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.

# Chi-Square Analysis : Investigating a Suspected Association Between Two Qualitative Properties

### 11.0 Learning Objectives

In this chapter, we describe a method for assessing a suspected association between two coexisting qualitative properties observed in a sample set of phenomena. This method is based on the following steps:

• constructing an appropriate contingency table describing the jointly occurring values of the two properties;
• constructing what is said to be a Chi-Square Statistic in which the actual observations of the two properties are compared with the observations expected if two properties were stochastically independent; and
• interpreting the Chi-Square Statistic and assessing its statistical significance.

### 11.1 Motivation

As described in Chapter 1, an explanatory study is one in which the investigator seeks to understand why different phenomena have different values for some property of interest, ...

• • • 