Analysis of Variance : The Fundamental Concepts

Department of Rehabilitation Sciences, School of Allied Health Sciences, Texas Tech University Health Sciences Center, Lubbock, TX Address all correspondence and requests for reprints to: Steven F. Sawyer, PT, PhD, [email protected] Analysis of variance (ANOVA) is a statistical tool used to detect differences between experimental group means. ANOVA is warranted in experimental designs with one dependent variable that is a continuous parametric numerical outcome measure, and multiple experimental groups within one or more independent (categorical) variables. In ANOVA terminology, independent variables are called factors, and groups within each factor are referred to as levels. The array of terms that are part and parcel of ANOVA can be intimidating to the uninitiated, such as: partitioning of variance, main effects, interactions, factors, sum of squares, mean squares, F scores, familywise alpha, multiple comparison procedures (or post hoc tests), effect size, statistical power, etc. How do these terms pertain to p values and statistical significance? What precisely is meant by a “statistically significant ANOVA”? How does analyzing variance result in an inferential decision about differences in group means? Can ANOVA be performed on non-parametric data? What are the virtues and potential pitfalls of ANOVA? These are the issues to be addressed in this primer on the use and interpretation of ANOVA. The intent is to provide the clinician reader, whose misspent youth did not include an enthusiastic reading of statistics textbooks, an understanding of the fundamentals of this widely used form of inferential statistical analysis. ANOVA General Linear Models