Factorial Experimental Design with Non-Normally Distributed Responses: an Application in Agriculture

Bahr Kadhim MOHAMMED
Ali Sadig Mohommed BAGER
Meshal Harbi ODAH

Keywords

Factorial experiments, Log-transformation, Confidence Intervals (CI), Wheat production

Abstract

In this paper, we study the factors that have the greatest impact on wheat production in Iraq, by using a factorial experimental design, which has three factors and each factor has two levels. These factors are described as: the type of wheat, agriculture date, and types of used fertilizer. In this study, we use two methods: first method is the variance of analysis (ANOVA) and the second is the Log-transformation method. The random error is distributed as non-normal distribution due to the fact that response variable is distributed as non-normal distribution. The comparison between the two methods is based on the effects of the main treatments, the interactions between factors, and expected of length of confidence intervals [E(LOCI)] for the response variable. We used R packages (vcd and MASS) for the application.