Date of this Version
HORTSCIENCE, VOL. 30(3), JUNE 1995
Plant breeders developing disease-resistant horticultural crops need flexible and powerful statistical methods to compare treatments efficiently. The most commonly used statistical methods are those based on analysis of variance (ANOVA), regression, and correlation. The valid use of these methods requires that the data have 1) normally distributed responses, 2) constant error variance, 3) independently distributed errors, and 4) a correctly specified model. However, many plant disease experiments yield data that do not adhere to these standard assumptions. For example, in an experiment involving population levels of a pathogen, rarely will population levels be normally distributed. Field counts of the number of nondiseased individuals in a plot many times will have different variances for various treatments. Laboratory experiments measuring the amount of a particular chemical compound produced by a pathogen may have a few cultures with extremely high amounts of the compound, indicating the presence of outliers.
Using standard methods (e.g., ANOVA) on data such as these is questionable for several reasons. Any conclusions based on unreasonable assumptions are suspect and may be wrong simply because the chosen method of analysis forces assumptions on the data that cannot be justified. More importantly, use of inappropriate statistical methods many times reduces the chances of correctly identifying differences that would have been found had the correct method been used.
Nonparametric (NP) statistical methods can be useful alternatives to classical statistical methods. Nonparametric methods require fewer assumptions about the data, but in many cases, allow one to draw valid conclusions with considerably better chances of detecting differences between treatments. The objective of this paper is to demonstrate how nonparametric statistical methods can be simply applied to data likely to result from plant disease experiments.
NONPARAMETRIC METHODS AND APPLICATIONS ANOVA
Many plant disease experiments involve measuring a quantitative response on each of several treatments. The main goal is to determine if responses differ among treatments. Some form of ANOVA is usually appropriate for testing equality of treatment effects. The specific type of ANOVA will depend on 1) the experiment design and 2) the distribution of the response variable. Nonparametric methods can be applied easily to several of the most commonly used designs, assuming the hypothesis of interest is no difference between true treatment medians. Use of medians is preferable to means when data are not normally distributed, because medians are less sensitive to extremes. However, when data are normal, the true mean equals the true median and statements about the medians apply to the means.
Completely randomized design (CRD). This type of experiment design consists of several experimental units being randomly assigned to each treatment, and a quantitative response is obtained from each unit. Nonparametric statistical methods are easily applied to data from a CRD. A simple approach is to use a nonparametric ANOVA based on ranks (Conover and Iman, 1981). The procedure is to 1) assign ranks to all data points; 2) using the classical CRD ANOVA, analyze the ranks as if they were the observed responses; and 3) if the F test is significant, conclude at least two treatment medians differ and use a multiple comparison method (e.g., LSD) on the ranked data to identify which treatments differ.