Experimental Design and Analysis with Emphasis on Communicating What Has Been Done: I. A Comparison of Statistical Models Using General Linear Model Procedure of SAS

Abstract

Statistical analyses are important methods for interpreting results of agricultural experiments for scientific writing, which should clearly communicate the particulars of the research being described in a way that it can be precisely repeated. Probabilities (p-values) are often described in articles in journals to compare treatment means to each other and to compare regression coefficients to zero. Most published data are subjected to ANOVA (analysis of variance) or regression models using the GLM (general linear models) procedure of the SAS program (SAS Institute, 2006). The object is to determine the significance levels that means are different. Different statistical models and programming statements may lead to quite different conclusions. Illustrative data from an experiment with two independent variables (X₁ and X₂) and one dependent variable (Y) were analyzed. There were 6 levels of X₁ and 2 levels of X₂. Several ANOVA and regression models are reported here with or without “class” statements in SAS. The ANOVA model requires a Class statement be included for each independent variable to signify classification variables. With the Class statement, SAS computes the Sums of Squares (SS) with n-1 degrees of freedom where n is the number of levels of each independent variable. However, without the Class statement, SAS computes the SS with only 1 degree of freedom, as in a regression model. By using either a one-way ANOVA with Duncan’s New Multiple Range Test or a two-way ANOVA, no differences between treatments were detected. When using a linear regression model, X₂ and the X₁ × X₂ interaction term had significant p-values (0.025 and 0.014, respectively). When using a second order polynomial regression model, only X₂ had a significant p-value (0.036). When an ANOVA with components including linear and quadratic terms was computed, the interaction term between X₂ and (linear X₁) had a significant p-value (0.023). The choice of an appropriate statistical model is important because conclusions from the subsequent analyses depend on the particular model used.