Chapter 1: Introduction to Statistics
Chapter Outline
1.1 Statistics, Science, and Observations
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 Data Structures, Research Methods, and Statistics
Individual Variables
Relationships between Variables
Statistics for the Correlational Method
Limitations of the Correlational Method
Statistics for Comparing Two (or More) Groups of Scores
Experimental and Nonexperimental Methods
The Experimental Method
Terminology in the Experimental Method
Nonexperimental Methods: Nonequivalent Groups and Pre-Post Studies
1.3 Variables and Measurement
Constructs and Operational Definitions
Discrete and Continuous Variables
Scales of Measurement
, The Nominal Scale
The Ordinal Scale
The Interval and Ratio Scales
1.4 Statistical Notation
Scores
Summation Notation
Learning Objectives and Chapter Summary
1. Define the terms population, sample, parameter, and statistic, and describe the
relationships between them.
The term statistics is used to refer to methods for organizing, summarizing, and
interpreting data.
Scientific questions usually concern a population, which is the entire set of
individuals one wishes to study. Usually, populations are so large that it is
impossible to examine every individual, so most research is conducted with
samples. A sample is a group selected from a population, usually for purposes of a
research study.
A characteristic that describes a sample is called a statistic, and a characteristic that
describes a population is called a parameter. Although sample statistics are usually
representative of corresponding population parameters, there is typically some
discrepancy between a statistic and a parameter.
2. Define descriptive and inferential statistics and describe how these two general
categories of statistics are used in a typical research study.
, Statistical methods can be classified into two broad categories: descriptive statistics,
which organize and summarize data, and inferential statistics, which use sample
data to draw inferences about populations.
3. Describe the concept of sampling error and explain how this concept creates the
fundamental problem that inferential statistics must address.
The naturally occurring difference between a statistic and a parameter is called
sampling error.
4. Differentiate correlational, experimental, and nonexperimental research and
describe the data structures associated with each.
5. Define independent, dependent, and quasi-independent variables and recognize
examples of each.
6. Explain why operational definitions are developed for constructs and identify the
two components of an operational definition.
The correlational method examines relationships between variables by measuring
two different variables for each individual. This method allows researchers to
measure and describe relationships, but cannot produce a cause-and-effect
explanation for the relationship.
The experimental method examines relationships between variables by
manipulating an independent variable to create different treatment conditions and
then measuring a dependent variable to obtain a group of scores in each condition.
The groups of scores are then compared. A systematic difference between groups
provides evidence that changing the independent variable from one condition to
another also caused a change in the dependent variable. All other variables are
controlled to prevent them from influencing the relationship. The intent of the
experimental method is to demonstrate a cause-and-effect relationship between
variables. The experimental method examines relationships between variables by
manipulating an independent variable to create different treatment conditions and
, then measuring a dependent variable to obtain a group of scores in each condition.
The groups of scores are then compared. A systematic difference between groups
provides evidence that changing the independent variable from one condition to
another also caused a change in the dependent variable. All other variables are
controlled to prevent them from influencing the relationship. The intent of the
experimental method is to demonstrate a cause-and-effect relationship between
variables.
Nonexperimental studies also examine relationships between variables by
comparing groups of scores, but they do not have the rigor of true experiments and
cannot produce cause-and-effect explanations. Instead of manipulating a variable to
create different groups, a nonexperimental study uses a preexisting participant
characteristic (such as male/female) or the passage of time (before/after) to create
the groups being compared.
7. Describe discrete and continuous variables and identify examples of each.
8. Differentiate nominal, ordinal, interval, and ratio scales of measurement.
A discrete variable consists of indivisible categories, often whole numbers that vary
in countable steps. A continuous variable consists of categories that are infinitely
divisible and each score corresponds to an interval on the scale. The boundaries that
separate intervals are called real limits and are located exactly halfway between
adjacent scores.
A measurement scale consists of a set of categories that are used to classify
individuals. A nominal scale consists of categories that differ only in name and are
not differentiated in terms of magnitude or direction. In an ordinal scale, the
categories are differentiated in terms of direction, forming an ordered series. An
interval scale consists of an ordered series of categories that are all equal-sized
intervals. With an interval scale, it is possible to differentiate direction and
magnitude (or distance) between categories. Finally, a ratio scale is an interval scale
for which the zero point indicates none of the variable being measured. With a ratio
scale, ratios of measurements reflect ratios of magnitude.
Chapter Outline
1.1 Statistics, Science, and Observations
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 Data Structures, Research Methods, and Statistics
Individual Variables
Relationships between Variables
Statistics for the Correlational Method
Limitations of the Correlational Method
Statistics for Comparing Two (or More) Groups of Scores
Experimental and Nonexperimental Methods
The Experimental Method
Terminology in the Experimental Method
Nonexperimental Methods: Nonequivalent Groups and Pre-Post Studies
1.3 Variables and Measurement
Constructs and Operational Definitions
Discrete and Continuous Variables
Scales of Measurement
, The Nominal Scale
The Ordinal Scale
The Interval and Ratio Scales
1.4 Statistical Notation
Scores
Summation Notation
Learning Objectives and Chapter Summary
1. Define the terms population, sample, parameter, and statistic, and describe the
relationships between them.
The term statistics is used to refer to methods for organizing, summarizing, and
interpreting data.
Scientific questions usually concern a population, which is the entire set of
individuals one wishes to study. Usually, populations are so large that it is
impossible to examine every individual, so most research is conducted with
samples. A sample is a group selected from a population, usually for purposes of a
research study.
A characteristic that describes a sample is called a statistic, and a characteristic that
describes a population is called a parameter. Although sample statistics are usually
representative of corresponding population parameters, there is typically some
discrepancy between a statistic and a parameter.
2. Define descriptive and inferential statistics and describe how these two general
categories of statistics are used in a typical research study.
, Statistical methods can be classified into two broad categories: descriptive statistics,
which organize and summarize data, and inferential statistics, which use sample
data to draw inferences about populations.
3. Describe the concept of sampling error and explain how this concept creates the
fundamental problem that inferential statistics must address.
The naturally occurring difference between a statistic and a parameter is called
sampling error.
4. Differentiate correlational, experimental, and nonexperimental research and
describe the data structures associated with each.
5. Define independent, dependent, and quasi-independent variables and recognize
examples of each.
6. Explain why operational definitions are developed for constructs and identify the
two components of an operational definition.
The correlational method examines relationships between variables by measuring
two different variables for each individual. This method allows researchers to
measure and describe relationships, but cannot produce a cause-and-effect
explanation for the relationship.
The experimental method examines relationships between variables by
manipulating an independent variable to create different treatment conditions and
then measuring a dependent variable to obtain a group of scores in each condition.
The groups of scores are then compared. A systematic difference between groups
provides evidence that changing the independent variable from one condition to
another also caused a change in the dependent variable. All other variables are
controlled to prevent them from influencing the relationship. The intent of the
experimental method is to demonstrate a cause-and-effect relationship between
variables. The experimental method examines relationships between variables by
manipulating an independent variable to create different treatment conditions and
, then measuring a dependent variable to obtain a group of scores in each condition.
The groups of scores are then compared. A systematic difference between groups
provides evidence that changing the independent variable from one condition to
another also caused a change in the dependent variable. All other variables are
controlled to prevent them from influencing the relationship. The intent of the
experimental method is to demonstrate a cause-and-effect relationship between
variables.
Nonexperimental studies also examine relationships between variables by
comparing groups of scores, but they do not have the rigor of true experiments and
cannot produce cause-and-effect explanations. Instead of manipulating a variable to
create different groups, a nonexperimental study uses a preexisting participant
characteristic (such as male/female) or the passage of time (before/after) to create
the groups being compared.
7. Describe discrete and continuous variables and identify examples of each.
8. Differentiate nominal, ordinal, interval, and ratio scales of measurement.
A discrete variable consists of indivisible categories, often whole numbers that vary
in countable steps. A continuous variable consists of categories that are infinitely
divisible and each score corresponds to an interval on the scale. The boundaries that
separate intervals are called real limits and are located exactly halfway between
adjacent scores.
A measurement scale consists of a set of categories that are used to classify
individuals. A nominal scale consists of categories that differ only in name and are
not differentiated in terms of magnitude or direction. In an ordinal scale, the
categories are differentiated in terms of direction, forming an ordered series. An
interval scale consists of an ordered series of categories that are all equal-sized
intervals. With an interval scale, it is possible to differentiate direction and
magnitude (or distance) between categories. Finally, a ratio scale is an interval scale
for which the zero point indicates none of the variable being measured. With a ratio
scale, ratios of measurements reflect ratios of magnitude.
