Chapter 1: Introduction to Statistics

Chapter 1: Introduction to Statistics

Chapter Outline

1.1 Statistics, Science, and Observation Introduction Definitions of Statistics Populations and Samples Variables and Data Parameters and Statistics Descriptive and Inferential Statistical Methods Statistics in the Context of Research 1.2 Variables and Measurement Constructs and Operational Definitions Discrete and Continuous Variables Scales of Measurement 1.3 Three Data Structures, Research Methods, and Statistics Data Structure 1. One Group with One or More Separate Variables Measured for Each

Individual: Descriptive Research

Relationships between Variables Data Structure 2. One Group with Two Variables Measured for Each Individual: The Correlational Method

Data Structure 3. Comparing Two (or More) Groups of Scores: Experimental and

Nonexperimental Methods Experimental and Nonexperimental Methods The Experimental Method

Nonexperimental Methods: Nonequivalent Groups and Pre-Post Studies

1.4 Statistical Notation Scores Summation Notation

(Essentials of Statistics for the Behavioral Sciences, 9e Frederick Gravetter, Larry Wallnau) (Solution Manual, For the Complete File, Download link at the end of this File) 1 / 2

Learning Objectives and Chapter Summary

• Students should be familiar with the terminology and special notation of statistical analysis.

Statistical Terms Measurement Terms Research Terms population operational definition correlational method sample nominal experimental method parameter ordinal independent variable statistic interval dependent variable descriptive statistics ratio nonexperimental method inferential statistics discrete variable quasi-independent variable sampling error continuous variable real limits

Figure 1.1 is useful for introducing the concepts of population and sample, and the related concepts of parameter and statistic. The same figure also helps differentiate descriptive statistics that focus on the sample data and inferential statistics that generalize from samples to populations.

• Students should learn how statistical techniques fit into the general process of science.

Although the concept of sampling error is not critical at this time in the course, it is a useful way to introduce and justify the need for inferential statistics. Figure 1.2 is a simple demonstration of the concept that sample statistics are representative of but not identical to the corresponding population parameters, and that two different samples will tend to have different statistics. The idea that differences can occur just by chance is an important concept. After the concept of sampling error is established, Figure 1.3 shows the overall research process and identifies where descriptive and inferential statistics are used.

Statistical techniques are mostly used near the end of the research process, after the researcher has obtained research results and needs to organize, summarize, and interpret the data. Chapter 1 includes discussion of two aspects of research that precede statistics: (1) the process of measurement, and (2) the idea that measurements take place in the context of a research study. The discussion includes the different scales of measurement and the information they provide, as well as an introduction to continuous and discrete variables. Research studies are described in terms of the kinds of data they produce: correlational studies that produce data suitable for computing correlations (see Figure 1.5), and experimental studies that produce groups of scores to be compared, usually looking for mean differences (see Figure 1.6). Other types of research (nonexperimental) that also involve comparing groups of scores are discussed (see Figure 1.7).

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