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 Working Paper 07  ### Analyzing ANOVA designs: biometrics information handbook no.5

Author(s) or contact(s): V. Sit
Source: Research Branch
Subject: Biometrics
Series: Working Paper
Other details:  Published 1995. Hardcopy is available.

### Abstract

Analysis of variance (ANOVA) is a powerful and popular technique for analyzing data. This handbook is an introduction to ANOVA for those who are not familiar with the subject. It is also a suitable reference for scientists who use ANOVA to analyze their experiments.

Most researchers in applied and social sciences have learned ANOVA at college or university and have used ANOVA in their work. Yet, the technique remains a mystery to many. This is likely because of the traditional way ANOVA is taught  loaded with terminology, notation, and equations, but few explanations. Most of us can use the formulae to compute sums of squares and perform simple ANOVAs, but few actually understand the reasoning behind ANOVA and the meaning of the F-test.

Today, all statistical packages and even some spreadsheet software (e.g., EXCEL) can do ANOVA. It is easy to input a large data set to obtain a great volume of output. But the challenge lies in the correct usage of the programs and interpretation of the results. Understanding the technique is the key to the successful use of ANOVA.

The concept of ANOVA is really quite simple: to compare different sources of variance and make inferences about their relative sizes. The purpose of this handbook is to develop an understanding of ANOVA without becoming too mathematical.

It is crucial that an experiment is designed properly for the data to be useful. Therefore, the elements of experimental design are discussed in Chapter 2. The concept of ANOVA is explained in Chapter 3 using a one-way fixed factor example. The meaning of degrees of freedom, sums of squares, and mean squares are fully explored. The idea behind ANOVA and the basic concept of hypothesis testing are also explained in this chapter. In Chapter 4, the various techniques for comparing several means are discussed briefly; recommendations on how to perform multiple comparisons are given at the end of the chapter. In Chapter 5, a completely randomized factorial design is used to illustrate the procedures for recognizing an experimental design, setting up the ANOVA table, and performing an ANOVA using SAS statistical software. Many designs commonly used in forestry trials are described in Chapter 6. For each design, the ANOVA table and SAS program for carrying out the analysis are provided. A set of rules for determining expected means squares is given in Appendix 1.

This handbook deals mainly with balanced ANOVAs, and examples are analyzed using SAS statistical software. Nonetheless, the information will be useful to all readers, regardless of which statistical package they use.

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###### Updated October 15, 2009 