Pioneering Use of Statistical Tests Paves the Way for Applications in Disease Management
Nonparametric statistical tests have great potential value for determining the effects of treatments on diseases and pests when some response variables consist of ordinal ratings for the magnitude of symptoms. An in-depth assessment of properties of several newly developed theoretical test statistics was performed for a wide range of typical experimental conditions in plant protection. Results provide a guide for researchers for choosing the appropriate statistical tests when comparing treatments or other factors.
Plant pathologists often assess disease and other damages using ordinal rating scales. Examples include: 1-healthy, 2-mild symptoms, 3-stunting and wilting, and 4-dead. Analysis of ordinal data should best be done with nonparametric methods. Recent theoretical research has extended nonparametric analysis to factorials and repeated measures, situations which are common in plant pathology. Many investigations, however, involve not just one response, but several response variables (e.g., ratings for each of several diseases, yield, etc.).
Multivariate methods are needed to fully explore the effects of treatments on these responses. Recently completed theoretical work by A. Bathke and S. Harrar has extended the nonparametric methodology to multivariate situations.
Statistical protocols were developed and evaluated for the new nonparametric methods for plant disease management applications. CFAES researcher Larry Madden, together with statisticians at the University of Kentucky and University of Montana, conducted an in-depth assessment of the properties of several newly- developed test statistics for multivariate nonparametric data analyses and for univariate nonparametric analyses of ordinal data from randomized blocks. Error rates and statistical power of the tests were determined for a wide range of experimental conditions (number of replications, number of treatments, and number of correlated response variables) when treatments were the same and when they were different. The so-called nonparametric ANOVA-Type test statistic was best for response variables that were positively correlated, and the nonparametric Lawley-Hotelling test was best for negatively correlated responses. Approximations were found to be very accurate when the number of treatments was large.
Results of this investigation will allow applied statisticians and other data analysts to choose the most appropriate and powerful test statistic when analyzing ordinal rating data. This will be especially valuable for researchers who are attempting to determine the most effective treatment for management of plant diseases and other pests. This pioneering use of meta-analytical protocols will pave the way for further applications in plant pathology and disease management.
Larry Madden, Department of Plant Pathology; Solomon Harrar, University of Montana; Arne Bathke, University of Kentucky