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
Learning Objectives and Chapter Summary
1. 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.
2. 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).
3. Students should learn the notation—particularly summation notation—that will be used
throughout the rest of the book.
There are three key concepts important to using summation notation:
1. Summation is a mathematical operation, just like addition or multiplication, and
the different mathematical operations must be performed in the correct order
(see Order of Mathematical Operations in Section 1.4).
2. In statistics, mathematical operations usually apply to a set of scores that can be
presented as a column of numbers.
3. Each operation, except for summation, creates a new column of numbers.
Summation calculates the sum for the column.
Other Lecture Suggestions
1. Early in the first class, I acknowledge that
a. Most students are not there by choice. (No one picked statistics as an elective
because it looked like a fun class.)
b. Many students have some anxiety about the course.
However, I also try to reassure them that the class will probably be easier and more
enjoyable (less painful) than they would predict, provided they follow a few simple rules:
a. Keep up. In statistics, each bit of new material builds on the previous material. As
long as you have mastered the old material, then the new stuff is just one small
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
Learning Objectives and Chapter Summary
1. 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.
2. 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).
3. Students should learn the notation—particularly summation notation—that will be used
throughout the rest of the book.
There are three key concepts important to using summation notation:
1. Summation is a mathematical operation, just like addition or multiplication, and
the different mathematical operations must be performed in the correct order
(see Order of Mathematical Operations in Section 1.4).
2. In statistics, mathematical operations usually apply to a set of scores that can be
presented as a column of numbers.
3. Each operation, except for summation, creates a new column of numbers.
Summation calculates the sum for the column.
Other Lecture Suggestions
1. Early in the first class, I acknowledge that
a. Most students are not there by choice. (No one picked statistics as an elective
because it looked like a fun class.)
b. Many students have some anxiety about the course.
However, I also try to reassure them that the class will probably be easier and more
enjoyable (less painful) than they would predict, provided they follow a few simple rules:
a. Keep up. In statistics, each bit of new material builds on the previous material. As
long as you have mastered the old material, then the new stuff is just one small
