Effective Analysis of Interactive Effects with Non-Normal Data Using the Aligned Rank Transform, ARTool and SAS® University Edition

Edward Durner

doi:10.3390/horticulturae5030057

Abstract

Most statistical techniques commonly used in horticultural research are parametric tests that are valid only for normal data with homogeneous variances. While parametric tests are robust when the data ‘slightly’ deviate from normality, a significant departure from normality leads to reduced power and the probability of a type I error increases. Transformations often used to normalize non-normal data can be time consuming, cumbersome and confusing and common non-parametric tests are not appropriate for evaluating interactive effects common in horticultural research. The aligned rank transformation allows non-parametric testing for interactions and main effects using standard ANOVA techniques. This has not been widely adapted due to its rigorous mathematical nature, however, a downloadable (ARTool) is now available, which performs the math needed for the transformation. This study provides step-by-step instructions for integrating ARTool with the free edition of SAS (SAS University Edition) in an easily employed method for testing normality, transforming data with aligned ranks, and analysing data using standard ANOVAs.

Highlights

The statistical methods used for data analysis of many horticultural studies are often subject to controversy during the review process
Many of the statistical techniques most commonly used in horticultural research such as the analysis of variance (ANOVA), t-tests, and linear regression, are parametric techniques that are valid only if the data in the analysis are normally and independently distributed with μ = 0 and common variance, σ2, i.e., ‘normal data with homogeneous variances’ [1,2,3]
Many of the most commonly used statistical techniques in horticultural research are parametric techniques, which are valid only if they are used on normal data

Summary

Introduction

The statistical methods used for data analysis of many horticultural studies are often subject to controversy during the review process. Many of the statistical techniques most commonly used in horticultural research such as the analysis of variance (ANOVA), t-tests, and linear regression, are parametric techniques that are valid only if the data in the analysis are normally and independently distributed with μ = 0 and common variance, σ2 , i.e., ‘normal data with homogeneous variances’ [1,2,3]. While parametric tests are robust when the data ‘slightly’ deviate from normality, a significant departure can lead to incorrect conclusions. When parametric procedures are used on non-normal data, power (the probability of detecting a treatment effect when it does exist) is greatly reduced and the probability of a type I error (declaring a significant treatment effect when there is none) greatly increases [3]

Methods

Results

Conclusion