STATISTICS AND DATA ANALYSIS FOR THE BEHAVIORAl SCIENCES docx

STATISTICS
AND
DATA
ANALYSIS
FOR
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5E~AVIORAl
SCIENCES
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STATISTICS
AND
DATA
ANALYSIS
FOR
T~E
5E~AVIORAL

SCIENCES
DANA
S.
DUNN
Moravian
College
Boston Burr
Ridge,
IL
Dubuque,IA Madison,
WI
New
York
San
Francisco
St.
Louis
Bangkok Bogota Caracas Lisbon London Madrid
Mexico City Milan
New
Delhi
Seoul Singapore Sydney
Taipei
Toronto
McGraw-Hill Higher Education
~
A
Division
of
The

McGraw-Hill
Companies
STATISTICS
AND
DATA
ANALYSIS
FOR THE
BEHAVIORAL
SCIENCES
Published by McGraw-Hill,
an
imprint
of
The McGraw-Hill Companies,
Inc_,
1221
Avenue
of
the Americas, New
York,
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10020. Copyright ©
2001
by The McGraw-Hill Companies, Inc.
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Some ancillaries, including electronic and print components, may not be available to customers
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Data
Dunn, Dana.
Statistics and data analysis for the behavioral sciences / Dana
S.
Dunn.
-1st
ed.
p.
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Includes bibliographical references and index.
ISBN
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1.
Psychometrics.
2.
Psychology-Research-Methodology. I. Title.
BF39.D825
2001
150'
.l'5195-dc21
www.mhhe.com
00-030546
CIP
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I
To
the
memory
of
my
father
and
grandfather,
James
L.
Dunn and
Foster
E.
Kennedy.
"WHAT'S
PAST
IS
PROLOGUE" -
THE
TEMPEST
(ACT
II,
SC.

I)
DANA S. DUNN
vi
ABOUT THE AUTHOR
Dana
S.
Dunn
is
currently an Associate Professor and the Chair
of
the Depart-
ment
of
Psychology at Moravian College, a liberal arts and sciences college in
Bethlehem, Pennsylvania. Dunn received his Ph.D. in
experimental social psychology from the University
of
Virginia in
1987,
having previously graduated with a
BA
in psychology from Carnegie Mellon University in
1982.
He
has taught statistics and data analysis for over
12
years.
Dunn has published numerous articles and chapters in the
areas
of

social cognition, rehabilitation psychology, the
teaching
of
psychology, and liberal education.
He
is
the author of a research methods book,
The
Practical
Researcher:
A Student
Guide
to
Conducting
Psychological
Research
(McGraw-Hill,
1999). Dunn
lives
in Bethlehem with his wife and two children.
)
i
J
/'
1
.;
CONTrNTS
IN
5Rlri
Preface

Acknowledgments
1 INTRODUCTION:
STATISTICS
AND
DATA
ANALYSIS
AS
TOOLS
FOR
RESEARCHERS
3
2
PROCESS
OF
RESEARCH
IN
PSYCHOLOGY
AND
RELATED
FIELDS
45
3
FREQUENCY
DISTRIBUTIONS, GRAPHING,
AND
DATA
DISPLAY
85
4
DESCRIPTIVE

STATISTICS:
CENTRAL
TENDENCY
AND
VARIABILITY
133
5
STANDARD
SCORES
AND
THE
NORMAL
DISTRIBUTION 177
6
CORRELATION
205
7
LINEAR
REGRESSION
241
8
PROBABILITY
273
9
INFERENTIAL
STATISTICS:
SAMPLING
DISTRIBUTIONS
AND
HYPOTHESIS

TESTING
315
10
MEAN
COMPARISON
I:
THE tTEST 365
11
MEAN
COMPARISON
II:
ONE-VARIABLE
ANALYSIS
OF
VARIANCE
411
12
MEAN
COMPARISON
III:
TWO-VARIABLE
ANALYSIS
OF
VARIANCE
459
13
MEAN
COMPARISON
IV:
ONE-VARIABLE

REPEATED-
MEASURES
ANALYSIS
OF
VARIANCE
499
14
SOME
NONPARAMETRIC
STATISTICS
FOR
CATEGORICAL
AND
ORDINAL
DATA
523
15
CONCLUSION:
STATISTICS
AND
DATA
ANALYSIS
IN
CONTEXT
563
vii
Contents
in
Brief
Appendix

A:
Basic
Mathematics
Review
and
Discussion
of
Math Anxiety A-I
Appendix
B:
Statistical
Tables
B-1
viii
Appendix
C:
Writing
Up
Research
in
APA
Style:
Overview
and
Focus
on
Results
C-l
Appendix D:
Doing

a
Research
Project
Using
Statistics
and
Data
Analysis:
Organization,
Time
Management,
and
Prepping
Data
for
Analysis
D-l
Appendix
E:
Answers
to
Odd-Numbered
End
of
Chapter
Problems
E-l
Appendix
F:
Emerging

Alternatives:
Qualitative
Research
Approaches
F-l
References
R-l
Credits
CR-l
Name
Index
NI-l
Subject
Index SI-l
!
)
1
)
CONTENTS
Preface
xxi
Acknowledgments
xxvi
Reader
Response
xxviii
1 INTRODUCTION: STATISTICS AND
DATA
ANALYSIS
AS

TOOLS FOR RESEARCHERS 3
DATA
BOX 1.A: What
Is
or Are Data? 5
Tools
for Inference: David
L.'s
Problem 5
College
Choice 6
College
Choice:
What Would (Did)
You
Do?
6
Statistics
Is
the Science of Data, Not Mathematics 8
Statistics, Data Analysis, and the Scientific Method 9
Inductive and Deductive Reasoning 10
Populations and Samples 12
Descriptive and Inferential Statistics
16
DATA
BOX 1.B: Reactions
to
the David
L.

Problem 18
Knowledge Base
19
Discontinuous and Continuous Variables
20
DATA
BOX 1.C: Rounding and Continuous
Variables
22
Writing About Data: Overview and Agenda
23
Scales
of
Measurement
24
Nominal
Scales
25
Ordinal
Scales
26
Interval
Scales
27
Ratio
Scales
28
Writing About
Scales
29

Knowledge Base
31
Overview
of
Statistical Notation
31
What
to
Do When: Mathematical Rules
of
Priority 34
DATA
BOX 1.D: The Size
of
Numbers
is
Relative
38
Mise
en
Place
39
ix
x
Contents
About Calculators
39
Knowledge
Base
40

PRO.JECT EXERCISE: Avoiding Statisticophobia 40
Looking Forward, Then
Back
41
Summary
42
Key
Terms
42
Problems
42
2 PROCESS OF RESEARCH IN PSYCHOLOGY AND
RELATED
FIELDS
45
The Research
Loop
of
Experimentation: An Overview
of
the
Research Process
45
Populations and Samples
Revisited:
The
Role
of
Randomness
48

Distinguishing Random Assignment from Random Sampling
48
Some Other Randomizing
Procedures
50
Sampling
Error
52
Knowledge
Base
53
DATA
BOX
2.A: Recognizing Randomness, Imposing Order
54
Independent and Dependent Variables
54
Types
of
Dependent Measures
58
Closing
or
Continuing the
Research
Loop?
60
DATA
BOX
2.B: Variable Distinctions: Simple, Sublime, and All

Too
Easily Forgotten
61
The Importance
of
Determining Causality
61
DATA
BOX
2.C:
The "Hot Hand in Basketball" and the
Misrepresentation
of
Randomness
62
Operational Definitions in Behavioral
Research
63
Writing Operational Definitions
64
Knowledge
Base
64
Reliability and Validity
65
Reliability
66
Validity
67
Knowledge

Base
69
Research Designs
70
Correlational Research
70
Experiments
72
Quasi-experiments
74
DATA
BOX
2.D: Quasi-experimentation in Action: What
to
Do
Without Random Assignment or a Control Group
75
Knowledge Base
76
PRO.JECT EXERCISE:
Using
a Random Numbers
Table
77
Looking Forward, Then
Back
81
Summary
81
Key

Terms
82
Problems
82
3 FREQUENCY DISTRIBUTIONS, GRAPHING, AND
DATA
DISPLAY
85
What
is
a Frequency Distribution?
87
Contents
DATA BOX 3.A: Dispositional Optimism and
Health:
A Lot About
the
LOT
88
Proportions
and
Percentages
90
Grouping
Frequency
Distributions
92
True
Limits and
Frequency

Distributions
95
Knowledge
Base
96
Graphing Frequency Distributions
97
Bar
Graphs
98
Histograms
99
Frequency
Polygons
100
Misrepresenting
Relationships:
Biased
or
Misleading
Graphs
102
New Alternatives for Graphing Data: Exploratory Data Analysis
104
Stem
and Leaf
Diagrams
105
DATA BOX 3.B:
Biased

Graphical
Display-Appearances
Can
Be
Deceiving
106
Tukey's
Tallies
108
Knowledge
Base
109
Envisioning the Shape
of
Distributions
III
DATA BOX 3.C:
Kurtosis,
or
What's
the
Point
Spread?
113
DATA BOX 3.D:
Elegant
Information-Napoleon's Ill-fated
March
to
Moscow

114
Percentiles and Percentile Ranks
115
Cumulative
Frequency
116
Cumulative
Percentage
117
Calculating
Percentile
Rank
118
Reversing
the
Process:
Finding
Scores
from
Percentile
Ranks
119
Exploring
Data:
Calculating
the
Middle
Percentiles
and
Quartiles

120
Writing About
Percentiles
122
Knowledge
Base
123
Constructing Tables and Graphs
123
Less
is
More:
Avoiding Chart junk and
Tableclutter,
and
Other
Suggestions
124
American
Psychological
Association
(APA)
Style
Guidelines
for
Data
Display
125
PROJECT EXERCISE:
Discussing

the
Benefits
of
Accurate
but
Persuasive
Data
Display
126
Looking Forward, Then Back
127
Summary
128
Key
Terms
129
Problems
129
4 DESCRIPTIVE STATISTICS: CENTRAL TENDENCY AND
VARIABILITY
133
Why Represent Data
By
Central Tendency
134
The Mean: The Behavioral Scientist's Statistic
of
Choice
136
DATA BOX 4.A:

How
Many
Are
There?
And
Where
Did
They
Come
From?
Proper
Use
of
Nand
n
138
Calculating
Means
from
Ungrouped
and
Grouped
Data
138
Caveat
Emptor:
Sensitivity
to
Extreme
Scores

140
xi
xii
Contents
Weighted
Means:
An
Approach
for
Determining
Averages
of
Different-Sized
Groups
142
DATA
BOX
4.8:
Self-Judgment
Under
Uncertainty-Being
Average
is
Sometimes
OK
143
The Median
144
The Mode
145

The Utility
of
Central Tendency
147
Shapes
of
Distributions
and
Central
Tendency
147
When
to
Use
Which
Measure
of
Central
Tendency
148
Writing
About
Central
Tendency
149
Knowledge
Base
150
Understanding Variability
151

The Range
153
The
Interquartile
and
the
Semi-Interquartile
Range
153
Variance and Standard Deviation
155
Sample
Variance
and
Standard
Deviation
157
Homogeneity
and
Heterogeneity:
Understanding
the
Standard
Deviations
of
Different
Distributions
159
Calcuklting
Variance

and
Standard
Deviation
from
a
Data
Array
160
Population
Variance
and
Standard
Deviation
161
Looking
Ahead:
Biased
and
Unbiased
Estimators
of
Variance
and
Standard
Deviation
162
DATA BOX 4.C:
Avoid
Computation
Frustration:

Get
to
Know
Your
Calculator
165
Knowledge
Base
165
Factors Affecting Variability
166
Writing
About
Range,
Variance,
and
Standard
Deviation
168
DATA
BOX
4.D:
Sample
Size
and
Variability-The
Hospital
Problem
169
PRO.IECT

EXERCISE:
Proving
the
Least
Squares
Principle
for
the
Mean
170
Looking Forward, Then Back
171
Summary
172
Key
Terms
173
Problems
173
5
STANDARD
SCORFS
AND
THE
NORMAL
DISTRIBUTION
177
DATA BOX IIA:
Social
Comparison

Among
Behavioral
and
Natural
Scientists:
How
Many
Peers
Review
Research
Before
Publication?
179
DATA
BOX
II.B:
Explaining
the
Decline
in
SAT
Scores:
Lay
Versus
Statistical
Accounts
180
Why Standardize Measures?
181
The

z
Score:
A
Conceptual
Introduction
182
Formulas
for
Calculating
z
Scores
185
The Standard Normal Distribution
186
Standard Deviation
Revisited:
The
Area
Under the Normal
Curve
187
Application:
Comparing
Performance
on
More
than
One
Measure
188

Knowledge
Base
189
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Contents
xiii
Working with z Scores
and

the Normal Distribution 190
Finding
Percentile
Ranks
with z
Scores
191
Further
Examples
of
Using
z
Scores
to
Identify
Areas
Under
the
Normal
Curve
192
DATA BOX S.C:
Intelligence,
Standardized
IQ
Scores,
and
the
Normal Distribution
194

A
Further
Transformed
Score:
The
T
Score
196
Writing
About
Standard
Scores
and
the
Normal Distribution
197
Knowledge
Base
198
Looking Ahead: Probability, z Scores, and the Normal Distribution
198
PRO.JECT EXERCISE:
Understanding
the
Recentering
of
Scholastic
Aptitude
Test
Scores

199
Looking Forward, Then Back
201
Summary 202
Key Terms 202
Problems 202
6 CORRELATION 205
Association, Causation,
and
Measurement 206
Galton,
Pearson,
and
the
Index
of
Correlation
207
A Brief But
Essential
Aside:
Correlation
Does
Not Imply
Causation
207
The
Pearson Correlation Coefficient 209
Conceptual
Definition

of
the
Pearson
r 209
DATA BOX 6.A:
Mood
as
Misbegotten:
Correlating
Predictors
with
Mood
States
213
Calculating
the
Pearson
r 216
Interpreting Correlation
221
Magnitude of r 222
Coefficients
of
Determination
and
Nondetermination 222
Factors
Influencing r
224
Writing About

Correlational
Relationships
226
Knowledge
Base
227
Correlation as Consistency
and
Reliability 228
DATA BOX 6.B:
Personality,
Cross-Situational
Consistency,
and
Correlation
228
Other
Types
of
Reliability
Defined
229
A Brief
Word
About Validity
229
DATA BOX 6.C: Examining a
Correlation
Matrix:
A Start

for
Research
230
What
to Do When: A Brief, Conceptual Guide to
Other
Measures
of
Association
231
DATA BOX 6.D:
Perceived
Importance
of
Scientific
Topics
and
Evaluation
Bias
232
PROJECT EXERCISE: Identifying
Predictors
of
Your
Mood
233
Looking Forward,
Then
Back 237
Summary 237

Key
Terms 238
Problems 238
xiv
Contents
7 LINEAR REGRESSION
241
Simple Linear Regression
242
The
z
Score
Approach
to
Regression
242
Computational
Approaches
to
Regression
243
The
Method
of
Least
Squares
for
Regression
245
Knowledge

Base
249
DATA
BOX
7oA:
Predicting
Academic
Success
250
Residual Variation and the Standard Error
of
Estimate
251
DATA
BOX
7.B.
The
Clinical
and
the
Statistical:
Intuition
Versus
Prediction
253
Assumptions
Underlying
the
Standard
Error

of
Estimate
253
Partitioning Variance: Explained and Unexplained Variation 256
A
Reprise
for
the
Coefficients
of
Determination and
Nondetermination
257
Proper
Use
of
Regression:
A Brief
Recap
258
Knowledge
Base
258
Regression to the Mean 259
DATA
BOX
7.C.
Reinforcement,
Punishment,
or

Regression
Toward
the
Mean?
260
Regression
as
a Research
Tool
261
Other
Applications
of
Regression
in
the
Behavioral
Sciences
262
Writing About
Regression
Results
263
Multivariate Regression: A Conceptual Overview
263
PRo.JECT EXERCISE.
Perceiving
Risk
and
Judging

the
Frequency
of
Deaths
264
Looking Forward, Then
Back
268
Summary
268
Key
Terms
269
Problems
269
8 PROBABILITY
273
The Gambler's Fallacy
or
Randomness Revisited
275
Probability: A Theory
of
Outcomes
277
Classical
Probability
Theory
277
DATA

BOX
8oA:
"I
Once
Knew
a
Man
Who

":
Beware
Man-
Who
Statistics
278
Probability's
Relationship
to
Proportion
and
Percentage
281
DATA
BOX
8.B.
Classical
Probability
and
Classic
Probability

Examples
282
Probabilities
Can
Be
Obtained
from
Frequency
Distributions
283
Knowledge
Base
283
DATA
BOX
S.C.
A Short
History
of
Probability
284
Calculating Probabilities Using the Rules for Probability
285
The
Addition
Rule
for
Mutually
Exclusive
and Nonmutually

Exclusive
Events
285
The
Multiplication
Rule
for
Independent and Conditional
Probabilities
287
DATA
BOX
8.D.
Conjunction
Fallacies:
Is
Linda
a Bank
Teller
or a
Feminist
Bank
Teller?
288
J
!
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Contents
Multiplication

Rule
for
Dependent
Events
293
Knowledge
Base
293
Using Probabilities with the Standard Normal Distribution: z Scores
Revisited 294
Determining Probabilities with the Binomial Distribution:
An
Overview
299
Working
with
the
Binomial Distribution
300
Approximating
the
Standard
Normal
Distribution with
the
Binomial Distribution
301
DATA
BOX
8.E:

Control,
Probability,
and
When
the
Stakes
Are
High
304
Knowledge
Base
305
p
Values:
A Brief Introduction
305
Writing About
Probability
306
PROJECT
EXERCISE:
Flipping
Coins
and
the
Binomial
Distribution
307
Looking Forward, Then
Back

310
Summary 310
Key
Terms
311
Problems
311
9 INFERENTIAL STATISTICS: SAMPLING DISTRIBUTIONS
AND HYPOTHESIS TESTING
315
Samples, Population, and Hypotheses: Links to Estimation and
Experimentation 316
Point
Estimation
317
Statistical
Inference
and
Hypothesis
Testing
318
The Distribution
of
Sample Means 319
Expected
Value
and
Standard
Error
320

The Central Limit Theorem 322
Law
of
Large
Numbers
Redux
322
DATA BOX
9oA:
The
Law
of
Small
Numbers
Revisited
323
Standard Error and Sampling Error in Depth 324
Estimating
the
Standard
Error
of
the
Mean
324
Standard
Error
of
the
Mean:

A
Concrete
Example
Using
Population
Parameters
326
Defining
Confidence
Intervals
Using
the
Standard
Error
of
the
Mean
327
DATA BOX 9.B:
Standard
Error
as
an
Index
of
Stability
and
Reliability
of
Means

328
Knowledge
Base
329
DATA BOX 9.C:
Representing
Standard
Error
Graphically
330
Asking and Testing Focused Questions: Conceptual Rationale for
Hypotheses
331
DATA BOX 9.D: What
Constitutes
a
Good
Hypothesis?
332
Directional
and
Nondirectional
Hypotheses
333
The
Null and
the
Experimental
Hypothesis
333

Statistical Significance: A Concrete Account
336
DATA BOX 9.E:
Distinguishing
Between
Statistical
and
Practical
Significance
337
xv
xvi
Contents
Critical
Values:
Establishing Criteria for Rejecting the Null
Hypothesis 338
One- and
Two-
Tailed
Tests
340
Degrees
of
Freedom
341
DATA
BOX 9.F: When the Null Hypothesis
is
Rejected-Evaluating

Results with the MAGIC Criteria 342
Knowledge Base 343
Single
Sample
Hypothesis
Testing:
The z
Test
and the
Significance
of
r
343
What
Is
the Probability a Sample
Is
from One Population or
Another? 344
Is
One Sample Different from a Known Population? 345
When
Is
a Correlation Significant? 347
Inferential Errors Types I and
II
349
Statistical Power and Effect
Size
351

Effect Size 354
Writing About Hypotheses and the Results
of
Statistical
Tests
355
Knowledge Base 357
PROJECT EXERCISE: Thinking About Statistical Significance in the
Behavioral Science Literature 357
Looking Forward, Then Back
360
Summary 360
Key
Terms 362
Problems
362
10
MEAN COMPARISON
I:
THE t TEST
365
Recapitulation: Why Compare Means? 367
The Relationship Between the
t and the z Distributions
368
The t Distribution 368
Assumptions Underlying the t
Test
369
DATA

BOX
10.A: Some Statistical
History:
Who
was
'~Student"?
371
Hypothesis Testing with
t:
One-Sample Case
372
Confidence Intervals for the One-Sample t Test
DATA
BOX 10.B: The Absolute Value
of
t 376
Power Issues and the One-Sample t
Test
377
Knowledge Base 377
375
Hypothesis Testing with
Two
Independent Samples
378
Standard Error Revised: Estimating the Standard Error
of
the
Difference Between Means
379

Comparing Means: A Conceptual Model and an Aside for Future
Statistical
Tests
383
The t
Test
for Independent Groups 384
DATA
BOX 10.C: Language and Reporting Results, or (Too) Great
Expectations 388
Effect Size and the t Test 388
Characterizing the Degree
of
Association Between the Independent
Variable and the Dependent Measure 389
DATA
BOX
10.D:
Small Effects Can Be Impressive
Too
390
Knowledge Base 392
Hypothesis Testing with Correlated Research Designs
393
,/
I
,.:

Contents
J

,)
11
I
!
(
(
!
/
The
Statistical
Advantage
of
Correlated
Groups
Designs:
Reducing
Error
Variance
395
The
t
Test
for
Correlated
Groups
396
Calculating
Effect
Size
for

Correlated
Research
Designs
399
A Brief Overview
of
Power Analysis: Thinking More Critically About
Research and Data Analysis 400
Knowledge
Base
402
PRO.JECT EXERCISE:
Planning
for
Data
Analysis:
Developing
a
Before
and
After
Data
Collection
Analysis
Plan
402
Looking Forward, Then Back 405
Summary 405
Key
Terms 406

Problems 406
MEAN
COMPARISON
II:
ONE-VARIABLE
ANALYSIS
OF
VARIANCE
411
Overview
of
the Analysis
of
Variance
413
Describing
the
F
Distribution
417
Comparing
the
ANOVA
to
the
t
Test:
Shared
Characteristics
and

Assumptions
418
Problematic
Probabilities:
Multiple
t
Tests
and
the
Risk
of
Type
I
Error
420
DATA
BOX
1104:
R.
A.
Fischer:
Statistical
Genius
and
Vituperative
Visionary
422
How
is
the

ANOVA
Distinct from Prior Statistical
Tests?
Some
Advantages 423
Omnibus
Test
Comparing
More
than
1Wo
Means
Simultaneously
423
DATA
BOX
11.B:
Linguistically
Between a
Rock
and Among
Hard
Places
424
Experimentwise
Error:
Protecting
Against
Type
I

Error
424
Causality
and
Complexity
425
Knowledge
Base
426
One-Factor Analysis
of
Variance 426
Identifying
Statistical
Hypotheses
for
the
ANOVA
427
Some
Notes
on
Notation
and
the
ANOVA's
Steps
429
DATA
BOX 11.C:

Yet
Another
Point
of
View
on
Variance:
The
General
Linear
Model
431
One-
Way
ANOVA
from
Start
to
Finish:
An
Example
with
Data
431
Post Hoc Comparisons
of
Means: Exploring Relations in the "Big,
Dumb
F"
439

Tukey's
Honestly
Significant
Difference
Test
440
Effect
Size
for
the
F
Ratio
442
Estimating
the
Degree
of
Association
Between
the
Independent
Variable
and
the
Dependent
Measure
443
DATA
BOX
11.D:

A
Variance
Paradox-Explaining
Variance
Due
to
Skill
or
Baseball
is
Life
444
Writing
About
the
Results
of
a
One-
Way
ANOVA
445
Knowledge
Base
446
xvii
xviii
Contents
An Alternative Strategy for Comparing Means: A Brief Introduction
to

Contrast Analysis
447
PRO.JECT
EXERCISE:
Writing
and
Exchanging
Letters
About
the
ANOVA
451
Looking Forward, Then Back
452
Summary
453
Key
Terms
454
Problems
454
12
MEAN
COMPARISON
III:
TWO-VARIABLE
ANALYSIS
OF
VARIANCE
459

Overview
of
Complex Research Designs:
Life
Beyond Manipulating
One Variable 460
Two-Factor Analysis
of
Variance
461
DATA BOX 12.A:
Thinking
Factorially
463
Reading
Main
Effects
and
the
Concept
of
Interaction
465
Statistical
Assumptions
of
the
Two-Factor
ANOVA
469

Hypotheses,
Notation,
and
Steps
for
Performing
for
the
Two-
Way
ANOVA
469
DATA BOX 12.B:
Interpretation
Qualification:
Interactions
Supercede
Main
Effects
471
The Effects
of
Anxiety
and
Ordinal Position
on
Affiliation: A
Detailed Example
of
a Two-Way

ANOVA
475
Knowledge
Base
475
DATA BOX 12.C:
The
General
Linear
Model
for
the
Two-
Way
ANOVA
476
Effect
Size
486
Estimated
Omega-Squared
(~2)
for
the
1Wo-
Way
ANOVA
487
Writing
About

the
Results
of a
1Wo-
Way
ANOVA
488
Coda:
Beyond
2 X 2
Designs
489
Knowledge
Base
490
PRO.JECT
EXERCISE:
More
on
Interpreting
Interaction-Mean
Polish
and
Displaying
Residuals
490
Looking Forward, Then Back
495
Summary
495

Key
Terms
495
Problems 496
13
MEAN
COMPARISION
IV:
ONE-VARIABLE
REPEATED-
MEASURES
ANALYSIS
OF
VARIANCE
499
One-Factor Repeated-Measures
ANOVA
501
Statistical
Assumptions
of
the
One-
Way
Repeated-Measures
ANOVA
502
Hypothesis,
Notation,
and

Steps
for
Performing
the
One-
Variable
Repeated-Measures
ANOVA
503
DATA BOX 13.A:
Cell
Size
Matters,
But
Keep
the
Cell
Sizes
Equat
Too
508
Thkey's
HSD
Revisited
510
Effect
Size
and
the
Degree

of
Association
Between
the
Independent
Variable
and
Dependent
Measure
511
-

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i
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/
Contents
Writing About
the
Results
of
a
One-Way
Repeated-Measures
Design
512

Knowledge
Base
513
DATA BOX 13.B:
Improved
Methodology
Leads
to
Improved
Analysis-Latin
Square
Designs
514
Mixed Design
ANOVA:
A Brief Conceptual Overview
of
Between-
Within Research Design
515
PROJECT EXERCISE:
Repeated-Measures
Designs:
Awareness
of
Threats
to
Validity and
Inference
516

Looking Forward, Then
Back
518
Summary
518
Key
Terms
519
Problems
519
14
SOME
NONPARAMETRIC
STATISTICS
FOR
CATEGORICAL
AND
ORDINAL
DATA
523
How Do Nonparametric
Tests
Differ from Parametric
Tests?
525
Advantages
of
Using
Nonparametric Statistical
Tests

Over
Parametric
Tests
526
Choosing
to
Use
a Nonparametric
Test:
A Guide for the Perplexed
527
DATA BOX 14.A:
The
Nonparametric
Bible
for
the
Behavioral
Sciences:
Siegel
and
Castellan
(1988)
528
The Chi-Square (X
2
)
Test
for Categorical Data
528

Statistical Assumptions
of
the
Chi-Square
529
The
Chi-Square
Test
for
One-
Variable:
Goodness-of-Fit
529
The
Chi-Square
Test
of
Independence
of
Categorical
Variables
534
DATA BOX 14.B: A Chi-Square
Test
for
Independence
Shortcut
for
2 X 2
Tables

538
Supporting
Statistics
for
the
Chi-Square
Test
of
Independence:
Phi
(cp)
and
Cramer's
V
538
Writing
About
the
Result
of a
Chi-Square
Test
for
Independence
539
DATA BOX 14.C:
Research
Using
the
Chi-Square

Test
to
Analyze
Data
540
Knowledge
Base
541
Ordinal Data: A Brief Overview
541
The Mann-Whitney UTest
541
DATA BOX
14.D:
Handling
Tied
Ranks
in
Ordinal
Data
544
Mann-Whitney U
Test
for
Larger
(Ns
> 20)
Samples:
A Normal
Approximation

of
the
U Distribution
546
Writing About
the
Results
of
the
Mann-Whitney U
Test
547
The Wilcoxon Matched-Pairs Signed-Ranks
Test
547
DATA BOX 14.E:
Even
Null
Results
Must
Be
Written
Up
and
Reported
550
Writing About
the
Results
of

the
Wilcoxon
ill
Test
551
The Spearman Rank Order Correlation Coefficient
551
Writing About
the
Results
of
a
Spearman
rs
Test
554
Knowledge
Base
554
DATA BOX 14.F:
Research
Using
An
Ordinal
Test
to
Analyze
Data
555
xix

xx
Contents
PROJECT EXERCISE: Survey Says-Using Nonparametric
Tests
on
Data
556
Looking Forward, Then Back
558
Summary
558
Key
Terms
559
Problems 559
15
CONCLUSION:
STATISTICS
AND
DATA
ANALYSIS
IN
CONTEXT
563
The Fuss Over Null Hypothesis Significance
Tests
564
Panel
Recommendations:
Wisdom

from
the
APA
Task
Force
on
Statistical
Inference
565
Knowledge
Base
567
Statistics
as
Avoidable Ideology 567
Reprise:
Right Answers
Are
Fine, but Interpretation Matters More
568
Linking Analysis to Research
569
Do
Something:
Collect
Some
Data,
Run
a
Study,

Get
Involved
569
Knowing
When
to
Say
When:
Seeking
Statistical
Help
in
the
Future
570
DATA BOX 1S.A: Statistical
Heuristics
and
Improving Inductive
Reasoning
571
Data Analysis with Computers: The Tools Perspective Revisited 572
Knowledge
Base
573
Thinking
Like
a Behavioral Scientist: Educational, Social, and Ethical
Implications
of

Statistics and Data Analysis
573
DATA BOX 1S.B:
Recurring
Problems
with
Fraudulent,
False,
or
Misleading
Data
Analysis:
The
Dracula
Effect
576
Conclusion
578
PROJECT EXERCISE: A
Checklist
for
Reviewing
Published
Research
or
Planning a Study
578
Looking Forward, Then Back
580
Summary 580

Key
Terms
581
Problems
581
Appendix
A:
Basic
Mathematics Review and
Discussion
of
Math Anxiety A-I
Appendix
B:
Statistical
Tables
B-1
Appendix
C:
Writing
Up
Research
in
APA
Style:
Overview and
Focus
on
Results
C-l

Appendix D:
Doing
a
Research
Project
Using
Statistics
and
Data
Analysis:
Organization,
Time
Management,
and
Prepping
Data
for
Analysis
D-l
Appendix
E:
Answers
to
Odd-Numbered
End
of
Chapter
Problems
E-l
Appendix

F:
Emerging
Alternatives:
Qualitative
Research
Approaches
F-l
References
R-l
Credits
CR-l
Name
Index NI-l
Subject
Index SI-l
/
;
/
,
(
r
/
!
./
,
)
i
I
i
)

)
['
r'
I
f'
r
I
r
r
PRriAcr
In
my
view statistics has
no
reason for existence except
as
a catalyst for learning and
discovery.

GEORGE
BOX
This quotation serves
as
the guiding rationale for this book and, I hope, provides an
outlook for teaching and learning about statistics. From the main content to the ped-
agogical aids
and
end-of-the-chapter exercises, this textbook fosters learning
and
dis-

covery.
As
students learn how to perform calculations
and
interpret the results, they will
discover new ways to think about the world around them, uncover previously unrec-
ognized relationships among disparate variables, and make better judgments about how
and
why people behave the way they do.
Statistics
and
Data
Analysis
for
the
Behavioral
Sciences
teaches the theory behind
statistics
and
the analysis
of
data through a practical, hands-on approach. Students will
learn the "how to" side
of
statistics: how to select an appropriate test, how to collect
data for research, how to perform statistical calculations
in
a step-by-step manner, how
to be intelligent consumers

of
statistical information,
and
how to write
up
analyses
and
results
in
American Psychological Association
(APA)
style. Linking theory with prac-
tice will help students retain what they learn for use
in
future behavioral science courses,
research projects, graduate school,
or
any career where problem solving
is
used. Com-
bining statistics with data analysis leads to a practical pedagogical
goal-helping
stu-
dents to see that
both
are tools for intellectual discovery that examine the world
and
events
in
it

in
new
ways.
•
To
the
Student
Two
events spurred me to write this book,
and
I want you to know that I wrote
it
with
students foremost
in
my mind. First, I have taught statistics for over
12
years. In that
time, I've come to believe that some students struggle with statistics
and
quantitative
material simply because
it
is
not
well presented by existing textbooks. Few authors, for
example, adequately translate abstract ideas into concrete terms
and
examples that can
be easily understood. Consequently,

as
I wrote this book, I consciously tried to make
even the most complex material as accessible as possible. I also worked to develop ap-
plications
and
asides that bring the material to life, helping readers to make connec-
tions between abstract statistical ideas
and
their concrete application
in
daily life.
xxi
xxii
Preface
Second, the first statistics course that I took
as
an undergraduate was an unmiti-
gated disaster, really, a
nightmare-it
was dull, difficult,
and
daunting. I literally had
no
idea what the professor was talking about,
nor
did I know how to use statistics for any
purpose. I lost that battle
but
later won the war by consciously trying to think about
how statistics and the properties

of
data reveal themselves
in
everyday life. I came to
appreciate the utility
and
even dare I say
it-the
beauty
of
statistics. In doing so, I
also vowed that when I became a professor, no student
of
mine would suffer the pain
and intellectual doubt that I did
as
a first-time statistics student. Thus, I wrote this book
with my unfortunate "growing" experience
in
mind. I never want anyone
in
my classes
or
using my book to feel the anxiety that I did and, though
it
is a cliche, I think that
the book is better because
of
my trying first experience.
How can you ensure that you

will do well
in
your statistics
class?
Simple: Attend
classes, do the reading, do the homework,
and
review what you learn regularly. Indeed,
it
is
a very good idea to reserve some meaningful period
of
time
each
day
for studying
statistics
and
data analysis
(yes,
I
am
quite serious). When you do
not
understand some-
thing mentioned
in
this book
or
during class, ask the instructor for clarification im-

mediately,
not
later, when your uncertainty has had time to blossom into full-blown
confusion (remember my first experience in a statistics
class-I
know whereof I speak).
Remember, too, the importance
of
reminding yourself that
statistics
is
for
something.
You
should be able to stop at any given point in the course
of
performing a statistical
test
in
order to identify what you are doing,
why,
and what you hope to find
out
by us-
ing it.
If
you cannot do so, then you must backtrack to the point where you last
un-
derstood what you were doing and why; to proceed without such understanding
is

not
only a waste
of
time,
it
is
perilous, even foolhardy, and will
not
help you to compre-
hend the material.
By
the
way,
if
you
feel
that you need a review
of
basic mathematics,
Appendix A provides one, including some helpful ideas
on
dealing with math anxiety.
Beyond these straightforward steps, you should also take advantage
of
the peda-
gogical tools I created for this book. They are reviewed in detail in the
To
the
Instruc-
tor

section,
and
I suggest you take a look at their descriptions below. I do, however, take
the time to explain these tools
and
their use
as
they
appear
in the first
few
chapters
of
the book. I urge you to take these devices seriously, to see them
as
complementary to
and
not
replacements for your usual study habits. I promise you that your diligence will
have a favorable payoff in the
end-actual
understanding, reduced anxiety,
and
prob-
ably a higher grade than you expected when you first began the class.
II
To
the
Instructor
This book was written for use in a basic, first, non-calculus-based statistics course for

undergraduate students in psychology, education, sociology,
or
one
of
the other be-
havioral sciences. I assume little mathematical sophistication,
as
any statistical proce-
dure is presented conceptually first, followed by calculations demonstrated
in
a step-
by-step manner. Indeed,
it
is
important for both students
and
instructors to remember
that statistics
is
not mathematics,
nor
is
it a subfield
of
mathematics (Moore, 1992).
This book has a variety
of
pedagogical features designed to make it appeal to in-
structors
of

statistics (as well
as
students) including the following:
Decision Trees. Appearing
on
the opening page
of
each chapter, these very simple
flow charts identify the main characteristics
of
the descriptive
or
inferential procedures
reviewed therein, guiding readers through what a given test
does
(e.g., mean compari-
son),
when
to use it (i.e., to what research designs does it apply), and what sort
of
data
it
analyzes (e.g., continuous). At the close
of
each chapter, readers are reminded to rely
I
I
i
i
/

,
j
i
I
,.
.'
,
Preface
xxiii
on
the decision trees in a section called "Looking forward, then back." A special icon
(
H)
prompts them to recall the features found in the decision tree(
s)
opening the
chapters.
Key Terms
and
Concepts.
Key
terms (e.g., mean, variance)
and
concepts (e.g., ran-
dom sampling, central limit theorem) are highlighted throughout the text to gain read-
ers' attention and to promote retention.
An
alphabetical list
of
key

terms (including the
page number where each
is
first cited) appears at the end
of
every chapter.
Marginal Notes. The reader's attention will occasionally be drawn by marginal
notes-key
concepts, tips, suggestions, important points, and the
like-appearing
in the
margins
of
the text. An icon III drawn from the book's cover design identifies these
brief marginal notes.
Straightforward Calculation
of
Descriptive
and
Inferential Statistics
by
Hand. Sta-
tistical symbols
and
notation are explained early in the book (chapter 1).
All
of
the de-
scriptive and inferential statistics in the book are presented conceptually in the context
of

an example,
and
then explained in a step-by-step manner. Each step in any calcula-
tion
is
numbered for ease
of
reference (example: [2.2.3] refers to chapter 2, formula 2,
step 3). Readers who have access to a basic calculator can do any statistical procedure
presented in the book. Naturally, step-by-step advice also teaches students to read, un-
derstand, and use statistical notation
as
well
as
the statistical tables presented in Ap-
pendix
B.
Appendix A reviews basic mathematics and algebraic manipulation for those
students who need a self-paced refresher course. The second half
of
Appendix A dis-
cusses math anxiety, providing suggestions
and
references to alleviate it.
Data
Boxes. Specific examples
of
published research
or
methodological issues using

germane statistical procedures
or
concepts appear in Data
Boxes
throughout the text.
By
reading Data
Boxes,
students learn
ways
in which statistics and data analysis are tools
to aid the problem solver.
To
quote
Box,
they are tools for "learning
and
discovery."
Focus
on
Interpretation
of
Results
and
Presenting
Them
in
Written Form.
All
sta-

tistical procedures conclude with a discussion
of
how to interpret what a result
actu-
ally
means. These discussions have two points: what the test literally concludes about
some statistical relationship in the data
and
what it means descriptively-how did par-
ticipants behave in a study, what did they
do?
The focus then turns to clearly commu-
nicating results in prose form. Students will learn how to
put
these results into words
for inclusion in American Psychological Association
(APA)
style reports or draft arti-
cles. I used this approach successfully in a previous book (Dunn, 1999). Appendix
C,
which provides a brief overview
of
writing
APA
style reports, gives special emphasis to
properly presenting research results and statistical information.
Statistical Power, Effect Size,
and
Planned
and

Post Hoc Comparisons. Increasingly,
consideration
of
statistical power and effect size estimates
is
becoming more common-
place in psychology textbooks
as
well
as
journals. I follow this good precedent by at-
taching discussion
of
the strength
of
association
of
independent to dependent variables
along with specific inferential tests (e.g., estimated omega-squared-c;)2
-is
presented
with the
F ratio). In the same
way,
review
of
planned
or
post hoc comparisons
of

means
are attached to discussions
of
particular tests. I focus
on
conceptually straightforward
approaches for doing mean comparisons (e.g., Tukey's Honestly Significant Difference
xxiv
Preface
[HSD}
test),
but
I also discuss the
important-but
often neglected-perspectives pro-
vided by contrast analysis (e.g., Rosenthal & Rosnow, 1985).
Knowledge Base Concept Checks. Periodically, readers encounter digressions
within each chapter called "Knowledge Bases:'
as
in "students will add to their statistical
knowledge base:' Any Knowledge
Base
provides a quick concept check for students. In
lieu
of
a diagnostic quiz, readers can think about and then answer a
few
questions deal-
ing with the key points in the chapter section they just finished reading (these exercises
will obviously help pace the students' reading

of
conceptually challenging material,
as
well). Completion
of
each Knowledge
Base
in the book will incrementally add to their
knowledge base
of
statistical concepts and data analysis techniques. Answers to Knowl-
edge
Base
questions are provided immediately after the questions.
Project Exercises. Each chapter contains a "Project Exercise," an activity that applies
or extends issues presented therein. Project Exercises are designed to
give
students the
opportunity to think about how statistical concepts can actually be employed in re-
search or to identify particular issues that can render data analysis useful for the design
of
experiments or the interpretation
of
behavior.
On
occasion, a chapter's Project
Ex-
ercise might be linked to a Data
Box.
End-of-Chapter Problems. Each chapter in the text concludes with a series

of
prob-
lems. Most problems require traditional numerical answers,
but
many are designed to
help students think coherently and write cogently about the properties
of
statistics and
data. Answers to the odd-numbered problems are provided in the back
of
the textbook
in Appendix
E.
Special Appendixes. Beyond the traditional appendixes devoted a review
of
basic
math (with suggestions about combating math anxiety; Appendix
A),
statistical tables
(Appendix
B),
and answers
to
odd-numbered end-of-chapter problems (Appendix E),
I also include three more specialized offerings. Appendix C presents guidance
on
writ-
ing up research in
APA
style, highlighting specific

ways
to write and cogently present
statistical results. Advice on organizing a research project using statistics and data analy-
sis
is
presented in Appendix
D.
I emphasize the importance
of
being organized, how to
manage time,
and-most
importantly-how
to prepare raw data for analysis in this ap-
pendix. Finally, Appendix F introduces qualitative research approaches
as
emerging al-
ternatives-not
foils-for
the statistical analysis
of
data. Though by no means com-
monplace, such approaches are gradually being accepted
as
new options-really,
opportunities-for
researchers .
•
Supplements
Statistics

and
Data
Analysis
for
the
Behavioral
Sciences
has several supplements designed
to help both instructors and students. These supplements include:
Elementary Data Analysis
Using
Microsoft Excel
by
Mehan
and
Warner
(2000).
This
easy to use workbook introduces students to Microsoft
Excel
speadsheets
as
a tool to
be used in introductory statistics courses.
By
utilizing a familiar program such
as
Ex-
cel,
students can concentrate more on statistical concepts and outcomes and

less
on the
mechanics
of
software.
j
I
I
(
{
!
;
r
r
i
;
/
/'
Preface
xxv
Instructor's
Manual
and
Test Bank. The book has a detailed Instructor's Manual
(1M)
and
Test
Bank (TB). The
1M
includes syllabus outlines for one- or two-semester

statistics courses, detailed chapter outlines,
key
terms, lecture suggestions, sugges-
tions for classroom activities and discussions, film recommendations (where avail-
able and appropriate), and suggested readings for the instructor (i.e., articles and
books containing teaching tips, exercises). The
TB
contains test items (i.e., multiple
choice items, short essays, problems), and
is
also available on computer diskette for
PC and Macintosh.
Dedicated Website. The book has a dedicated website (www.mhhe.com.dunn)
so
that
potential instructors can examine a synopsis
of
the book, its table
of
contents, descrip-
tions
of
the available supplements, and ordering information. Links to other sites on
the
Web
related to statistics, data analysis, and psychology (including links to other parts
of
the McGraw-Hill site) are available. In addition, portions
of
the Instructor's Manual

and
Test
Bank appear on the website and are "password" accessible to instructors who
have selected the text and their students. The website also has an online
SPSS
guide,
which
is
an alternative to the expensive printed guides. Beginning with computing a
correlation between two variables and a continuing with
t tests,
ANOVAs,
and chi-
square, this site will help your students understand the basics
of
the
SPSS
program.
Study
Guide
for
Statistics
and
Data
Analysis for the Behavioral Sciences. Instruc-
tors (or students) can order a study guide to accompany
Statistics and Data Analysis for
the Behavioral Sciences.
The Study Guide contains a review
of

key
terms, concepts, and
practice problems designed to highlight statistical issues. Answers to any problems will
be provided in the back
of
the Study Guide.