculate the L statistic, which was compared to the Chi-square critical value to determine significance as described in Thomas et al [18]. When the MANOVA was significant, post-hoc Mann-Whitney U tests were performed to determine which measures were different between groups.…”

“…A non-parametric multivariate analysis of variance (MANOVA) was performed to determine the effect of Group (stroke vs. controls) on five dependent variables (AP RMS COP displacement, AP RMS COP velocity, ML RMS COP displacement, ML RMS COP velocity, and Asymmetry Index) for the EO condition. Due to the non-normality of the dependent variables, data was rank transformed before entering the MANOVAs [18]. Subsequently, Pillai's Trace value was used to calculate the L statistic, which was compared to the Chi-square critical value to determine significance as described in Thomas et al [18].…”

The aligned rank transform and discrete variables: A warning

“…A good introduction offer Thomas et al (1999). The idea dates back to the 60s, when Bennett (1968) and Scheirer, Ray & Hare (1976) as well as later Shirley (1981) generalized the H test for multifactorial designs.…”