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Exploring robust aternatives to Pearson's r through secondary analysis of published behavioral science data
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Exploring robust aternatives to Pearson's r through secondary analysis of published behavioral science data
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Content
EXPLORING ROBUST ALTERNATIVES TO PEARSON’S r THROUGH
SECONDARY ANALYSIS OF PUBLISHED BEHAVIORAL SCIENCE DATA
by
Veronica Mejia Stuart
_______________________________________________________________________
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(PSYCHOLOGY)
December 2008
Copyright 2008 Veronica Mejia Stuart
ii
Dedication
This dissertation is dedicated to my husband, David. Thank you
for all your love, support and encouragement throughout this process. I
would also like to thank my committee members, Richard John, Bill
McClure, Stephen Read, and my committee chair and advisor Rand
Wilcox. I would especially like to thank Bill McClure for introducing me
to the world of neuroscience and psychology so many years ago, inciting
a passion for research that has stayed with me all this time, and Rand
Wilcox for introducing me to the world of quantitative psychology,
teaching me how to think critically about research methods and
analytical techniques in psychology, fueling a commitment to strive to
become a more creative and resourceful researcher in the field of
behavioral science.
iii
Table of Contents
Dedication ii
List of Tables iv
List of Figures x
Abstract xix
Chapter 1: Introduction 1
Robust alternatives to Pearson’s r 4
The NHST controversy and the role of confidence intervals 5
Robust, simple (one-predictor) regression alternatives to Pearson’s r 9
Relevance of the current study 11
Research questions addressed in the current investigation 13
Chapter 2: Method 14
Sample 14
Procedure 15
Measures of association and effect magnitude 16
Chapter 3: Results 19
Andreoletti, Zebrowitz, & Lachman (2001) 20
Bryan & Luszcz (2000) 180
Frone (2000) 192
McKelvey & McKenry (2000) 204
Ullman & Brecklin (2003) 260
Chapter 4: Discussion 279
Revisiting our research questions 280
Problems and limitations of the current study 282
Practical implications for applied behavioral science researchers 282
References 284
iv
List of Tables
Table 1.1.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) –
Correlations 37
Table 1.1.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) –
Correlations 38
Table 1.1.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) –
Correlations 39
Table 1.1.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) –
Correlations 40
Table 1.1.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) –
Correlations 41
Table 1.2.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) –
Regression Estimates 42
Table 1.2.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) –
Regression Estimates 43
Table 1.2.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) –
Regression Estimates 44
Table 1.2.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) –
Regression Estimates 45
Table 1.2.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) –
Regression Estimates 46
Table 2.1.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women)
- Correlations 63
Table 2.1.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women)
- Correlations 64
Table 2.1.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women)
- Correlations 65
Table 2.1.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women)
- Correlations 66
Table 2.1.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women)
- Correlations 67
v
Table 2.2.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women)
– Regression Estimates 68
Table 2.2.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women)
– Regression Estimates 69
Table 2.2.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women)
– Regression Estimates 70
Table 2.2.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women)
– Regression Estimates 71
Table 2.2.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women)
– Regression Estimates 72
Table 3.1.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Men) - Correlations 90
Table 3.1.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Men) - Correlations 91
Table 3.1.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Men) - Correlations 92
Table 3.1.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Men) - Correlations 93
Table 3.1.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Men) - Correlations 94
Table 3.2.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Men) – Regression Estimates 95
Table 3.2.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Men) – Regression Estimates 96
Table 3.2.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Men) – Regression Estimates 97
Table 3.2.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Men) – Regression Estimates 98
Table 3.2.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Men)
– Regression Estimates 99
Table 4.1.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Women) - Correlations 117
vi
Table 4.1.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Women) - Correlations 118
Table 4.1.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Women) - Correlations 119
Table 4.1.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Women) - Correlations 120
Table 4.1.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Women) - Correlations 121
Table 4.2.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Women) – Regression Estimates 122
Table 4.2.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Women) – Regression Estimates 123
Table 4.2.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Women) – Regression Estimates 124
Table 4.2.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Women) – Regression Estimates 125
Table 4.2.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age
Women) – Regression Estimates 126
Table 5.1.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) -
Correlations 144
Table 5.1.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) -
Correlations 145
Table 5.1.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) -
Correlations 146
Table 5.1.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) -
Correlations 147
Table 5.1.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) -
Correlations 148
Table 5.2.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
Regression Estimates 149
Table 5.2.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
Regression Estimates 150
vii
Table 5.2.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
Regression Estimates 151
Table 5.2.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
Regression Estimates 152
Table 5.2.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
Regression Estimates 153
Table 6.1.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) -
Correlations 170
Table 6.1.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) -
Correlations 171
Table 6.1.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) -
Correlations 172
Table 6.1.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) -
Correlations 173
Table 6.1.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) -
Correlations 174
Table 6.2.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) –
Regression Estimates 175
Table 6.2.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) –
Regression Estimates 176
Table 6.2.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) –
Regression Estimates 177
Table 6.2.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) –
Regression Estimates 178
Table 6.2.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) –
Regression Estimates 179
Table 7.1.1 – Bryan & Luszcz (2000) - Correlations 188
Table 7.1.2 – Bryan & Luszcz (2000) - Correlations 189
Table 7.2.1 – Bryan & Luszcz (2000) – Regression Estimates 190
Table 7.2.2 – Bryan & Luszcz (2000) – Regression Estimates 191
viii
Table 8.1.1 – Frone (2000) - Correlations 200
Table 8.1.2 – Frone (2000) - Correlations 201
Table 8.2.1 – Frone (2000) – Regression Estimates 202
Table 8.2.2 – Frone (2000) – Regression Estimates 203
Table 9.1.1- – McKelvey & McKenry (2000 - Black mothers) -
Correlations 222
Table 9.1.2- – McKelvey & McKenry (2000 - Black mothers) -
Correlations 223
Table 9.1.3- – McKelvey & McKenry (2000 - Black mothers) -
Correlations 224
Table 9.1.4- – McKelvey & McKenry (2000 - Black mothers) -
Correlations 225
Table 9.1.5- – McKelvey & McKenry (2000 - Black mothers) -
Correlations 226
Table 9.2.1- – McKelvey & McKenry (2000 - Black mothers) – Regression
Estimates 227
Table 9.2.2- – McKelvey & McKenry (2000 - Black mothers) – Regression
Estimates 228
Table 9.2.3- – McKelvey & McKenry (2000 - Black mothers) – Regression
Estimates 229
Table 9.2.4- – McKelvey & McKenry (2000 - Black mothers) – Regression
Estimates 230
Table 9.2.5- – McKelvey & McKenry (2000 - Black mothers) – Regression
Estimates 231
Table 10.1.1- – McKelvey & McKenry (2000 - White mothers) -
Correlations 250
Table 10.1.2- – McKelvey & McKenry (2000 - White mothers) -
Correlations 251
Table 10.1.3- – McKelvey & McKenry (2000 - White mothers) -
Correlations 252
ix
Table 10.1.4- – McKelvey & McKenry (2000 - White mothers) -
Correlations 253
Table 10.1.5- – McKelvey & McKenry (2000 - White mothers) -
Correlations 254
Table 10.2.1- – McKelvey & McKenry (2000 - White mothers) –
Regression Estimates 255
Table 10.2.2- – McKelvey & McKenry (2000 - White mothers) –
Regression Estimates 256
Table 10.2.3- – McKelvey & McKenry (2000 - White mothers) –
Regression Estimates 257
Table 10.2.4- – McKelvey & McKenry (2000 - White mothers)– Regression
Estimates 258
Table 10.2.5- – McKelvey & McKenry (2000 - White mothers) –
Regression Estimates 259
Table 11.1.1 – Ullman & Brecklin (2003) - Correlations 273
Table 11.1.2 – Ullman & Brecklin (2003) - Correlations 274
Table 11.1.3 – Ullman & Brecklin (2003) - Correlations 275
Table 11.2.1 – Ullman & Brecklin (2003) – Regression Estimates 276
Table 11.2.2 – Ullman & Brecklin (2003) – Regression Estimates 277
Table 11.2.3 – Ullman & Brecklin (2003) – Regression Estimates 278
x
List of Figures
Figure 1.1: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) –
Attractiveness & SES 22
Figure 1.2: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) –
Attractiveness & External Constraints 23
Figure 1.3: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) –
Attractiveness & Personal Control 24
Figure 1.4: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) –
Attractiveness & Work Control 25
Figure 1.5: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) –
Attractiveness & Health Control 26
Figure 1.6: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) –
SES & External Constraints 27
Figure 1.7: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) –
SES & Personal Control 28
Figure 1.8: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) –
SES & Work Control 29
Figure 1.9: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) –
SES & Health Control 30
Figure 1.10: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) –
External Constraints & Personal Control 31
Figure 1.11: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) –
External Constraints & Work Control 32
Figure 1.12: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) –
External Constraints & Health Control 33
Figure 1.13: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) –
Personal Control & Work Control 34
Figure 1.14: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) –
Personal Control & Health Control 35
Figure 1.15: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) –
Work Control & Health Control 36
xi
Figure 2.1- Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) –
Attractiveness & SES 48
Figure 2.2 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) –
Attractiveness & External Constraints 49
Figure 2.3 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) –
Attractiveness & Personal Constraints 50
Figure 2.4 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) –
Attractiveness & Work Control 51
Figure 2.5 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) –
Attractiveness & Health Control 52
Figure 2.6 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women)–
SES & External Constraints 53
Figure 2.7 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) –
SES & Personal Control 54
Figure 2.8 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) –
SES & Work Control 55
Figure 2.9 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) –
SES & Health Control 56
Figure 2.10 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women)
– External Constraints & Personal Control 57
Figure 2.11 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women)
– External Constraints & Work Control 58
Figure 2.12 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women)
– External Constraints & Health Control 59
Figure 2.13 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women)
– Personal Control & Work Control 60
Figure 2.14 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women)
– Personal Control & Health Control 61
Figure 2.15 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women)–
Work Control & Health Control 62
Figure 3.1 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men)
– Attractiveness & SES 75
xii
Figure 3.2 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men)
– Attractiveness & External Constraints 76
Figure 3.3 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men)
– Attractiveness & Personal Constraints 77
Figure 3.4 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men)
– Attractiveness & Work Control 78
Figure 3.5 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men)
– Attractiveness & Health Control 79
Figure 3.6 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men)
– SES & External Constraints 80
Figure 3.7 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men)
– SES & Personal Control 81
Figure 3.8 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men)
– SES & Work Control 82
Figure 3.9 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men)
– SES & Health Control 83
Figure 3.10 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Men) – External Constraints & Personal Control 84
Figure 3.11 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Men) – External Constraints & Work Control 85
Figure 3.12 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Men) – External Constraints and Health Control 86
Figure 3.13 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Men) – Personal Control & Work Control 87
Figure 3.14 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Men) – Personal Control & Health Control 88
Figure 3.15 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Men) – Work Control & Health Control 89
Figure 4.1 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Women) – Attractiveness & SES 102
Figure 4.2 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Women) – Attractiveness & External Constraints 103
xiii
Figure 4.3 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Women) – Attractiveness & Personal Constraints 104
Figure 4.4 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Women) – Attractiveness & Work Control 105
Figure 4.5 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Women) – Attractiveness & Health Control 106
Figure 4.6 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Women) – SES & External Constraints 107
Figure 4.7 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Women) – SES & Personal Control 108
Figure 4.8 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Women) – SES & Work Control 109
Figure 4.9 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Women) – SES & Health Control 110
Figure 4.10 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Women) – External Constraints & Personal Control 111
Figure 4.11 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Women)– External Constraints & Work Control 112
Figure 4.12 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Women) – External Constraints & Health Control 113
Figure 4.13 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Women) – Personal Control & Work Control 114
Figure 4.14 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Women) – Personal Control & Health Control 115
Figure 4.15 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age
Women) – Work Control & Health Control 116
Figure 5.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
Attractiveness & SES 129
Figure5.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
Attractiveness & External Constraints 130
Figure 5.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
Attractiveness & Personal Control 131
xiv
Figure 5.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
Attractiveness & Work Control 132
Figure 5.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
Attractiveness & Health Control 133
Figure 5.6 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
SES & External Constraints 134
Figure 5.7 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
SES & Personal Control 135
Figure 5.8 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
SES & Work Control 136
Figure 5.9 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
SES & Health Control 137
Figure 5.10 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
External Constraints & Personal Control 138
Figure 5.11 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
External Constraints & Work Control 139
Figure 5.12 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
External Constraints & Health Control 140
Figure 5.13 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
Personal Control & Work Control 141
Figure 5.14 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
Personal Control & Health Control 142
Figure 5.15 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) –
Work Control & Health Control 143
Figure 6.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) –
Attractiveness & SES 155
Figure 6.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women)
– Attractiveness & External Constraints 156
Figure 6.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women)
– Attractiveness & Personal Control 157
Figure 6.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) –
Attractiveness & Work Control 158
xv
Figure 6.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women)
– Attractiveness & Health Control 159
Figure 6.6 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women)
– SES & External Constraints 160
Figure 6.7 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women)
– SES & Personal Control 161
Figure 6.8 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women)
– SES & Work Control 162
Figure 6.9 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women)
– SES & Health Control 163
Figure 6.10 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women)
– External Constraints & Personal Control 164
Figure 6.11 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women)
– External Constraints & Work Control 165
Figure 6.12 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women)
– External Constraints & Health Control 166
Figure 6.13 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women)
– Personal Control & Work Control 167
Figure 6.14 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women)
– Personal Control & Health Control 168
Figure 6.15 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women)
– Work Control & Health Control 169
Figure 7.1 - Bryan & Luszcz (2000) – Age & CES-D Score 182
Figure 7.2 - Bryan & Luszcz (2000) – Age & Self-rated Health 183
Figure 7.3 - Bryan & Luszcz (2000) – Age & Age when left school 184
Figure 7.4 - Bryan & Luszcz (2000) –CES-D Score & Self-rated Health 185
Figure 7.5 - Bryan & Luszcz (2000) –CES-D Score & Age when left school
186
Figure 7.6 - Bryan & Luszcz (2000) – Self-rated Health & Age when left
school 187
xvi
Figure 8.1 - Frone (2000) – Work-family conflict & Family-work conflict
194
Figure 8.2 - Frone (2000) – Work-family conflict & Age 195
Figure 8.3 - Frone (2000) – Work-family conflict & Number of work hours
196
Figure 8.4 - Frone (2000) – Family-work conflict & Age 197
Figure 8.5 - Frone (2000) – Family-work conflict & Number of work hours
198
Figure 8.6 - Frone (2000) – Age & Number of work hours 199
Figure 9.1 - McKelvey & McKenry (2000 - Black mothers) –CES-D score
& Self-esteem 207
Figure 9.2 - McKelvey & McKenry (2000 - Black mothers)– CES-D score
& Personal mastery 208
Figure 9.3 - McKelvey & McKenry (2000 - Black mothers) –CES-D score
& Happiness 209
Figure 9.4 - McKelvey & McKenry (2000 - Black mothers) – CES-D
score & Economic well-being 210
Figure 9.5 - McKelvey & McKenry (2000 - Black mothers) –CES-D score
& Parental satisfaction 211
Figure 9.6 - McKelvey & McKenry (2000 - Black mothers) – Self-esteem
& Personal mastery 212
Figure 9.7 - McKelvey & McKenry (2000 - Black mothers) – Self-esteem
& Happiness 213
Figure 9.8 - McKelvey & McKenry (2000 - Black mothers) – Self-esteem
& Economic well-being 214
Figure 9.9 - McKelvey & McKenry (2000 - Black mothers) – Self-esteem
& Parental satisfaction 215
Figure 9.10 - McKelvey & McKenry (2000 - Black mothers) – Personal
mastery & Happiness 216
Figure 9.11 - McKelvey & McKenry (2000 - Black mothers)– Personal
mastery & Economic well-being 217
xvii
Figure 9.12 - McKelvey & McKenry (2000 - Black mothers)– Personal
mastery & Parental satisfaction 218
Figure 9.13 - McKelvey & McKenry (2000 - Black mothers)–Happiness
& Economic wellbeing 219
Figure 9.14 - McKelvey & McKenry (2000 - Black mothers) –Happiness
& Parental satisfaction 220
Figure 9.15 - McKelvey & McKenry (2000 - Black mothers) –Economic
well-being & Parental satisfaction 221
Figure 10.1 - McKelvey & McKenry (2000 - White mothers) –CES-D score
& Self-esteem 235
Figure 10.2 - McKelvey & McKenry (2000 - White mothers) –CES-D score
& Personal mastery 236
Figure 10.3 - McKelvey & McKenry (2000 - White mothers)– CES-D score
& Happiness 237
Figure 10.4 - McKelvey & McKenry (2000 - White mothers)– CES-D score
& Economic well-being 238
Figure 10.5 - McKelvey & McKenry (2000 - White mothers) –CES-D score
& Parental satisfaction 239
Figure 10.6 - McKelvey & McKenry (2000 - White mothers) – Self-esteem
& Personal mastery 240
Figure 10.7 - McKelvey & McKenry (2000 - White mothers)– Self-esteem
& Happiness 241
Figure 10.8 - McKelvey & McKenry (2000 - White mothers) – Self-esteem
& Economic well-being 242
Figure 10.9 - McKelvey & McKenry (2000 - White mothers)– Self-esteem
& Parental satisfaction 243
Figure 10.10 - McKelvey & McKenry (2000 - White mothers) – Personal
mastery & Happiness 244
Figure 10.11 - McKelvey & McKenry (2000 - White mothers) – Personal
mastery & Economic wellbeing 245
Figure 10.12 - McKelvey & McKenry (2000 - White mothers) – Personal
mastery & Parental satisfaction 246
xviii
Figure 10.13 - McKelvey & McKenry (2000 - White mothers) –Happiness
& Economic wellbeing 247
Figure 10.14 - McKelvey & McKenry (2000 - White mothers) –Happiness
& Parental satisfaction 248
Figure 10.15 - McKelvey & McKenry (2000 - White mothers) –Economic
wellbeing & Parental satisfaction 249
Figure 11.1 - Ullman & Brecklin (2003) – Age & Trauma 263
Figure 11.2 - Ullman & Brecklin (2003) – Age & Stressful 264
Figure 11.3 - Ullman & Brecklin (2003) – Age & Support 265
Figure 11.4 - Ullman & Brecklin (2003) – Age & Conflict 266
Figure 11.5 - Ullman & Brecklin (2003) – Trauma & Stressful 267
Figure 11.6 - Ullman & Brecklin (2003) – Trauma & Support 268
Figure 11.7 - Ullman & Brecklin (2003) – Trauma & Conflict 269
Figure 11.8 - Ullman & Brecklin (2003) – Stressful & Support 270
Figure 11.9 - Ullman & Brecklin (2003) – Stressful & Conflict 271
Figure 11.10 - Ullman & Brecklin (2003) – Support & Conflict 272
xix
Abstract
Eleven data sets from five recently published articles in the field of
psychology were re-analyzed to examine the extent to which reliance on
Pearson’s r to assess the relationship between two variables resulted in
missed information. The robust techniques examined include three
robust alternatives to r: the percentage bend correlation (rpb), the
Winsorized correlation (rw), and the skipped correlation (rp); and two
simple (one-predictor) regression techniques: the Theil-Sen ( ) and
Coakley-Hettmansperger ( ) regression estimators. Several variables
from each study were selected to replicate the correlational findings in
the originating study. The relationships between these variables were
examined through computation of these alternatives to Pearson’s r using
S-Plus and R statistical software. The properties of each computed
statistic or confidence interval were then qualitatively compared and
contrasted. Results indicate that the skipped correlation (rp) may be best
suited to efficiently and accurately assess the relationship between two
variables. Applied researchers in the behavioral sciences are challenged
to recognize the advantages of these robust alternatives to Pearson’s r
and other traditional statistical methods.
1
Chapter 1: Introduction
Many investigations in behavioral science research begin with the
simple question: Are these variables related? Once resolved, however,
this simple question quickly leads to other questions that may not be so
simple: In what way are these variables related? How strongly are these
variables related? How meaningful is the relationship between these
variables? Knowing what we know about this relationship, can one
variable be used to predict the other variable?
The most widely used and accepted method of assessing whether
two variables are related is Pearson’s r. Pearson’s r is a numerical
representation of the degree and direction of relationship between two
variables, always ranging between -1.00 and +1.00. The numerical value
of r, ignoring the sign, is considered an indication of the magnitude of the
relationship between two variables. A rule of thumb followed by many
researchers, originally suggested by Cohen (1977; as cited in Leary,
2004), interprets the relationship represented by Pearson’s r as weak if it
is at or below .10, moderate at or around .30, and strong if r is greater
than .50. The direction of the relationship is indicated by the sign of r. If
r is positive, this indicates a positive (direct) relationship between two
variables; that is, as the score or value of one variable increases, so does
the score or value of the other variable. If r is negative, this indicates a
2
negative (inverse) relationship between two variables; that is, as the score
or value of one variable increases, the score or value of the other variable
decreases.
In addition to magnitude and direction, the statistical significance
of r is another important factor for researchers to consider. Due to the
near omnipresence of error variance in research (e.g., due to sampling
error, measurement error, etc.) it is extremely unlikely that one would
obtain an r of exactly .00 but this non-zero r does not necessarily
indicate the existence of a non-zero (rho, the population estimate of r)
in the population under investigation. Therefore, researchers rely on
testing the null hypothesis that rho is zero ( ) to determine the
existence of a relationship in the population. The null hypothesis
significance test (NHST) is based on calculating the conditional
probability (p), or p-value, of the data given H0. One might also interpret
a statistically significant result as a way to minimize or exclude
alternative explanations such as confounds or sampling error if, given
that p is the conditional probability of the data given H0, one extrapolates
that “p is the probability that the departure of the test result from null
would have resulted from sampling error alone” (Cortina and Dunlap,
1997, p. 164).
A calculated r is determined to be statistically significant if p is
found to be sufficiently low (usually less than .05). Statistical
3
significance is affected by sample size and the magnitude or r. As a
sample size increases, the minimum value of r considered to be
statistically significant decreases. Therefore, it is important to emphasize
that a statistically significant r means only that some relationship likely
exists between two variables. The p-level of r alone says nothing about
the magnitude or meaningfulness of this linear relationship.
Statistical significance, magnitude, and direction of Pearson’s r are
what most researches rely on to answer the questions listed at the
opening of this paper. There is some risk, however, to relying only on the
properties of r to interpret one’s data. The magnitude of r is extremely
vulnerable to distortion from several factors. Many of these are
discussed in Wilcox (2003, chap. 6). Two of these factors are particularly
relevant to the current discussion: Restriction of range of the observed
values and outliers.
Restriction of the range of scores represented can artificially
increase or decrease r and mislead the researcher into making an
inaccurate inference about the true nature of the relationship between
variables. This situation is exacerbated if any curvature occurs in the
data set, because if one is only examining a restricted range of data, the
curvilinear relationship between two variables may appear to be a linear
relationship.
4
Outliers can have a profound effect on r because of its close
relationship to the slope of the least squares regression line (b1)
which is known to have a breakdown point of (Wilcox, 2003, chap. 6).
This means that one unusual value can sway the value of r so that it
appears large when there is no association among the rest of the values
or small when the remaining points are clearly centered around a line
with a nonzero slope. Without careful (visual) examination of raw data,
researchers can be easily misled into an inaccurate interpretation of
effect size.
Robust alternatives to Pearson’s r
One way to address the problem of outliers is to use a robust
alternative to Pearson’s r that will be less affected by outlying values.
Wilcox (2005) proposes many robust alternatives to r. The most
successful of these has been the percentage bend correlation (rpb).
Whereas rpb behaves similarly to r under normality, unlike r, rpb is less
sensitive to outliers and other changes in its distribution because of a
higher finite-sample breakdown point. The finite-sample breakdown
point of a statistic is the smallest proportion of observations that renders
that statistic meaningless (Wilcox, 2003). The finite-sample breakdown
5
point of rpb is equal to , where usually, , but can be as high as
(Wilcox, 2003; Wilcox, 2005).
Another robust alternative to r is the Winsorized correlation (rw).
Winsorizing refers to the practice of transforming (“pulling in”) a fixed
percentage of the smallest and largest observations in a data set (Wilcox,
2003). A certain percentage of the smallest values are pulled up to the
smallest value not Winsorized and an equal percentage of the highest
values are pulled down to the highest value not Winsorized. Then,
Pearson’s r is applied to the newly transformed set of observations. This
method competes well with r, but does not outperform rpb (Wilcox, 2005).
The NHST controversy and the role of confidence intervals
There is an on-going debate among researchers in the behavioral
sciences about the value and usefulness of the NHST. Broadly speaking,
the stakeholders of this debate can be classified as either NHST-
promoters or detractors with the majority taking a smattering of nuanced
moderate positions within each group. Part of the controversy over NHST
is based on a strong criticism of the current over-reliance on probability
(p) values and their widespread misinterpretation and misuse in
psychological research. This problem is likely related to another ardent
criticism of NHST (shared even by the NHST promoters), namely that
NHST encourages an automated approach to statistical analysis. The
6
main danger of over-reliance on p-levels alone to interpret research
findings is that they are often misunderstood and therefore
misinterpreted and misused by researchers leading to inappropriate
conclusions drawn about data and possible confusion to consumers of
that research. For example: p-levels without supporting information
may tempt the researcher into misuse as an indicator of effect size (cf.
Nickerson, 2000; Steiger and Fouladi, 1997) or replicability (cf.
Balluerka, Gómez, & Hidalgo, 2005; Nickerson, 2000). Many researchers
think that failure to reject the null hypothesis means “accepting” the null
hypothesis (cf. Balluerka, Gómez, & Hidalgo, 2005; Nickerson, 2000) or
that statistical significance means the same thing as practical
significance (cf. Balluerka, Gómez, & Hidalgo, 2005; Nickerson, 2000).
Additionally, many NHST proponents also have strong opinions
about proposed alternative and supplementary methods and incorporate
these views into their side of the debate. One such alternative or
supplementary method often discussed is the calculation of confidence
intervals (CIs). The need for more prevalent use of CIs in behavioral
science research is one issue upon which NHST promoters and
detractors largely agree (Harlow, 1997).
Confidence intervals (CIs) provide much more information about
research findings than p-values alone. In addition to reporting the NHST
7
outcome
1
, CIs also give an indication of the magnitude of a given effect
(distance of the mean from zero), precision of measurement (width of the
CI), and power (based on magnitude of effect and precision of
measurement) in a given study (Steiger and Fouladi, 1997). Most
importantly to supporters of CIs versus NHST,
If the sample estimate has low sampling variability and high
precision of estimate, then even a narrow confidence interval will
bracket the true parameter a high percentage of the time, over
repeated samples. Thus the outcome of the confidence interval
calculation is a report of a parameter value, together with an
indication of how precisely it has been determined. (Steiger and
Fouladi, 1997, p. 231).
Still there are substantive criticisms of the recommendation to replace
NHST with CIs. One criticism, acknowledged even by Steiger and
Fouladi (1997), is that “the width of a confidence interval is generally a
random variable, subject to sampling fluctuations of its own, and may be
too unreliable at small sample sizes to be useful for some purposes” (p.
254). One way to address this concern would be to use a percentile
bootstrap method to calculate confidence intervals.
The purpose of bootstrap methods is to provide a way to estimate
the sampling distribution of some statistic based on observed data
(Wilcox, 2003, chap. 7). The percentile bootstrap method has been
shown to be a successful approach to controlling the probability of Type I
error (Wilcox, 2005, chap. 4) when calculating a .95 confidence interval
1 Demonstrated by the inclusion of zero (fail to reject Ho) or the exclusion of zero (reject
Ho) in the calculated confidence interval.
8
for various population parameters. This approach results in more
information than a traditional CI, namely, a better estimate of the
direction and magnitude of the population parameter of interest.
Hypothesis testing and estimating effect size through the calculation of
heteroscedastic percentile bootstrap confidence intervals
Conventional approaches to testing the hypothesis that Pearson’s r
is zero (i.e., ) and effect size estimation about Pearson’s r rely on
an assumption of homoscedasticity (equal variances) that is routinely
violated. The result of this violated assumption is loss of power, leading
to loss in the likelihood of detecting a relationship, and an inaccurate
estimation of the standard error, leading to an inaccurate estimation of
effect size (Wilcox, 2003, chap. 6). Although the percentage bend
correlation (rpb) and the Winsorized correlation (rw) address to some
extent the distortional effects of outliers, they are not immune to these
same undesirable effects of heteroscedasticity (unequal variances) under
the conventional approach of testing for no relationship (i.e., ;
). Rejecting the null hypothesis that no relationship exists tells
us that some type of relationship does exist, but does not tell us much
more. An alternative approach that allows for heteroscedasticity is the
use of a heteroscedastic percentile bootstrap method to calculate a .95
confidence interval for the correlation of interest.
9
Robust, simple (one-predictor) regression alternatives to Pearson’s r
Once a relationship between two variables has been established
(e.g., by obtaining a statistically significant r, rpb, or rw), it may be
appropriate to examine the relationship between these two variables
more closely by applying simple (one-predictor) regression methods.
Using the slope of regression line as indicator of effect magnitude may be
a more reliable and accurate approach, especially if the regression
estimator is robust and adequately addresses the problem of outliers.
Here, two robust simple regression methods that may work well in these
situations are examined.
Theil-Sen regression estimator (one predictor)
The Theil-Sen estimator is a robust regression estimator well
known to offer important advantages over the conventional least squares
estimator in terms of resistance to outliers and increased power (Wilcox,
2003, chap 13; Wilcox, 2003a). In the single-predictor case, Dietz (1989,
as cited in Wilcox, 2003, chap 13 and Wilcox, 2005 chap. 10) estimates
the finite-sample breakdown point of the Theil-Sen estimator to be
approximately .29. Theil-Sen also appears to result in a smaller
standard error term estimate than least squares (Wilcox, 2003a). Theil-
Sen is calculated by first computing “the slope for all pairs of points
having distinct X values and then computing the median of these slopes;
the result will be labeled b1ts” (Wilcox, 2003, pp. 477).
10
Coakley-Hettmansperger estimator (one predictor)
The Coakley-Hettmansperger regression estimator is the result of a
successful attempt by Coakley and Hettmansperger (1993) to find a
robust regression estimator that simultaneously achieves, “(a) a
breakdown point of roughly .50; (b) a bounded influence function; and (c)
a high efficiency (say .95) vs. LS [least squares] when [the error
distribution] F is Gaussian [normal]” (Coakley and Hettmansperger,
1993, pp. 872).
Calculation of the Coakley-Hettmansperger estimator ( ), as
described in Wilcox, 2003, chap. 13 and Wilcox, 2005, chap. 10), begins
by calculating the least trimmed squares (LTS) estimator ( ), another
robust regression estimator developed by Rousseeuw (1984, as cited in
Wilcox, 2005, chap. 10) and adjusting it with empirically determined
weights which are calculated based on how deeply each Xi is nested
within the other X values using the minimum ellipsoid method
minimum-volume ellipsoid (MVE) estimator proposed by Rousseeuw and
van Zomeren (1990, as cited in Wilcox, 2003, chap. 13)
2
with Huber’s (
). So,
2
Using the MVE estimator, all ellipses containing half of the data of a data set are
examined and the one with the smallest area is identified. Then, robust measures of
location and covariance are calculated among the points located within that ellipse.
The MVE method replaces the means and sample covariance matrix of the Mahalanobis
distance with estimators that have a high breakdown point and this analog is then used
to identify outliers (Wilcox, 2003).
11
where ( refers to the median of all r’s),
where , and
,
where
where mx and C are the MVE estimators of location and covariance (with
a breakdown point of approximately .5), b is the .95 quantile of a chi-
square distribution with p degrees of freedom and a = 2. (Wilcox, 2005,
chap. 10.).
Relevance of the current study
This investigation examines the extent to which recently published
studies relying on the use of Pearson’s r successfully answer the five
questions stated at the opening of this paper:
1. Are these variables related?
2. In what way are these variables related?
3. How strongly are these variables related?
4. How meaningful is the relationship between these variables?
5. Knowing what we know about this relationship, can one
variable be used to predict the other variable?
It is proposed that applying more robust methods to these same
data will provide more informative answers and a richer contribution to
12
the original author’s area of investigation. As Pearson’s r is commonly
used across several different areas of psychology, it is believed that the
secondary analyses proposed here have the potential to make an equally
broad and important contribution.
To date, most robust techniques (particularly the ones addressed
in this proposal) have been compared and contrasted using only
simulated data. By performing these comparisons using existing data
the practical advantages of these modern methods should become even
more apparent. Therefore, an additional motivation to focus here on
published data is to demonstrate how even the most recently published
investigations in major behavioral science journals may be missing
potentially important information because data are not being fully
explored. Instead, authors continue to rely on traditional techniques of
statistical analysis that, based on the more robust modern methods
widely available, seem out-dated, and sometimes inappropriate. It is
hypothesized that in at least some of the data sets re-analyzed,
important issues will be clarified due to the use of these modern
statistical techniques.
13
Research questions addressed in the current investigation
1. Are recently published correlational studies relying on Pearson’s r
to evaluate the relationship between variables missing important
information?
2. Using these same data, what are the comparative properties of
some robust correlation or regression alternatives to Pearson’s r?
3. Which of these robust correlation or regression alternatives to
Pearson’s r are the most informative?
14
Chapter 2: Method
Sample
Data for the present study were drawn from previously analyzed
and published data sets. The Inter-university Consortium for Political
and Social Research database (http://www.icpsr.umich.edu/), an
archive of digital social science data, was queried with the keyword
“Psychology” to find publications within the field of Psychology using
data available to the public. Initially, 497 articles were found. The year
2000 was used as a publication date cutoff to ensure relative
contemporaneity, narrowing the field of candidates down to 127 studies.
These 127 studies were inspected to determine inclusion of correlational
data, narrowing the field even further to 59 studies. The field was
restricted further to 28 studies by only including those with correlational
analyses of a priori variables, that is, those variables that were part of
the initial hypotheses of each study. Finally, the accompanying data sets
for each of these studies was examined and to ensure accessibility and
usability and to make sure the variables in question were included or
could be calculated with the information available, narrowing the final
sample down to only five studies. The five studies included in the
present investigation are:
15
1. Andreoletti, Zebrowitz and Lachman (2001), using data
drawn from a subset of the Midlife Development in the
United States (MIDUS) survey, the Boston Study of
Management processes (Lachman, 2004).
2. Bryan & Luszcz (2000), using data drawn from the
Australian [Adelaide] Longitudinal Study of Aging (ALSA;
Andrews & Myers, 2000).
3. Frone (2000), using data drawn from the National
Comorbidity Survey (Kessler, 2007).
4. McKelvey & McKenry (2000), using data drawn from the
National Survey of Families and Households (Bumpass &
Sweet, 1997).
5. Ullman and Brecklin (2003), using data drawn from the
National Comorbidity Survey (Kessler, 2007).
Procedure
Each data set selected for this study was re-analyzed using S-Plus
or R statistical software incorporating the following eight approaches to
assess strength of association and effect magnitude. The properties of
each computed statistic or CI were then qualitatively compared and
contrasted. Prior to re-analysis, each variable combination was visually
inspected using the S-Plus/R function “lplot” (Wilcox, 2005, p.491) to
16
identify outliers that may have had an undue influence on vulnerable
correlation calculations.
Measures of association and effect magnitude
Pearson’s r
All of the data selected for this study have already been analyzed
using Pearson’s r, but this statistic was recomputed to make sure the
data analyzed in the current investigation were consistent in form with
the data analyzed for publication by the author(s) of the originating
study. A modified percentile bootstrap method was used to calculate a
.95 confidence interval to better assess effect direction and magnitude.
To achieve this, the S-Plus/R function “pcorb” (Wilcox, 2005, p. 403) was
applied.
Spearman’s rho (rs)
The S-Plus/R function “spear” (Wilcox, 2005, p.402) was used to
calculate rs. Spearman’s rho (rs) is calculated by assigning ranks to the
given X and Y values and then calculating Pearson’s r based on those
rankings instead of the given frequency distribution. This approach may
provide protection against some types of outliers.
Percentage bend correlation (rpb)
The S-Plus/R function “pbcor” (Wilcox, 2005, p.392) was used to
calculate rpb and the function “corb” (Wilcox, 2005, p. 403) was used to
17
calculate heteroscedastic percentile bootstrap confidence intervals for the
percentage bend correlation.
Winsorized correlation (rw)
The S-Plus/R function “wincor” (Wilcox, 2005, p. 397) was used to
calculate rw and the function “corb” (Wilcox, 2005, p. 403) was used to
calculate heteroscedastic percentile bootstrap confidence intervals for the
Winsorized correlation.
Skipped correlation (rp)
For the skipped correlation, outliers are removed using the MVE or
MCD method and then Pearson’s correlation is calculated with the data
that remain. The S-Plus/R function “scor” (Wilcox, 2005, p. 407) was
used to calculate rp.
Theil-Sen regression estimator ( )
The S-Plus/R function “tsreg” (Wilcox, 2005, p. 426) was used to
calculate and the function “mgvreg” (Wilcox, 2005, p. 441) was used to
calculate the skipped version of , which simply means outliers were
addressed prior to calculation using the MGV method of outlier
detection. Additionally, the function “regci” (Wilcox, 2005, p. 475) was
used to calculate heteroscedastic percentile bootstrap confidence
intervals for .
18
Coakley-Hettmansperger estimator ( )
The S-Plus/R function “chreg” (Wilcox, 2005, p. 440) was used to
calculate and the function “mgvreg” (Wilcox, 2005, p. 441) was used
to calculate the skipped version of . As with the Theil-Sen estimator,
the function “regci” (Wilcox, 2005, p. 475) was used to calculate
heteroscedastic percentile bootstrap confidence intervals for .
Ordinary Least Squares estimator (ls)
For comparison, the S-Plus/R function “lsfitci” (Wilcox, 2005, p.
421) was used to calculate a .95 confidence interval for the Ordinary
Least Squares (OLS) estimate (ls) using a percentile bootstrap method.
19
Chapter 3: Results
Before examining the results on a case by case basis, it is
important to note the failure in this study to successfully compute the
“mgvreg” function, which was to calculate the skipped versions of the
Theil-Sen and Coakley-Hettmansperger estimators. Each attempt with
every data set failed. In some instances, failure would occur after
running for 24 hours or more.
3
So, for practical reasons, the skipped
versions of these regression estimators are not examined here.
Secondly, please note that any differences between Pearson’s r as
listed in the publication and Pearson’s r computed here are due to
sampling differences. Samples in the current investigation were drawn
from larger studies as specified in each article. Execution of this
sampling revealed however, that sometimes information in the article
was inadequate or variables in the available dataset were missing so
perfect replication of each sample was not always possible.
3
Most common S-Plus error associated with mgvreg function: “Problem in 1:ncol (x):
No data to interpret as numerical value”
20
Andreoletti, Zebrowitz, & Lachman (2001)
The goal of Andreoletti, Zebrowitz, and Lachman (2001) was to
investigate the relationship between physical appearance and control
beliefs among different age groups. Data were drawn from a subset of
the Midlife Development in the United States (MIDUS) survey, the Boston
Study of Management processes (Lachman, 2004). Andreoletti, et al.
(2001) calculated correlations between all variables in preparation for
regression analysis. The present investigation focused on the following
six variables: Attractiveness (a composite score based on ratings of
participant frontal and profile photographs), socioeconomic status (SES),
External Constraints (score based on the mean level of agreement with
three items reflecting external factors that interfere with goal
achievement), Personal Control (score based on the mean level of
agreement with nine items reflecting feelings self-efficacy in carrying out
goals), Work Control (score based on participants self ratings on the
amount of control they presently felt they had over their work) and
Health Control (score based on participants self ratings on the amount of
control they presently felt they had over their health). As in Andreoletti,
et al. (2001), results are presented here by age group and sex: Young
men and women (ages 25-39), middle-aged men and women (ages 40-59)
and older men and women (ages 60-76).
21
Variable relationships for the Young Men sample are plotted in
figures 1.1 through 1.15 with suspected outliers identified. Correlation
results for the sample of young men are listed in tables 1.1.1 through
1.1.5. Within the Young Men sample (N = 43), re-analysis revealed
statistically significant relationships between External Constraints &
Personal Control and External Constraints & Health Control. Significant
relationships between Personal Control & Work Control, Personal Control
& Health Control, and Work Control & Health Control from Andreoletti et
al. (2001) were not replicated.
The highest correlation value for External Constraints & Personal
Control was calculated by the Winsorized correlation (rw = -.55). The
highest correlation value for External Constraints & Health Control was
calculated by Spearman’s rho (rs = -.40).
Regression estimator results for the Young Men sample are listed
in tables 1.2.1 through 1.2.5. Significant Coakley-Hettmansperger
(chreg) slope estimates were detected for Attractiveness & SES (ch =
1.51), External Constraints & Personal Control (ch = -.32), and Personal
Control & Health Control (ch = 1.93). A significant Theil-Sen (tsreg)
slope estimate was also detected for External Constraints & Personal
Control (ts = -.33). The tsreg slope estimate was accompanied by a
slightly shorter confidence interval and a slightly smaller standard error
than the chreg slope estimate.
22
Figure 1.1: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) – Attractiveness & SES
23
Figure 1.2: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) – Attractiveness & External Constraints
24
Figure 1.3: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) – Attractiveness & Personal Control
25
Figure 1.4: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) – Attractiveness & Work Control
26
Figure 1.5: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) – Attractiveness & Health Control
27
Figure 1.6: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) – SES & External Constraints
28
Figure 1.7: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) – SES & Personal Control
29
Figure 1.8: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) – SES & Work Control
30
Figure 1.9: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) – SES & Health Control
31
Figure 1.10: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) – External Constraints & Personal Control
32
Figure 1.11: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) – External Constraints & Work Control
33
Figure 1.12: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) – External Constraints & Health Control
34
Figure 1.13: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) – Personal Control & Work Control
35
Figure 1.14: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) – Personal Control & Health Control
36
Figure 1.15: Andreoletti, Zebrowitz, & Lachman (2000 -Young Men) – Work Control & Health Control
37
Table 1.1.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) – Correlations
38
Table 1.1.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) – Correlations
39
Table 1.1.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) – Correlations
40
Table 1.1.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) – Correlations
41
Table 1.1.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) – Correlations
42
Table 1.2.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) – Regression
Estimates
43
Table 1.2.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) – Regression
Estimates
44
Table 1.2.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) – Regression
Estimates
45
Table 1.2.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) – Regression
Estimates
46
Table 1.2.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Men) – Regression
Estimates
47
Variable relationships for the Young Women sample are plotted in
figures 2.1 through 2.15 with suspected outliers identified. Correlation
results for the sample of young women are listed in tables 2.1.1 through
2.1.5. Within the Young Women sample (N = 26), re-analysis only
revealed a significant relationship between External Constraints &
Personal Control. The significant relationship between Attractiveness &
SES from Andreoletti et al. (2001) was not replicated.
The highest correlation values for External Constraints & Personal
Control were calculated by the modified percentile bootstrap Pearson’s r
(pcorb) method (r* = -.83) and the Winsorized correlation (rw = -.83).
Regression estimator results for the Young Women sample are listed in
tables 2.2.1 through 2.2.5. Significant slope estimates were revealed
only for the relationship between External Constraints & Personal
Control by the modified percentile bootstrap ordinary least squares (OLS)
method (C.I. ls : -.72, -.41), the Theil-Sen (tsreg) estimator
(ts = -.52), and the Coakley-Hettmansperger (chreg) estimator (ch = -.50).
The confidence intervals for tsreg and chreg were the same length but the
chreg standard error was slightly smaller (s.e. = .07) than that of the
tsreg (s.e. = .08).
48
Figure 2.1- Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) – Attractiveness & SES
49
Figure 2.2 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) – Attractiveness & External Constraints
50
Figure 2.3 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) – Attractiveness & Personal Constraints
51
Figure 2.4 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) – Attractiveness & Work Control
52
Figure 2.5 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) – Attractiveness & Health Control
53
Figure 2.6 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women)– SES & External Constraints
54
Figure 2.7 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) – SES & Personal Control
55
Figure 2.8 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) – SES & Work Control
56
Figure 2.9 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) – SES & Health Control
57
Figure 2.10 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) – External Constraints & Personal Control
58
Figure 2.11 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) – External Constraints & Work Control
59
Figure 2.12 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) – External Constraints & Health Control
60
Figure 2.13 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) – Personal Control & Work Control
61
Figure 2.14 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women) – Personal Control & Health Control
62
Figure 2.15 - Andreoletti, Zebrowitz, & Lachman (2000 - Young Women)– Work Control & Health Control
63
Table 2.1.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women) - Correlations
4
Error message: Problem in apply.default(x, 2, rank): dim(X) must have a positive
length
5
Error message: Problem in apply.default(x, 2, rank): dim(X) must have a positive
length
6
Error message: Problem in m[temp, ]: No dim attribute for array subset of object of
class "numeric"
7
Error message: Problem in m[temp, ]: No dim attribute for array subset of object of
class "numeric"
64
Table 2.1.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women) - Correlations
8
Error message: Problem in apply.default(x, 2, rank): dim(X) must have a positive
length
9
Error message: Problem in m[temp, ]: No dim attribute for array subset of object of
class "numeric"
65
Table 2.1.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women) - Correlations
10
Error message: Problem in apply.default(x, 2, rank): dim(X) must have a positive
length
11
Error message: Problem in m[temp, ]: No dim attribute for array subset of object of
class "numeric"
66
Table 2.1.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women) - Correlations
12
Error message: Problem in apply.default(x, 2, rank): dim(X) must have a positive
length
13
Error message: Problem in m[temp, ]: No dim attribute for array subset of object of
class "numeric"
67
Table 2.1.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women) - Correlations
68
Table 2.2.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women) – Regression
Estimates
69
Table 2.2.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women) – Regression
Estimates
14
Error message: Problem in mahalanobis(x, mx, mve$cov): Covariance matrix is
apparently singular
70
Table 2.2.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women) – Regression
Estimates
15
Error message: Problem in mahalanobis(x, mx, mve$cov): Covariance matrix is
apparently singular
16
Error message: Problem in mahalanobis(x, mx, mve$cov): Covariance matrix is
apparently singular
17
Error message: Problem in mahalanobis(x, mx, mve$cov): Covariance matrix is
apparently singular
71
Table 2.2.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women) – Regression
Estimates
18
Error message: Problem in mahalanobis(x, mx, mve$cov): Covariance matrix is
apparently singular
72
Table 2.2.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Young Women) – Regression
Estimates
19
Error message: Problem in mahalanobis(x, mx, mve$cov): Covariance matrix is
apparently singular
73
Variable relationships for the Middle-Age Men sample are plotted
in figures 3.1 through 3.15. Suspected outliers are identified.
Correlation results for this sample are listed in tables 3.1.1 through
3.1.5. Within the Middle-Age Men sample (N = 43), re-analysis revealed
statistically significant relationships between Attractiveness & External
Constraints (highest correlation values calculated by the pcorb method,
r* = -.42 and the skipped correlation, scor, rp = -.42), Attractiveness &
Personal Control (highest correlation value calculated by the pcorb
method, r = .36), SES & External Constraints (highest correlation value
calculated by scor, rp = -.43) , SES & Personal Control (highest
correlation value calculated by wincor, rw = .46), SES & Work Control
(only significant correlation value calculated by scor, rp = -.34), External
Constraints & Personal Control (highest correlation values calculated by
the pcorb method, r* = -.70 and scor, rp = -.70), External Constraints &
Work Control (highest correlation value calculated by the pcorb method,
r* = -.31), External Constraints & Health Control (highest correlation
value calculated by scor, rp = -.46), Personal Control & Work Control
(highest correlation value calculated by the pcorb method, r* = .35), and
Work Control & Health Control (highest correlation value calculated by
spear, rs = .34).
Notably, the statistically significant relationship between SES &
Work Control, uncovered here using the scor method, was not revealed in
74
the original publication using Pearson’s r, whereas, the significant
relationship between Personal Control & Health Control for this sample
from Andreoletti et al. (2001) was not replicated.
Regression estimator results for the Middle-Age Men sample are
listed in tables 3.2.1 through 3.2.5. Significant slope estimates were
revealed for the relationships between Attractiveness & External
Constraints (shortest confidence interval calculated by lsfitci, C.I. ls : -
1.24, -.24), Attractiveness & Personal Control (shortest confidence
interval and smallest error estimate calculated by chreg, ch = .51), SES
& External Constraints (shortest confidence interval and smallest error
estimate calculated by tsreg, ts = -.11), SES & Personal Control (shortest
confidence interval and smallest error estimate calculated by tsreg,
ts = .11), External Constraints & Personal Control (shortest confidence
interval and smallest error estimate calculated by tsreg, ts = -.61),
External Constraints & Work Control (shortest confidence interval
calculated by lsfitci, C.I. ls : -1.21, -.03), External Constraints & Health
Control (shortest confidence interval calculated by lsfitci, C.I. ls : -1.46,
-.38), and Personal Control & Work Control (only significant slope
detected by lsfitci, C.I. ls : .10, 1.35).
75
Figure 3.1 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men) – Attractiveness & SES
76
Figure 3.2 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men) – Attractiveness & External Constraints
77
Figure 3.3 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men) – Attractiveness & Personal Constraints
78
Figure 3.4 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men) – Attractiveness & Work Control
79
Figure 3.5 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men) – Attractiveness & Health Control
80
Figure 3.6 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men) – SES & External Constraints
81
Figure 3.7 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men) – SES & Personal Control
82
Figure 3.8 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men) – SES & Work Control
83
Figure 3.9 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men) – SES & Health Control
84
Figure 3.10 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men) – External Constraints & Personal Control
85
Figure 3.11 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men) – External Constraints & Work Control
86
Figure 3.12 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men) – External Constraints and Health Control
87
Figure 3.13 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men) – Personal Control & Work Control
88
Figure 3.14 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men) – Personal Control & Health Control
89
Figure 3.15 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Men) – Work Control & Health Control
90
Table 3.1.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Men) -
Correlations
91
Table 3.1.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Men) -
Correlations
92
Table 3.1.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Men) -
Correlations
93
Table 3.1.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Men) -
Correlations
94
Table 3.1.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Men) -
Correlations
95
Table 3.2.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Men) – Regression
Estimates
96
Table 3.2.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Men) –
Regression Estimates
97
Table 3.2.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Men) – Regression
Estimates
98
Table 3.2.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Men) – Regression
Estimates
99
Table 3.2.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Men) – Regression
Estimates
20
Error Message: Problem in mahalanobis(x, mx, mve$cov): Covariance matrix is
apparently singular
100
Variable relationships for the Middle Age Women sample are
plotted in figures 4.1 through 4.15 with suspected outliers identified.
Correlation results for this sample are listed in tables 4.1.1 through
4.1.5. Within the Middle Age Women sample (N = 35), re-analysis
revealed significant relationships between Attractiveness & SES (highest
statistically significant correlation value calculated by the pcorb method,
r* = .39), SES & External Constraints (highest correlation values
calculated by pcorb, r* = -.48 and scor, rp = -.48), SES & Personal
Control (highest correlation value calculated by pcorb, r* = -.47), External
Constraints & Personal Control (highest correlation values calculated by
pcorb, r* = -.69, pbcor and corb, rpb = -.69). Notably, the statistically
significant relationships between External Constraints & Work Control,
External Constraints & Health Control, and Personal Control & Health
Control for this sample from Andreoletti et al. (2001) were not replicated.
Regression estimator results for the Middle-Age Women sample are
listed in tables 4.2.1 through 4.2.5. Significant slope estimates were
revealed for the relationships between Attractiveness & SES (shortest
confidence interval calculated by lsfitci, C.I. ls : .22, 3.75), SES &
External Constraints (shortest confidence interval calculated by lsfitci,
C.I. ls : -.32, -.04), SES & Personal Control (tsreg and chreg calculated
equal length confidence intervals and equal error estimates, ts = .13;
ch = .13), and External Constraints & Personal Control (shortest
101
confidence interval and smallest error estimate calculated by tsreg,
ts = -.50).
102
Figure 4.1 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Women) – Attractiveness & SES
103
Figure 4.2 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Women) – Attractiveness & External Constraints
104
Figure 4.3 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Women) – Attractiveness & Personal Constraints
105
Figure 4.4 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Women) – Attractiveness & Work Control
106
Figure 4.5 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Women) – Attractiveness & Health Control
107
Figure 4.6 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Women) – SES & External Constraints
108
Figure 4.7 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Women) – SES & Personal Control
109
Figure 4.8 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Women) – SES & Work Control
110
Figure 4.9 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Women) – SES & Health Control
111
Figure 4.10 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Women) – External Constraints & Personal Control
112
Figure 4.11 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Women)– External Constraints & Work Control
113
Figure 4.12 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Women) – External Constraints & Health Control
114
Figure 4.13 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Women) – Personal Control & Work Control
115
Figure 4.14 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Women) – Personal Control & Health Control
116
Figure 4.15 - Andreoletti, Zebrowitz, & Lachman (2000 - Middle Age Women) – Work Control & Health Control
117
Table 4.1.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Women) -
Correlations
118
Table 4.1.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Women) -
Correlations
119
Table 4.1.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Women) -
Correlations
120
Table 4.1.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Women) -
Correlations
121
Table 4.1.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Women) -
Correlations
122
Table 4.2.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Women) –
Regression Estimates
123
Table 4.2.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Women) –
Regression Estimates
124
Table 4.2.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Women) –
Regression Estimates
125
Table 4.2.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Women) –
Regression Estimates
126
Table 4.2.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Middle Age Women) –
Regression Estimates
127
Variable relationships for the Older Men sample are plotted in
figures 5.1 through 5.15 with suspected outliers identified. Correlation
results for this sample are listed in tables 5.1.1 through 5.1.5. Within
the Older Men sample (N = 40), re-analysis revealed significant
relationships between Attractiveness & SES (highest statistically
significant correlation values calculated by pcorb, r* = .37, and scor,
rp = -.37), Attractiveness & Work Control (highest correlation values
calculated by pbcor and corb, rpb = -.37), SES & Work Control (highest
correlation value calculated by pcorb, r* = -.36), External Constraints &
Personal Control (highest correlation values calculated by pcorb,
r* = -.71, and pbcor/corb, rpb = -.71), and Work Control & Health Control
(highest correlation value calculated by spear, rs = .32). Notably, the
statistically significant relationship between Personal Control & Health
Control for this sample from Andreoletti et al. (2001) was not replicated.
Regression estimator results for the Older Men sample are listed in
tables 5.2.1 through 5.2.5. Significant slope estimates were revealed for
the relationships between Attractiveness & SES (shortest confidence
interval calculated by lsfitci, C.I. ls : 1.03, 5.46), Attractiveness & Work
Control (shortest confidence interval and smallest error estimate
calculated by chreg, ch = -1.13), SES & Work Control (shortest
confidence interval and smallest error estimate calculated by chreg,
128
ch = -.15), and External Constraints & Personal Control (shortest
confidence interval calculated by lsfitci, C.I. ls : -.64, -.36).
129
Figure 5.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – Attractiveness & SES
130
Figure5.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – Attractiveness & External Constraints
131
Figure 5.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – Attractiveness & Personal Control
132
Figure 5.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – Attractiveness & Work Control
133
Figure 5.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – Attractiveness & Health Control
134
Figure 5.6 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – SES & External Constraints
135
Figure 5.7 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – SES & Personal Control
136
Figure 5.8 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – SES & Work Control
137
Figure 5.9 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – SES & Health Control
138
Figure 5.10 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – External Constraints & Personal Control
139
Figure 5.11 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – External Constraints & Work Control
140
Figure 5.12 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – External Constraints & Health Control
141
Figure 5.13 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – Personal Control & Work Control
142
Figure 5.14 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – Personal Control & Health Control
143
Figure 5.15 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – Work Control & Health Control
144
Table 5.1.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) - Correlations
145
Table 5.1.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) - Correlations
146
Table 5.1.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) - Correlations
147
Table 5.1.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) - Correlations
148
Table 5.1.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) - Correlations
149
Table 5.2.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – Regression
Estimates
150
Table 5.2.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – Regression
Estimates
151
Table 5.2.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – Regression
Estimates
152
Table 5.2.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – Regression
Estimates
153
Table 5.2.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Men) – Regression
Estimates
21
Error Message: Problem in mahalanobis(x, mx, mve$cov): Covariance matrix is
apparently singular
154
Variable relationships for the Older Women sample are plotted in
figures 6.1 through 6.15 with suspected outliers identified. Correlation
results for this sample are listed in tables 6.1.1 through 6.1.5. Within
the Older Women sample (N = 18), correlational re-analysis revealed a
statistically significant relationship only between External Constraints &
Personal Control (highest correlation values calculated by pcorb,
r* = .68). Notably, the statistically significant relationships between SES
& Personal Control and Personal Control & Health Control for this
sample from Andreoletti et al. (2001) were not replicated.
Regression estimator results for the Older Women sample are
listed in tables 6.2.1 through 6.2.5. A significant slope estimate was
revealed only for the relationship between External Constraints &
Personal Control (shortest confidence interval calculated by lsfitci,
C.I. ls : -.64, -.28).
155
Figure 6.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – Attractiveness & SES
156
Figure 6.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – Attractiveness & External Constraints
157
Figure 6.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – Attractiveness & Personal Control
158
Figure 6.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – Attractiveness & Work Control
159
Figure 6.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – Attractiveness & Health Control
160
Figure 6.6 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – SES & External Constraints
161
Figure 6.7 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – SES & Personal Control
162
Figure 6.8 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – SES & Work Control
163
Figure 6.9 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – SES & Health Control
164
Figure 6.10 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – External Constraints & Personal Control
165
Figure 6.11 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – External Constraints & Work Control
166
Figure 6.12 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – External Constraints & Health Control
167
Figure 6.13 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – Personal Control & Work Control
168
Figure 6.14 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – Personal Control & Health Control
169
Figure 6.15 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – Work Control & Health Control
170
Table 6.1.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) - Correlations
171
Table 6.1.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) - Correlations
172
Table 6.1.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) - Correlations
173
Table 6.1.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) - Correlations
174
Table 6.1.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) - Correlations
175
Table 6.2.1 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – Regression
Estimates
176
Table 6.2.2 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – Regression
Estimates
22
Error Message: Problem in ltsreg.default: Missing value where logical needed:
if(ans$rsquared > 1) {ans$rsquared <- 1}
177
Table 6.2.3 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – Regression
Estimates
23
Error Message: Problem in ltsreg.default: Missing value where logical needed:
if(ans$rsquared > 1) {ans$rsquared <- 1}
178
Table 6.2.4 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – Regression
Estimates
24
Error Message: Problem in ltsreg.default: Missing value where logical needed:
if(ans$rsquared > 1) {ans$rsquared <- 1}
179
Table 6.2.5 - Andreoletti, Zebrowitz, & Lachman (2000 – Older Women) – Regression
Estimates
25
Error Message: Problem in mahalanobis(x, mx, mve$cov): Covariance matrix is
apparently singular
26
Error Message: Problem in ltsreg.default: Missing value where logical needed:
if(ans$rsquared > 1) {ans$rsquared <- 1}
27
Error Message: Problem in mahalanobis(x, mx, mve$cov): Covariance matrix is
apparently singular
180
Bryan & Luszcz (2000)
The goal of this study was to assess the relationship between
verbal fluency and incidental memory. Data for this study were drawn
from the Australian [Adelaide] Longitudinal Study of Aging (ALSA;
Andrews & Myers, 2000). Bryan and Luszcz (2000) calculated
correlations between all variables in preparation for regression analysis.
The present study focused on the background variables Age, Depression,
Self-rated health , and Age when left school. Depression was measured
by the Center for Epidemiological Studies – Depression Scale (CES-D;
Radloff, 1977 as cited in Bryan & Luszcz, 2000). For the Self-rated
health variable, Participants rated their current health on a five point
scale, where 1 = Excellent, 2 = good, 3 = moderate, 4 = fair, 5 = Poor.
Age when left school was scored on a seven point scale, where 1 = never
went to school, 2 = under 14 years, 3 = 14 years, 4 = 15 years, 5 = 16
years, 6 = 17 years, 7 = 18 years or over.
Variable relationships are plotted in figures 7.1 through 7.6 with
suspected outliers identified. Correlation results are listed in tables
7.1.1 and 7.1.2. Re-analysis revealed significant correlational
relationships between Age & CES-D (highest statistically significant
correlation value calculated by spear, rs = .16), Age & Self-rated health
(highest statistically significant correlation values calculated by spear, rs
= .08, pbcor/corb, rpb = .08, wincor, rw = .08 and scor, rp = .08), Age &
181
Age when left school (highest statistically significant correlation value
calculated by scor, rp = -.12), CES-D & Self-rated health (highest
correlation value calculated by pcorb, r* = .44), CES-D & Age when left
school (highest correlation value calculated by scor, rp = -.11), and Self-
rated health & Age when left school (highest correlation value calculated
by scor, rp = -.11).
Regression estimator results are listed in tables 7.2.1 and 7.2.2.
Significant slope estimates were revealed for the relationships between
Age & CES-D (tsreg and chreg calculated equal length confidence
intervals and equal error estimates, ts = .11; ch = .10), Age & Self-rated
health (shortest confidence interval calculated by lsfitci, C.I. ls : .003,
.02), Age & Age when left school (shortest confidence interval and
smallest error estimate calculated by chreg, ch = -.02), CES-D & Self-
rated health (shortest confidence interval calculated by lsfitci, C.I. ls :
.06, .07), CES-D & Age when left school (shortest confidence interval
calculated by lsfitci, C.I. ls : -.02, -.01), and Self-rated health & Age
when left school (lsfitci and chreg calculated equal length confidence
intervals, C.I. ls : -.17, -.06; C.I. ch : -.18, -.07).
182
Figure 7.1 - Bryan & Luszcz (2000) – Age & CES-D Score
183
Figure 7.2 - Bryan & Luszcz (2000) – Age & Self-rated Health
184
Figure 7.3 - Bryan & Luszcz (2000) – Age & Age when left school
185
Figure 7.4 - Bryan & Luszcz (2000) –CES-D Score & Self-rated Health
186
Figure 7.5 - Bryan & Luszcz (2000) –CES-D Score & Age when left school
187
Figure 7.6 - Bryan & Luszcz (2000) – Self-rated Health & Age when left school
188
Table 7.1.1 – Bryan & Luszcz (2000) - Correlations
189
Table 7.1.2 – Bryan & Luszcz (2000) - Correlations
190
Table 7.2.1 – Bryan & Luszcz (2000) – Regression Estimates
191
Table 7.2.2 – Bryan & Luszcz (2000) – Regression Estimates
192
Frone (2000)
The purpose of this study was to investigate the relationship
between work-family conflict and mental health. Data for this study
were drawn from the National Comorbidity Survey (Kessler, 2007). Frone
(2000) calculated the correlations among all variables in preparation for
regression analysis. The present study focused on the relationships
between the variables work-family conflict (i.e., work to family
interference), family-work conflict (i.e., family to work interference), age,
and number of hours worked per week.
Variable relationships are plotted in figures 8.1 through 8.6 with
suspected outliers identified. Correlation results are listed in tables
8.1.1 and 8.1.2. Re-analysis revealed significant correlational
relationships between Work-family conflict and Family-work conflict
(highest statistically significant correlation value calculated by scor,
rp = .52), Work-family conflict number of hours worked per week (highest
correlation values calculated by wincor, rw = .21 and scor, rp = .21),
Family-work conflict & Age (highest statistically significant correlation
value calculated by pcorb, r* = .04) and Family-work conflict & number
of hours worked per week (highest and only statistically significant
correlation value calculated by wincor, rw = ..05).
Notably, the statistically significant relationship between Work-
family conflict and Age from Frone (2000) was not replicated here,
193
whereas the statistically significant relationship between Family-work
conflict & number of work hours, uncovered here using the wincor
method, was not revealed in the original publication using Pearson’s r.
Regression estimator results are listed in tables 8.2.1 and 8.2.2.
Significant slope estimates were revealed for the relationships between
Work-family conflict & Family-work conflict (shortest confidence interval
calculated by lsfitci, C.I. ls : .30, .36), Work-family conflict & number of
hours worked per week (shortest confidence interval and smallest error
estimate calculated by chreg, ch = .81), and Family-work conflict & Age
(shortest confidence interval calculated by lsfitci, C.I. ls : -.51, -.01).
194
Figure 8.1 - Frone (2000) – Work-family conflict & Family-work conflict
195
Figure 8.2 - Frone (2000) – Work-family conflict & Age
196
Figure 8.3 - Frone (2000) – Work-family conflict & Number of work hours
197
Figure 8.4 - Frone (2000) – Family-work conflict & Age
198
Figure 8.5 - Frone (2000) – Family-work conflict & Number of work hours
199
Figure 8.6 - Frone (2000) – Age & Number of work hours
200
Table 8.1.1 – Frone (2000) - Correlations
201
Table 8.1.2 – Frone (2000) - Correlations
202
Table 8.2.1 – Frone (2000) – Regression Estimates
203
Table 8.2.2 – Frone (2000) – Regression Estimates
204
McKelvey & McKenry (2000)
The purpose of this study was to examine differences in overall
well-being between Black and White divorced or separated mothers.
Data for this study were drawn from the National Survey of Families and
Households (Bumpass & Sweet, 1997). McKelvey and McKenry (2000)
examined correlations of all variables for each racial group in preparation
for regression analysis. The present study focused on the relationships
between the variables Depression (CES-D score), Self-esteem
28
, Personal
Mastery, Overall Happiness, Economic Well-being, and Parental
Satisfaction for each racial group.
For the Black Mother sample (N=235), variable relationships are
plotted in figures 9.1 through 9.15 with suspected outliers identified.
Correlation results are listed in tables 9.1.1 through 9.1.5. Re-analysis
revealed significant correlational relationships between CES-D & Self-
esteem (highest statistically significant correlation values calculated by
scor, rp = .29), CES-D & Overall happiness (highest statistically
significant correlation values calculated by pbcor/corb, rpb = -.48 and
wincor, rw = -.48), Self-esteem & Personal Mastery (highest statistically
28
In the present study, the correlations calculated between Self-esteem and other
variables resulted in negative values whereas the published correlations for this
variable were positive. In the description of this measure, McKelvey & McKenry (2000)
note that responses to the items used to measure self-esteem ranged from “strongly
agree (1) to strongly disagree (5)” (p. 7). No mention of reverse scoring these items was
made so this was not done in the present study. However, the calculation of a positive
correlation in McKelvey & McKenry (2000) indicates that this measure was likely
reverse scored.
205
significant correlation value calculated by spear, rs = .40), Self-esteem &
Overall happiness (highest statistically significant correlation value
calculated by wincor, rw = -.17), Overall happiness & Economic well-
being (highest statistically significant correlation value calculated by
wincor, rw = .28), Overall happiness & Parental satisfaction (highest
statistically significant correlation values calculated by scor, rp = .32),
and Economic well-being & Parental satisfaction (highest statistically
significant correlation value calculated by spear, rs = .81). Notably, the
statistically significant relationships between Self-esteem & Overall
happiness, Overall happiness & Economic well-being, and Economic
well-being (all detected here by multiple methods) were not revealed in
McKelvey & McKenry (2000) using Pearson’s r.
Regression estimator results for the Black mother sample are listed
in tables 9.2.1 through 9.2.5. Significant slope estimates were revealed
for the relationships between CES-D & Self-esteem (shortest confidence
interval calculated by lsfitci, C.I. ls : .02, ..15), CES-D & Overall
happiness (shortest confidence interval calculated by lsfitci, C.I. ls : -
.55, -.31), Self-esteem & Personal Mastery (shortest confidence interval
calculated by lsfitci, C.I. ls : .20, .63), Self-esteem & Overall happiness
(only chreg detected a significant slope, ch = -.74), Overall happiness &
Economic well-being (only lsfitci detected a significant slope, C.I. ls :
206
.01, .35), and Economic well-being & Parental satisfaction (only lsfitci
detected a significant slope, C.I. ls : .05, .36).
207
Figure 9.1 - McKelvey & McKenry (2000 - Black mothers) –CES-D score & Self-esteem
208
Figure 9.2 - McKelvey & McKenry (2000 - Black mothers)– CES-D score & Personal mastery
209
Figure 9.3 - McKelvey & McKenry (2000 - Black mothers) –CES-D score & Happiness
210
Figure 9.4 - McKelvey & McKenry (2000 - Black mothers) – CES-D score & Economic well-being
211
Figure 9.5 - McKelvey & McKenry (2000 - Black mothers) –CES-D score & Parental satisfaction
212
Figure 9.6 - McKelvey & McKenry (2000 - Black mothers) – Self-esteem & Personal mastery
213
Figure 9.7 - McKelvey & McKenry (2000 - Black mothers) – Self-esteem & Happiness
214
Figure 9.8 - McKelvey & McKenry (2000 - Black mothers) – Self-esteem & Economic well-being
215
Figure 9.9 - McKelvey & McKenry (2000 - Black mothers) – Self-esteem & Parental satisfaction
216
Figure 9.10 - McKelvey & McKenry (2000 - Black mothers) – Personal mastery & Happiness
217
Figure 9.11 - McKelvey & McKenry (2000 - Black mothers)– Personal mastery & Economic well-being
218
Figure 9.12 - McKelvey & McKenry (2000 - Black mothers)– Personal mastery & Parental satisfaction
219
Figure 9.13 - McKelvey & McKenry (2000 - Black mothers)–Happiness & Economic wellbeing
220
Figure 9.14 - McKelvey & McKenry (2000 - Black mothers) –Happiness & Parental satisfaction
221
Figure 9.15 - McKelvey & McKenry (2000 - Black mothers) –Economic well-being & Parental satisfaction
222
Table 9.1.1- – McKelvey & McKenry (2000 - Black mothers) - Correlations
223
Table 9.1.2- – McKelvey & McKenry (2000 - Black mothers) - Correlations
224
Table 9.1.3- – McKelvey & McKenry (2000 - Black mothers) - Correlations
225
Table 9.1.4- – McKelvey & McKenry (2000 - Black mothers) - Correlations
226
Table 9.1.5- – McKelvey & McKenry (2000 - Black mothers) - Correlations
227
Table 9.2.1- – McKelvey & McKenry (2000 - Black mothers) – Regression Estimates
228
Table 9.2.2- – McKelvey & McKenry (2000 - Black mothers) – Regression Estimates
229
Table 9.2.3- – McKelvey & McKenry (2000 - Black mothers) – Regression Estimates
230
Table 9.2.4- – McKelvey & McKenry (2000 - Black mothers) – Regression Estimates
231
Table 9.2.5- – McKelvey & McKenry (2000 - Black mothers) – Regression Estimates
232
For the White Mother sample (N=662), variable relationships are
plotted in figures 10.1 through 10.15 with suspected outliers identified.
Correlation results are listed in tables 10.1.1 through 10.1.5.
Re-analysis revealed significant correlational relationships between
CES-D & Self-esteem (highest statistically significant correlation value
calculated by spear, rs = .28), CES-D & Personal Mastery (highest
statistically significant correlation value calculated by spear, rs = .11),
CES-D & Overall happiness (highest statistically significant correlation
value calculated by scor, rp = -.52), CES-D & Economic well-being
(highest statistically significant correlation value calculated by scor,
rp = --.21), CES-D & Parental satisfaction (highest statistically significant
correlation value calculated by pcorb, r* = .21), Self-esteem & Personal
Mastery (highest statistically significant correlation value calculated by
spear, rs = .29), Self-esteem & Overall happiness (highest statistically
significant correlation value calculated by scor, rp = -.30), Self-esteem &
Economic well-being (highest statistically significant correlation value
calculated by scor, rp = -.12), Self-esteem & Parental satisfaction (highest
statistically significant correlation value calculated by scor, rp = -.28),
Personal mastery & Overall happiness (highest statistically significant
correlation value calculated by scor, rp = -.18), Overall happiness &
Economic well-being (highest statistically significant correlation value
calculated by scor, rp = .37), Overall happiness & Parental satisfaction
233
(highest statistically significant correlation values calculated by pcorb,
r* = .34), and Economic well-being & Parental satisfaction (highest
statistically significant correlation value calculated by spear, rs = .71).
Regression estimator results for the White mother sample are
listed in tables 10.2.1 through 10.2.5. Significant slope estimates were
revealed for the relationships between CES-D & Self-esteem (shortest
confidence interval calculated by chreg, ch = .09), CES-D & Personal
Mastery (only lsfitci detected a significant slope, C.I. ls : .01, .11),
CES-D & Overall happiness (shortest confidence interval calculated by
lsfitci, C.I. ls : -.53, -.35), CES-D & Economic well-being (shortest
confidence interval calculated by lsfitci, C.I. ls : -.27, -.11), CES-D &
Parental satisfaction (only lsfitci detected a significant slope, C.I. ls : -
.23, -.08), Self-esteem & Personal Mastery (shortest confidence interval
calculated by lsfitci, C.I. ls : .28, .52), Self-esteem & Overall happiness
(shortest confidence interval calculated by lsfitci, C.I. ls : -.90, -.48),
Self-esteem & Parental satisfaction (shortest confidence interval
calculated by lsfitci, C.I. ls : -.55, -.16), Personal Mastery & Overall
happiness (shortest confidence interval calculated by lsfitci,
C.I. ls : -.32, -.06), Personal Mastery & Parental satisfaction (only lsfitci
detected a significant slope, C.I. ls : .20, .03), Overall happiness &
Economic well-being (shortest confidence interval calculated by lsfitci,
C.I. ls : .24, .42), Overall happiness & Parental satisfaction (shortest
234
confidence interval calculated by lsfitci, C.I. ls : .19, .34), and Economic
well-being & Parental satisfaction (shortest confidence interval
calculated by lsfitci, C.I. ls : .24, .36).
235
Figure 10.1 - McKelvey & McKenry (2000 - White mothers) –CES-D score & Self-esteem
236
Figure 10.2 - McKelvey & McKenry (2000 - White mothers) –CES-D score & Personal mastery
237
Figure 10.3 - McKelvey & McKenry (2000 - White mothers)– CES-D score & Happiness
238
Figure 10.4 - McKelvey & McKenry (2000 - White mothers)– CES-D score & Economic well-being
239
Figure 10.5 - McKelvey & McKenry (2000 - White mothers) –CES-D score & Parental satisfaction
240
Figure 10.6 - McKelvey & McKenry (2000 - White mothers) – Self-esteem & Personal mastery
241
Figure 10.7 - McKelvey & McKenry (2000 - White mothers)– Self-esteem & Happiness
242
Figure 10.8 - McKelvey & McKenry (2000 - White mothers) – Self-esteem & Economic well-being
243
Figure 10.9 - McKelvey & McKenry (2000 - White mothers)– Self-esteem & Parental satisfaction
244
Figure 10.10 - McKelvey & McKenry (2000 - White mothers) – Personal mastery & Happiness
245
Figure 10.11 - McKelvey & McKenry (2000 - White mothers) – Personal mastery & Economic wellbeing
246
Figure 10.12 - McKelvey & McKenry (2000 - White mothers) – Personal mastery & Parental satisfaction
247
Figure 10.13 - McKelvey & McKenry (2000 - White mothers) –Happiness & Economic wellbeing
248
Figure 10.14 - McKelvey & McKenry (2000 - White mothers) –Happiness & Parental satisfaction
249
Figure 10.15 - McKelvey & McKenry (2000 - White mothers) –Economic wellbeing & Parental satisfaction
250
Table 10.1.1- – McKelvey & McKenry (2000 - White mothers) - Correlations
251
Table 10.1.2- – McKelvey & McKenry (2000 - White mothers) - Correlations
252
Table 10.1.3- – McKelvey & McKenry (2000 - White mothers) - Correlations
253
Table 10.1.4- – McKelvey & McKenry (2000 - White mothers) - Correlations
254
Table 10.1.5- – McKelvey & McKenry (2000 - White mothers) - Correlations
255
Table 10.2.1- – McKelvey & McKenry (2000 - White mothers) – Regression Estimates
256
Table 10.2.2- – McKelvey & McKenry (2000 - White mothers) – Regression Estimates
257
Table 10.2.3- – McKelvey & McKenry (2000 - White mothers) – Regression Estimates
258
Table 10.2.4- – McKelvey & McKenry (2000 - White mothers)– Regression Estimates
259
Table 10.2.5- – McKelvey & McKenry (2000 - White mothers) – Regression Estimates
260
Ullman & Brecklin (2003)
The purpose of this study was to examine how demographic and
psychological factors relate to health conditions in a sample of women
with varying sexual assault histories. Data were drawn from the
National Comorbidity Survey (Kessler, 2007). Ullman and Brecklin
(2003) calculated correlations between all independent variables in
preparation for regression analysis. The present study will focus on the
variables: age, Number of Traumatic Life Events (“Trauma”; excluding
sexual assault already indicated; e.g., life-threatening accident, fire, flood
or natural disaster), Stressful Life Events (“Stressful”; e.g., robbed or
burglarized, serious trouble with police or the law), perceived Social
Support (“Support”), and Social Conflict (“Conflict”).
Variable relationships are plotted in figures 11.1 through 11.10
with suspected outliers identified. Correlation results are listed in tables
11.1.1 through 11.1.3. Re-analysis revealed significant correlational
relationships between Age & Trauma (highest statistically significant
correlation value calculated by spear, rs = .11), Age and Stressful (highest
statistically significant correlation values calculated by pcorb, r* = -.12
and scor, rp = -.12), Age & Support (highest statistically significant
correlation values calculated by spear, rs = .10, pbcor/corb, rpb = .10,
and wincor, rw = .10), Age & Conflict (highest statistically significant
correlation value calculated by spear, rs = -.14), Trauma & Stressful
261
(highest statistically significant correlation values calculated by pcorb,
r* = -.36 and scor, rp = -.36), Trauma & Support (highest statistically
significant correlation value calculated by pcorb, r* = -.16), Trauma &
Conflict (highest statistically significant correlation value calculated by
pcorb, r* = .15), Stressful & Support (highest statistically significant
correlation value calculated by pcorb, r* = -.12), Stressful & Conflict
(highest statistically significant correlation value calculated by scor,
rp = .19), and Support & Conflict (highest statistically significant
correlation value calculated by scor, rp = -.43). Notably, the statistically
significant relationships between Age & Trauma and Stressful & Support,
were not revealed in the original publication using Pearson’s r.
Regression estimator results are listed in tables 11.2.1 through
11.2.3. Significant slope estimates were revealed for the relationships
between, Age & Trauma (shortest confidence interval calculated by lsfitci,
C.I. ls : .004, .03), Age & Stressful (shortest confidence interval
calculated by lsfitci, C.I. ls : -.03, -.01), Age & Support (shortest
confidence interval calculated by lsfitci, C.I. ls : .0002, .01), Age &
Conflict (shortest confidence interval calculated by chreg, ch = -.01),
Trauma & Stressful (shortest confidence interval calculated by lsfitci, C.I.
ls : .25, .38), Trauma & Support (equal length confidence intervals
calculated by lsfitci, C.I. ls : -.07, -.02 and chreg, ch = -.04), Trauma &
Conflict (shortest confidence interval and smallest error estimate
262
calculated by tsreg, ts = .04), Stressful & Support (shortest confidence
interval and smallest error estimate calculated by chreg, ch = -.03),
Stressful & Conflict (shortest confidence interval and smallest error
estimate calculated by tsreg, ts = .06), and Support & Conflict (shortest
confidence interval and smallest error estimate calculated by tsreg,
ts = -.45).
263
Figure 11.1 - Ullman & Brecklin (2003) – Age & Trauma
264
Figure 11.2 - Ullman & Brecklin (2003) – Age & Stressful
265
Figure 11.3 - Ullman & Brecklin (2003) – Age & Support
266
Figure 11.4 - Ullman & Brecklin (2003) – Age & Conflict
267
Figure 11.5 - Ullman & Brecklin (2003) – Trauma & Stressful
268
Figure 11.6 - Ullman & Brecklin (2003) – Trauma & Support
269
Figure 11.7 - Ullman & Brecklin (2003) – Trauma & Conflict
270
Figure 11.8 - Ullman & Brecklin (2003) – Stressful & Support
271
Figure 11.9 - Ullman & Brecklin (2003) – Stressful & Conflict
272
Figure 11.10 - Ullman & Brecklin (2003) – Support & Conflict
273
Table 11.1.1 – Ullman & Brecklin (2003) - Correlations
274
Table 11.1.2 – Ullman & Brecklin (2003) - Correlations
275
Table 11.1.3 – Ullman & Brecklin (2003) - Correlations
276
Table 11.2.1 – Ullman & Brecklin (2003) – Regression Estimates
277
Table 11.2.2 – Ullman & Brecklin (2003) – Regression Estimates
278
Table 11.2.3 – Ullman & Brecklin (2003) – Regression Estimates
279
Chapter 4: Discussion
An attempt was made in this study to better understand the
properties of robust correlation and single predictor regression measures,
as specific alternatives to Pearson’s r, by re-analyzing previously
published behavioral science data. All the variable relationships
included here had previously been published having been analyzed using
Pearson’s r. Specifically, 143 variable relationships were examined, first
visually and then through the lens of eight different alternatives to
measuring the relationship between two variables. Following are the
main criteria used by the author to judge a “successful” alternative to
Pearson’s r:
1. Accurately captures strength and direction of the relationship
between two variables. Accuracy was judged based on visual
inspection of plotted relationship and on consistency in magnitude
and direction with other similar measures.
2. Stable performance of this alternative measure across different
data sets and variables. Did the measure consistently perform well
in a variety of situations?
Interestingly, the two measures that performed the best across these 143
pairs of variables were measures that rely on a traditional approach to
assessing the relationship between two variables AFTER dealing with
outliers: scor, which calculates the skipped correlation (rp), and lsfitci,
280
which calculates a .95 confidence interval for the Ordinary Least Squares
(OLS) regression estimator (ls) using a percentile bootstrap method.
More often than any of the other methods tested here, scor revealed the
strongest (largest magnitude) statistically significant relationships and
lsfitci revealed the shortest and therefore most meaningful .95 confidence
intervals. The skipped correlation appears to be best suited to efficiently
and accurately assess the relationship between two variables mainly
because it deals effectively with problematic outliers. With this
information in mind, we now revisit the research questions posed at the
beginning of this investigation.
Revisiting our research questions
1. Are recently published correlational studies relying on Pearson’s r
to evaluate the relationship between variables missing important
information?
Answer: Yes. In several instances we see that statistically significant
relationships were uncovered using robust techniques that were not
uncovered relying only on Pearson’s r. What is even more concerning,
however, were the instances where a statistically significant relationship
from the publication could not be replicated using any of the robust
techniques examined here. Visually inspecting a plot of the two variables
in question shows that in these cases one or a few outliers were causing
this “false detection”.
281
2. Using these same data, what are the comparative properties of
some robust correlation or regression alternatives to Pearson’s r?
Answer: Robust methods can be more sensitive to statistical differences
because they deal more effectively with issues such as heteroscedasticity
and outliers. They therefore provide a more efficient tool to test for
statistical significance. The inclusion of additional pieces of information
such as slope estimates (regression coefficients), confidence intervals and
standard error estimates of those confidence intervals, we can assess not
just statistical significance but we can also better assess
meaningfulness. Too often researchers rely on only a p-value and do not
think too much about the actual meaningfulness (or lack thereof) of the
statistic they have computed. Thus, it seems that robust alternatives to
Pearson’s r are actually a safer bet if one wants to feel more confident in
their analytic processes.
3. Which of these robust correlation or regression alternatives to
Pearson’s r are the most informative?
Answer: Skipped correlation (scor). Different measures give us different
levels of information about the relationship between two variables.
However, as it is a more familiar way of judging the strength of a
relationship between two variables, the skipped correlation value is a
quicker read for most and therefore a nice way to describe the
relationship between two variables. Having seen the evidence in the
282
current study, one’s level of confidence that the skipped correlation is an
accurate reflection of the relationship between two variables is increased.
Problems and limitations of the current study
Although this study is apparently the first to provide an in-depth
examination of real life performance of these alternatives to Pearson’s r,
with only 5 studies involved here, there is obviously much left to be
desired in terms of quantitative proof of the “best performing” alternative
to Pearson’s r. Investigations of this nature should continue, and the
scor method especially should be further tested to better understand its
properties under an even wider variety of situations.
Practical implications for applied behavioral science researchers
Compared to more commonly used statistical packages such as
SPSS, S-Plus and R software can seem foreign and difficult to use. For
example, there are memory limitations in S-Plus and R that make
working with large data sets somewhat impractical. Running some
intricate functions can take hours and sometimes more than a day. Add
to this the declining numbers of doctoral students in Psychology who
receive training in advanced research methods and quantitative analysis
(Rossen & Oakland, 2008) and the situation for adoption of new
statistical techniques using unfamiliar software appears bleak. Usability
improvements must be made to these software programs to encourage
283
wider adoption and in turn, wider acceptance and usage of robust
alternatives to traditional statistical methods.
However, the risk of missing valuable information because we have
grown too comfortable with our analytical tools is too great and cannot
be tolerated. Applied researchers in the behavioral sciences must
continue to push themselves to approach their data analyses with the
same level of creativity and vigor that accompanies research design and
clinical practice. It makes no sense to put so much effort and energy
into our research only to be saddled with ambiguous results
To date most studies comparing these statistical measures have
been conducted using simulated data. Using actual data in this instance
does reveal problematic usability issues but also further validates the
premise that outliers are a real problem in today’s data sets, even the
publishable ones, and can lead to misleading conclusions (perhaps even
in existing recent publications).
284
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Abstract (if available)
Abstract
Eleven data sets from five recently published articles in the field of psychology were re-analyzed to examine the extent to which reliance on Pearson's r to assess the relationship between two variables resulted in missed information. The robust techniques examined include three robust alternatives to r: the percentage bend correlation, the Winsorized correlation, and the skipped correlation
Linked assets
University of Southern California Dissertations and Theses
Conceptually similar
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Comparing skipped correlations: the overlapping case
Asset Metadata
Creator
Stuart, Veronica Mejia
(author)
Core Title
Exploring robust aternatives to Pearson's r through secondary analysis of published behavioral science data
School
College of Letters, Arts and Sciences
Degree
Doctor of Philosophy
Degree Program
Psychology
Publication Date
12/13/2008
Defense Date
06/16/2008
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
correlation,OAI-PMH Harvest,Pearson's r,robust statistics,secondary analysis,skipped correlation
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Wilcox, Rand R. (
committee chair
), John, Richard S. (
committee member
), McClure, William O. (
committee member
), Read, Stephen J. (
committee member
)
Creator Email
roni.stuart@gmail.com,vymejia@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-m1926
Unique identifier
UC1139204
Identifier
etd-Stuart-2418 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-152126 (legacy record id),usctheses-m1926 (legacy record id)
Legacy Identifier
etd-Stuart-2418.pdf
Dmrecord
152126
Document Type
Dissertation
Rights
Stuart, Veronica Mejia
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Repository Name
Libraries, University of Southern California
Repository Location
Los Angeles, California
Repository Email
cisadmin@lib.usc.edu
Tags
correlation
Pearson's r
robust statistics
secondary analysis
skipped correlation