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 12: The t−Test of Statistical Significance : Comparing a Quantitative Property Assessed for Two Different Groups

### 12.0 Learning Objectives

A common problem in an association study is to assess the difference in the character of the occurrences of a quantitative property assessed for two different groups of phenomena. In this chapter, we address this modeling concern by

• establishing the descriptive statistics—mean and standard deviation—by which each of the two groups might be characterized with regard to the occurrences of the property of interest;
• constructing a “compound” statistic—said to be the t-statistic—for comparing the two groups with regard to their means and standard deviations; and
• describing a method by which the t-statistic may be used to determine whether or not the difference observed between the two groups is likely “real” ...
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