Quantitative and statistical research methods form hypothesis to results by martin brigmon

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QUANTITATIVE
AND STATISTICAL
RESEARCH METHODS
From Hypothesis to Results
WILLIAM E. MARTIN
KRISTA D. BRIDGMON

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Copyright © 2012 by John Wiley & Sons, Inc. All rights reserved.
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Library of Congress Cataloging-in-Publication Data
Martin, William E. (William Eugene), 1948Quantitative and statistical research methods : from hypothesis to results / William E. Martin, Krista D.
Bridgmon.— First edition.
pages cm.— (Research methods for the social sciences; 42)
Includes bibliographical references and index.
ISBN 978-0-470-63182-9 (pbk.); ISBN 978-1-118-22075-7 (ebk.); ISBN 978-1-118-23457-0 (ebk.);
ISBN 978-1-118-25908-5 (ebk.)
1. Psychology—Methodology. 2. Social sciences—Methodology. 3. SPSS (Computer file)
I. Bridgmon, Krista D., 1979- II. Title.
BF38.5.M349 2012
150.72'7—dc23
2012010748
Printed in the United States of America
FIRST EDITION

PB Printing

10 9 8 7 6 5 4 3 2 1

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CONTENTS

Tables and Figures
Preface
The Authors

ix
xvii
xix

Chapter 1

Introduction and Overview
Review of Foundational Research Concepts
Review of Foundational Statistical Information
The Normal Distribution

1
3
6
14

Chapter 2

Logical Steps of Conducting Quantitative Research:
Hypothesis-Testing Process
Hypothesis-Testing Process

29
30

Chapter 3

Maximizing Hypothesis Decisions Using Power Analysis
Balance between Avoiding Type I and Type II Errors

39
41

Chapter 4

Research and Statistical Designs
Formulating Experimental Conditions
Reducing the Imprecision in Measurement
Controlling Extraneous Experimental Influences
Internal Validity and Experimental Designs
Choosing a Statistic to Use for an Analysis

53
54
55
57

59
67

Chapter 5

Introduction to IBM SPSS 20
The IBM SPSS 20 Data View Screen
Naming and Defining Variables in Variable View

77
80
80

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Chapter 6

Chapter 7

Chapter 8

Entering Data
Examples of Basic Analyses
Examples of Modifying Data Procedures

86
87

96

Diagnosing Study Data for Inaccuracies and
Assumptions
Research Example

99
100

Randomized Design Comparing Two Treatments
and a Control Using a One-Way Analysis of Variance
Research Problem
Study Variables
Research Design
Stating the Omnibus (Comprehensive) Research
Question
Hypothesis Testing Step 1: Establish the Alternative
(Research) Hypothesis (Ha)
Hypothesis Testing Step 2: Establish the Null
Hypothesis (H0)
Hypothesis Testing Step 3: Decide on a Risk
Level (Alpha) of Rejecting the True H0 Considering
Type I and II Errors and Power
Hypothesis Testing Step 4: Choose Appropriate Statistic
and Its Sampling Distribution to Test the H0
Assuming H0 Is True
Hypothesis Testing Step 5: Select Sample, Collect
Data, Screen Data, Compute Statistic, and
Determine Probability Estimates
Hypothesis Testing Step 6: Make Decision Regarding

the H0 and Interpret Post Hoc Effect Sizes and
Confidence Intervals
Formula Calculations of the Study Results
Repeated-Treatment Design Using a
Repeated-Measures Analysis of Variance
Research Problem
Study Variables
Research Design

iv  C O N T E N T S

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129
130
131
133
135
136
137

138

143

144

162

166
183
184
185
186


Stating the Omnibus (Comprehensive)
Research Question
Hypothesis Testing Step 1: Establish the Alternative
(Research) Hypothesis (Ha)
Hypothesis Testing Step 2: Establish the Null
Hypothesis (H0)
Hypothesis Testing Step 3: Decide on a Risk
Level (Alpha) of Rejecting the True H0
Considering Type I and II Errors and Power
Hypothesis Testing Step 4: Choose Appropriate
Statistic and Its Sampling Distribution to Test
the H0 Assuming H0 Is True
Hypothesis Testing Step 5: Select Sample, Collect Data,
Screen Data, Compute Statistic, and Determine
Probability Estimates
Hypothesis Testing Step 6: Make Decision Regarding
the H0 and Interpret Post Hoc Effect Sizes and
Confidence Intervals
Formula Calculations of the Study Results
Chapter 9

Randomized Factorial Experimental Design Using
a Factorial ANOVA

Research Problem
Study Variables
Research Design
Stating the Omnibus (Comprehensive) Research
Questions
Hypothesis Testing Step 1: Establish the Alternative
(Research) Hypothesis (Ha)
Hypothesis Testing Step 2: Establish the Null
Hypothesis (H0)
Hypothesis Testing Step 3: Decide on a Risk
Level (Alpha) of Rejecting the True H0 Considering
Type I and II Errors and Power
Hypothesis Testing Step 4: Choose Appropriate Statistic
and Its Sampling Distribution to Test the H0
Assuming H0 Is True

189
190
191

192

195

196

216
218
231
232

232
233
237
238
240

241

247

CONTENTS  v

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Hypothesis Testing Step 5: Select Sample, Collect Data,
Screen Data, Compute Statistic, and Determine
Probability Estimates
248
Hypothesis Testing Step 6: Make Decision Regarding
the H0 and Interpret Post Hoc Effect Sizes and
Confidence Intervals
271
Formula Calculations of the Study Results
278
Chapter 10 Analysis of Covariance
Research Problem
Study Variables

Research Design
Stating the Omnibus (Comprehensive) Research
Question
Hypothesis Testing Step 1: Establish the Alternative
(Research) Hypothesis (Ha)
Hypothesis Testing Step 2: Establish the Null
Hypothesis (H0)
Hypothesis Testing Step 3: Decide on a Risk
Level (Alpha) of Rejecting the True H0
Considering Type I and II Errors and Power
Hypothesis Testing Step 4: Choose Appropriate Statistic
and Its Sampling Distribution to Test the H0
Assuming H0 Is True
Hypothesis Testing Step 5: Select Sample, Collect
Data, Screen Data, Compute Statistic, and
Determine Probability Estimates
Hypothesis Testing Step 6: Make Decision Regarding
the H0 and Interpret Post Hoc Effect Sizes and
Confidence Intervals
Formula ANCOVA Calculations of the Study Results
ANCOVA Study Results
Chapter 11 Randomized Control Group and Repeated-Treatment
Designs and Nonparametics
Research Problem
Study Variables

vi  C O N T E N T S

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297
298
299
300
301
301
302

302

306

307

324
327
339
345
346
346


Research Design
Stating the Omnibus (Comprehensive) Research
Question
Hypothesis Testing Step 1: Establish the Alternative
(Research) Hypothesis (Ha)
Hypothesis Testing Step 2: Establish the Null

Hypothesis (H0)
Hypothesis Testing Step 3: Decide on a Risk Level
(Alpha) of Rejecting the True H0 Considering
Type I and II Errors and Power
Hypothesis Testing Step 4: Choose Appropriate
Statistic and Its Sampling Distribution to
Test the H0 Assuming H0 Is True
Hypothesis Testing Step 5: Select Sample, Collect
Data, Screen Data, Compute Statistic, and
Determine Probability Estimates
Hypothesis Testing Step 6: Make Decision
Regarding the H0 and Interpret Post Hoc Effect Sizes
Formula Calculations
Nonparametric Research Problem Two: Friedman’s
Rank Test for Correlated Samples and Wilcoxon’s
Matched-Pairs Signed-Ranks Test
Chapter 12 Bivariate and Multivariate Correlation Methods
Using Multiple Regression Analysis
Research Problem
Study Variables
Research Method
Stating the Omnibus (Comprehensive) Research Question
Hypothesis Testing Step 1: Establish the
Alternative (Research) Hypothesis (Ha)
Hypothesis Testing Step 2: Establish the Null
Hypothesis (H0)
Hypothesis Testing Step 3: Decide on a Risk
Level (Alpha) of Rejecting the True H0 Considering
Type I and II Errors and Power

347
349
349
350

350

354

355
370
376

382
401
402
402
403
405
405
406

406

CONTENTS  vii

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Hypothesis Testing Step 4: Choose Appropriate Statistic
and Its Sampling Distribution to Test the H0
Assuming H0 Is True
407
Hypothesis Testing Step 5: Select Sample, Collect Data,
Screen Data, Compute Statistic, and Determine
Probability Estimates
407
Hand Calculations of Statistics
423
Chapter 13 Understanding Quantitative Literature and Research
Interpretation of a Quantitative Research Article

439
440

References
Index

461
465

viii  C O N T E N T S

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TABLES AND FIGURES

TABLES
Table 1.1
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table

1.2
1.3
3.1
3.2
3.3
3.4
4.1
5.1
5.2
5.3
5.4

Table
Table

Table
Table

6.1
6.2
6.3
6.4

Table
Table
Table
Table

6.5
6.6
6.7
6.8

Values Used to Illustrate Measures of Central Tendency and
Variability
Frequency Distribution of Scores of Depressive Symptoms
Scores and Difference Measures for Dependent t Analysis
Decision Balance between Type I and Type II Errors
Cohen’s Strength of d Effect Sizes
Cohen’s Strength of η2 Effect Sizes
Cohen’s Strength of r Effect Sizes
Threats to Internal Validity: THIS MESS DREAD
Frequencies Table of Ethnicity
Descriptive Statistics of Status
An Independent t-Test Analysis

Correlation Matrix of Age, COSE Confidence in Executing
Microskills, and COSE Dealing with Difficult Client Behaviors
Mean and Standard Deviation of MAAS Scores
Frequencies of MAAS Scores
Missing Case for TotalMAAS
Skewness and Kurtosis Values with Standard Errors of the
Dependent Variable for Both Conditions
Shapiro-Wilk Statistic Results to Assess Normality
Results of Levene’s Test of Homogeneity of Variance
One-Way ANOVA Results before Log10 Data Transformation
Skewness and Kurtosis Values after Log10 Transformation

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Table 6.9
Table 6.10
Table 6.11
Table 6.12
Table 7.1
Table
Table
Table
Table
Table
Table
Table
Table

Table
Table
Table
Table
Table
Table
Table

7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
7.13
8.1
8.2
8.3

Table
Table
Table
Table
Table
Table

8.4
8.5
8.6
8.7
8.8
8.9

Table
Table
Table
Table
Table
Table

8.10
8.11
8.12
8.13
8.14
9.1

Shapiro-Wilk Statistics after Log10 Transformation
Levene’s Test of Homogeneity of Variance after Log10
Transformation
One-Way ANOVA Results for the Log10 Transformed Data
Data Diagnostics Study Example
Descriptive Statistics of Depressive Symptoms by Condition
Group
Highest 6z-Scores by Condition Group

Skewness, Kurtosis, and Standard Error Values by Group
Skewness z-Scores by Condition Group
Kurtosis z-Scores by Condition Group
Shapiro-Wilk Statistics by Condition Group
Levene’s Test of Homogeneity of Variance
One-Way Analysis Results
HSD Post Hoc Analysis
ANOVA Summary Table Specifications
ANOVA Summary Table
Matrix of Mean Differences
One-Way Analysis of Variance Data
Descriptive Statistics of Weight Loss by Condition Group
Highest 6z-Scores by Condition Group
Skewness, Kurtosis, and Standard Error Values by
Condition Group
Skewness z-Scores by Condition Group
Kurtosis z-Scores by Condition Group
Shapiro-Wilk Statistics by Condition Group
Mauchly’s Test of Sphericity
RM-ANOVA Results for the Omnibus Null Hypothesis
Post Hoc Comparisons Using the Fisher’s Protected Least
Significant Differences (PLSD) Statistic
Trends of Weight Loss Means Across the Condition Groups
RM-ANOVA Summary Table Specifications MST/MSE
Study Data with Column and Row Means by Subject and Condition
RM-ANOVA Summary Table Specifications
Repeated-Measures Analysis of Variance Data
2 3 2 Factorial Design Matrix

x  TA B L E S A N D F I G U R E S

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Table 9.2
Table
Table
Table
Table
Table
Table

9.3
9.4
9.5
9.6
9.7
9.8

Table 9.9
Table
Table
Table
Table
Table
Table

9.10

9.11
9.12
9.13
9.14
9.15

Table 9.16
Table 9.17
Table 9.18
Table
Table
Table
Table
Table
Table

9.19
9.20
9.21
9.22
9.23
10.1

Table
Table
Table
Table
Table

10.2

10.3
10.4
10.5
10.6

Descriptive Statistics of Treatment Retention by Treatment
Condition 3 Treatment Status Groups
Highest 6z-Scores by Group
Skewness, Kurtosis, and Standard Error Values by Group
Skewness z-Scores by Condition Group
Kurtosis z-Scores by Condition Group
Shapiro-Wilk Statistics by Condition Group
Levene’s Test Comparing Variances of the Treatment Condition
Groups (SC vs. SC 1 CM)
Levene’s Test Comparing Variances of the Treatment Status
Groups (0–1 vs. $2)
Descriptive Statistics by Conditions
Levene’s Test of Equality of Error Variancesa
Two-Way Analysis of Variance Results
Treatment Condition at Each Treatment Status Level Results
Treatment Status at Each Level of Treatment Condition Results
Decisions and Conclusions Regarding Null Hypotheses of Main
Effects and Interaction Effect
Decisions and Conclusions Regarding Null Hypotheses of Simple
Effects
CI.99 for Mean Difference of Treatment Retention by Treatment
Condition
CI.99 for Mean Difference of Treatment Retention by Treatment
Status
Two-Way ANOVA Summary Table Specifications

Study Data with Column and Row Means by Subject and Condition
Two-Way ANOVA Summary Table
Simple Effects Summary Table
Two-Way Analysis of Variance Data
Highest 6z-Scores for the Covariate Age and the Dependent
Variable Longest Duration of Abstinence
Skewness, Kurtosis, and Standard Error Values by Group
Skewness z-Scores by Treatment Condition Group
Kurtosis z-Scores by Substance Treatment Group
Shapiro-Wilk Statistics by Substance Treatment Condition
Levene’s Test of Homogeneity of Variance for CovAge and DVLDA

TABLES AND FIGURES  xi

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Table 10.7
Table 10.8
Table 10.9
Table 10.10
Table 10.11
Table
Table
Table
Table
Table
Table

Table

10.12
10.13
10.14
10.15
10.16
11.1
11.2

Table 11.3
Table
Table
Table
Table
Table
Table
Table
Table

11.4
11.5
11.6
11.7
11.8
11.9
11.10
11.11

Table 11.12

Table 11.13
Table 11.14
Table 11.15
Table 11.16
Table 11.17

Homogeneity of Regression (Slope)
Test of Homogeneity of Variance of DVLDA Including CovAge
and IVTreatmentCondition
ANCOVA Results
Estimated Marginal Means
Confidence Interval (.99) for the Mean Difference between SC
and SC 1 CM
Data and Summary Statistics for LDALDA DV (Y )
Data and Summary Statistics for Age
Summary of Previous Calculations
Summary of ANCOVA Results
Analysis of Covariance Data
K-WÀMWU Data
Descriptive Statistics of Pain Improvement by Electric Simulation
Condition
Three Highest 6z-Scores of Pain Improvement by Electric
Stimulation Condition
Skewness, Kurtosis, and Standard Error Values by Group
Skewness z-Scores by Condition Group
Kurtosis z-Scores by Condition on Pain Improvement Scores
Shapiro-Wilk Statistics by Conditions
Levene’s Test of Homogeneity of Variance
Mean Ranks of Pain Improvement by Conditions
K-W Results

Mean Ranks of the Low Electric Stimulation Condition
Compared to the Placebo Condition
MWU Results Comparing Low Electric Stimulation to Placebo
Mean Ranks of the Placebo Condition Compared to the High
Electric Stimulation Condition
MWU Results Comparing Placebo to High Electric Stimulation
Formula Kruskal-Wallis and Mann-Whitney U Calculations of
the Study Results
Low Electric Stimulation Condition Compared to Placebo
Condition on Pain Improvement
High Stimulation Condition Compared to Placebo Condition on
Pain Improvement

xii  T A B L E S A N D F I G U R E S

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Table 11.18 Friedman-Wilcoxon Data
Table 11.19 Descriptive Statistics of Pain Improvement by High Electric
Conditions
Table 11.20 Mean Ranks of Pain Improvement by High Electric Conditions
Table 11.21 Friedman’s Statistic of Pain Improvement by High Electric
Conditions
Table 11.22 Wilcoxon Results
Table 11.23 Friedman’s Rank Test
Table 11.24 Wilcoxon’s Matched-Pairs Signed-Ranks Test: First Treatment
Scores Compared to Removed Treatment Scores

Table 11.25 Wilcoxon’s Matched-Pairs Signed-Ranks Test: Restored
Treatment Scores Compared to Removed Treatment Scores
Table 12.1 Highest 6z-Scores for DSI, SPIPract, and SPIScient
Table 12.2 Largest (Maximum) Mahalanobis Distance Value
Table 12.3 Bivariate Correlation Coefficients between the Study Variables
Table 12.4 Multicollinearity Measures of Tolerance and Variance Inflation
Factor (VIF)
Table 12.5 Model Summary of Sequential MRA
Table 12.6 Analysis of Variance of the Two Sequential MRA Models
Table 12.7 Significance Values of Each Predictor Variable
Table 12.8 Matrix of Correlation Coefficients, Means, and Standard
Deviations
Table 12.9 Sequential MRA Data
Table 13.1 Comparisons of Effect Sizes of the Mozart Effect
FIGURES
Figure 1.1
Figure 1.2
Figure 1.3
Figure
Figure
Figure
Figure
Figure

1.4
1.5
3.1
3.2
4.1

Bar Chart of Scores of Depressive Symptoms
Histogram of Scores of Depressive Symptoms
Normal Curve Superimposed on Histogram of Scores of
Depressive Symptoms
Q-Q Plot of Scores of Depressive Symptoms
The Normal Distribution and Standardized Scores
G*Power First Page
A Priori Power Analysis for the Example
Issues in Choosing a Statistic to Use for an Analysis

TABLES AND FIGURES  xiii

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Figure
Figure
Figure
Figure
Figure
Figure
Figure

5.1
5.2
5.3
5.4
5.5

5.6
5.7

Figure 5.8
Figure 5.9
Figure 6.1
Figure 6.2
Figure 6.3
Figure 6.4
Figure 6.5
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure

6.6
7.1
7.2
7.3
7.4
7.5
7.6
8.1

Figure 8.2
Figure 8.3

Figure 8.4
Figure 8.5
Figure 8.6
Figure 8.7

IBM SPSS 20 Initial Screen
Data View Screen of IBM SPSS 20
Variable View Screen of IBM SPSS 20
Variables Named and Defined in Variable View
Example Data in Data View
Bar Chart of Ethnicity
Scatter Plot of Age and COSE Dealing with Difficult
Client Behaviors
COSE Composite Sum Variable
COSE Composite Mean Variable
Histogram of Mindfulness Attention Awareness Scores for the
Treatment Group
Histogram of Mindfulness Attention Awareness Scores for the
Control Group
Q-Q Plot to Assess Normality of Treatment Condition Scores
Q-Q Plot to Assess Normality of Control Condition Scores
Histograms of the Dependent Variable by Condition Groups
after Log10 Data Transformation
Normal Q-Q Plots after Log10 Data Transformation
A Priori Power Analysis of ANOVA Problem
Normal Q-Q Plot of Depressive Symptoms for CBT Group
Normal Q-Q Plot of Depressive Symptoms for IPT Group
Normal Q-Q Plot of Depressive Symptoms for Control Group
Matrix Scatterplot to Assess Independence
Hypothesis Testing Graph—One-Way ANOVA

Repeated-Treatment Design with One Group for
Study Example
Same Participants Measured Repeatedly over Time
Same Participants Measured under Different Conditions
Matched Pairs of Participants Measured under Different
Conditions
Power Analysis for the RM-ANOVA Problem
Histograms of Weight Loss by Weight Loss Intervention
Normal Q-Q Plots of Weight Loss by Weight Loss Intervention
Conditions

xiv  T A B L E S A N D F I G U R E S

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Figure 8.8
Figure 8.9
Figure 9.1
Figure 9.2
Figure 9.3
Figure 9.4
Figure 9.5
Figure
Figure
Figure
Figure
Figure

Figure
Figure
Figure
Figure
Figure

9.6
9.7
10.1
10.2
10.3
10.4
10.5
10.6
11.1
11.2

Figure 11.3
Figure 11.4
Figure 11.5
Figure 11.6
Figure 11.7
Figure 11.8
Figure 11.9

Profile Plot of Means of Weight Loss by Condition Groups
Hypothesis Testing Graph RM-ANOVA
Power Analysis for Treatment Condition of the Factorial
ANOVA Problem
Power Analysis for Treatment Status of the Factorial ANOVA

Problem
Power Analysis for Treatment Condition 3 Treatment Status
Interaction of the Factorial ANOVA Problem
Normal Q-Q Plot by Condition Groups
Matrix Scatter Plot to Assess Independence on Treatment
Retention Across the Condition Groups
Estimated Marginal Means of Treatment Retention
Hypothesis Testing Graph Factorial ANOVA
G*Power Screen Shots for ANCOVA Problem
Normal Q-Q Plots of CovAge by Groups
Normal Q-Q Plots of DVLDA by Groups
Matrix Scatter Plot to Assess Independence
Profile Plot
Hypothesis Testing Graph ANCOVA
Randomized Pretest-Posttest Control Group Design
A Priori Power Analysis Results for Low Electric Stimulation
Versus Placebo
A Priori Power Analysis Results for High Electric Stimulation
Versus Placebo
Histogram of the Low Electric Stimulation Condition on Pain
Improvement
Histogram of the Placebo Condition on Pain Improvement
Histogram of the High Electric Stimulation Condition on Pain
Improvement
Normal Q-Q Plot of Pain Improvement Scores for the Low
Electric Stimulation Condition
Normal Q-Q Plot of Pain Improvement Scores for the Placebo
Condition
Normal Q-Q Plot of Pain Improvement Scores for the High
Electric Stimulation Condition

TABLES AND FIGURES  xv

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Figure 11.10 Post Hoc Effect Size and Power Analysis for Low Electric
Stimulation versus Placebo
Figure 11.11 Post Hoc Effect Size and Power Analysis for High Electric
Stimulation versus Placebo
Figure 11.12 A Priori Power Analysis Results for High Electric Stimulation
at First Treatment (or Restored Treatment) versus Removed
Treatment
Figure 11.13 Post Hoc Effect Size and Power Analysis for High Electric
Stimulation at First Treatment versus Removed Treatment
Figure 11.14 Post Hoc Effect Size and Power Analyses Using G*Power 3.1 for
High Electric Stimulation at First Treatment versus Restored
Treatment
Figure 11.15 Post Hoc Effect Size and Power Analysis for High Electric
Stimulation at Removed Treatment versus Restored Treatment
Figure 12.1 A Priori Power Analysis of MRA Problem
Figure 12.2 Histogram of Residuals of DSI Predicted by SPIScient and
SPIPract
Figure 12.3 Normal P-P Plot of Residuals of DSI Predicted by SPIScient
and SPIPract
Figure 12.4 Scatter Plot of Residuals of DSI Predicted by SPIScient and
SPIPract

xvi  T A B L E S A N D F I G U R E S

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PREFACE

Working through a solution to a research problem is a stimulating process. The
focus of this book is learning statistics while progressing through the steps of the
hypothesis-testing process from hypothesis to results. The hypothesis-testing
process is the most commonly used tool in science and entails following a logical
sequence of actions, judgments, decisions, and interpretations as statistics are
applied to research problems. Statistics emerged as a discipline with the purpose
of developing and applying mathematical theory and scientific operations to
enhance human understanding of phenomena experienced in life. For example,
William Gossett developed the t-statistic while working at the Guinness Brewery
in the late 1800s. He worked to explain the factors that contribute to Guinness
beer remaining suitable for drinking and what fertilizers produce the best yield
of barley used in brewing. Analysis of variance is the most widely used family of
statistics in the world, and Sir Ronald A. Fisher developed the procedure in 1921
while researching the factors contributing to better yields of wheat and potatoes.
The research problems used in the book reflect statistical applications related to
interesting and important topics. For example, research problems for students
to work through include findings on the efficacy of using cognitive-behavioral
therapy to treat depression among adolescents and evaluating if support partners
added to weight loss treatment can improve weight loss among persons who are
overweight. It is hoped that students will find the problems that they work through
to be interesting and relevant to their field of study. The research problems presented are consistent with findings in the field.

The format for each chapter on a major statistic is to cover the research problem
by taking the student through identifying research questions and hypotheses;
identifying, classifying, and operationally defining the study variables; choosing

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appropriate research designs; conducting power analysis; choosing an appropriate
statistic for the problem; using a data set; conducting data screening and analyses
(IBM SPSS); interpreting the statistics; and writing the results related to the
problem.
It is the intent of the authors to provide a user-friendly guide to students to
understand and apply procedural steps in completing quantitative studies. Students will know how to plan research and conduct statistical analyses using
several common statistical and research designs after completion of the book. The
quantitative methodological tools learned by students can actually be applied to
their own research with less oversight by faculty.
Students will develop competencies in using IBM SPSS for statistical analyses.
Computer-generated statistical analysis is the primary method used by quantitative
researchers. Students will have the opportunity to also calculate statistics by hand
for a fuller understanding of mathematics used in computations.
Moreover, the curriculum includes having students analyze research articles
in psychology using a research analysis and interpretation guide. These learning
experiences allow students to enhance their understanding of consuming research
using the information they have learned about statistical and research methods.

ACKNOWLEDGMENTS
The authors would like to gratefully acknowledge the outstanding editorial
leadership and support provided by Andrew Pasternack, Senior Editor; Seth

Schwartz, Associate Editor; and Kelsey McGee, Senior Production Editor, all of
Jossey-Bass. We also wish to thank the following reviewers for their thoughtful
and valuable feedback in the early stages of the manuscript: Joel Nadler, Kathryn
Oleson, Richard Osbaldiston, and Joseph Taylor.

xviii  P R E F A C E

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THE AUTHORS

William E. Martin Jr. is a professor of educational psychology and senior scholar
in the College of Education at Northern Arizona University. His areas of
teaching include intermediate, computer, and multivariate statistics; research
methods; and psychodiagnostics. His research relates to person-environment
psychology and psychosocial adaptation.
Krista D. Bridgmon received a PhD in educational psychology from Northern
Arizona University with emphasis in counseling. She is an assistant professor of
psychology at Colorado State UniversityÀPueblo. She has taught undergraduate
courses in abnormal psychology, child psychology, clinical psychology, statistics,
tests and measurements, and theories of personality, and has taught graduate
courses in appraisal and assessment, clinical counseling, ethics, and school
counseling. Her doctoral dissertation examined the stress factors that all-butdissertation (ABD) students encounter in the disciplines of counselor education and
supervision, counseling psychology, and clinical psychology. The study created an
instrument using multivariate correlational methods to measure stress factors
associated with being ABD, named the BASS (Bridgmon All-But-Dissertation
Stress Survey).

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To my wife Susan and my children and their spouses:
Neil and Jennifer, Kurt and Michelle, and Carol and Kyle
To my grandchildren: Grace, Adriana, Hudson, Lillee,
Uriah, Naaman, and Isaac
—W.E.M. Jr.
To Jerrad and Coltin: Thank you for always making me laugh!
—K.B

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Chapter 1

INTRODUCTION
AND OVERVIEW

LEARNING OBJECTIVES

 Understand the purpose of the book and the structure of
the book.

 Review independent, dependent, and extraneous variables

and their scales of measurement.

 Review measures of central tendency and variability.
 Review visual representations of data, including the normal
distribution.

 Review descriptive and inferential statistical applications of
the normal distribution.

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T

he purpose of this book is to provide a hands-on approach for
students to understand and apply procedural steps in completing
quantitative studies. The book emphasizes a step-by-step guide using
research examples for students to move through the hypothesis-testing process
for commonly used statistical procedures and research methods. Statistical
and research designs are integrated as they are applied to the examples.
The structure of each chapter covers the following nine quantitative research
procedural steps:
1. A description of a research problem, taking the student through identifying
research questions and hypotheses.
2. A method of identifying, classifying, and operationally defining the study
variables.
3. A discussion of appropriate research designs.
4. A procedure for conducting an a priori power analysis.

5. A discussion of choosing an appropriate statistic for the problem.
6. A statistical analysis of a data set.
7. A process for conducting data screening and analyses (IBM SPSS) to test null
hypotheses.
8. A discussion of interpretation of the statistics.
9. A method of writing the results related to the problem.
The underlying philosophy of the book is to view the quantitative research
process from a more holistic and sequential perspective. Concepts are discussed as
they are applied during the procedural steps. It is hoped that after completion of
the book readers will be better able to plan research and conduct statistical
analyses using several commonly used statistical and research designs. The
quantitative methodological tools learned by students can actually be applied to
their own research, hopefully with less oversight by faculty.
The use of statistical software is an essential tool of researchers. Psychological,
educational, social, and behavioral areas of research typically have multifactor
or multivariate explanations. Statistical software provides a researcher with
sophisticated techniques to analyze the effects and relationships among

2  CHAPTER 1

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many independent variables (factors) and dependent variables (variates) in various combinations all at once and instantly. We will use IBM SPSS statistical
software, which has been developed over many decades and is one of the most
widely used statistics programs in the world.
Statistical techniques may have more meaning, understandability, and relevance when learned within the context of research. One needs to have an
understanding of statistical analyses to consume and construct professional

research competently. Knowledge of quantitative research methods is especially
important today because of the emphasis on evidence-based practice in psychology (EBPP) to improve clinical work with clients. EBPP refers to using the
best available research with clinical expertise in the context of patient characteristics, culture, and preferences (American Psychological Association, 2006).
Ideally, the goal is to help a student achieve self-efficacy in understanding,
planning, and conducting actual independent research. Information and skills
grow, leading to advanced understanding. We next present a review of foundational information related to research and statistics that will be useful to review
prior to completing the chapters that follow.
REVIEW OF FOUNDATIONAL RESEARCH CONCEPTS
A review of foundational concepts related to research and statistics is presented
next. Quantitative research involves the interplay among variables after they have
been operationalized, allowing a researcher to measure study outcomes. Essential
statistical methods used to assess scores of variables include central tendency,
variability, and the characteristics of the normal distribution.
Independent, Dependent, and Extraneous Variables

At the core of quantitative research is studying and measuring how variables
change. Kerlinger and Pedhazur (1973) stated, “It can be asserted that all the
scientist has to work with is variance. If variables do not vary, if they do not have
variance, the scientist cannot do his work” (p. 3). Even the father of modern
statistics, Sir Ronald Fisher (1973), said, “Yet, from the modern point of view,
the study of the causes of variation of any variable phenomenon, from the yield of
wheat to the intellect of man, should be begun by the examination and measurement of the variation which presents itself ” (p. 3).
INTRODUCTION AND OVERVIEW  3

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