Understanding Statistical Analysis and Modeling is a text for graduate and advanced undergraduate students in the social, behavioral, or managerial sciences seeking to understand the logic of statistical analysis. Robert Bruhl covers all the basic methods of descriptive and inferential statistics in an accessible manner by way of asking and answering research questions. Concepts are discussed in the context of a specific research project and the book includes probability theory as the basis for understanding statistical inference. Instructions on using SPSS® are included so that readers focus on interpreting statistical analysis rather than calculations. Tables are used, rather than formulas, to describe the various calculations involved with statistical analysis and the exercises in the book are intended to encourage students to formulate and execute their own empirical investigations.

# Chapter 13: Analysis of Variance : Comparing a Quantitative Property Assessed for Several Different Groups

### 13.0 Learning Objectives

In this chapter, we address research projects in which three or more groups of phenomena are compared with regard to a quantitatively assessed property. We describe a method said to be Analysis of Variance (or ANOVA) by which we can address such a comparison in the following steps:

• establishing the descriptive statistics—mean and standard deviation—by which each of the groups might be characterized with regard to the occurrences of the property of interest;
• constructing a “compound” statistic—said to be the F-statistic—for comparing the groups with regard to their variances; and
• describing a method by which the F-statistic may be used to determine whether or not the differences in variance observed among the ...