Elementary Statistics in Social Research

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Jack Levin, Ph.D. is the Brudnick Professor of Sociology and Criminology at Northeastern University in Boston, where he co-directs its Center on Violence and Conflict. He has authored or co-authored 30 books, including the recently published volumes Serial Killers and Sadistic Murderers–Up Close and Personal and The Violence of Hate. Dr. Levin was honored by the Massachusetts Council for Advancement and Support of Education as its “Professor of the Year” and by the American Sociological Association with its Public Understanding of Sociology Award. He has spoken to a wide variety of community, academic, and professional groups, including the White House Conference on Hate Crimes, the Department of Justice, the Department of Education, OSCE’s Office for Democratic Institutions and Human Rights (a membership of 59 countries) and the International Association of Chiefs of Police.

James Alan Fox, Ph.D. is the Lipman Family Professor of Criminology, Law, and Public Policy at Northeastern University. He has written 18 books, including his newest, Violence and Security on Campus: From Preschool through College. He has also published dozens of journal and magazine articles, and hundreds of freelance columns in newspapers around the country. Fox often gives keynote talks and testimony before Congress and in criminal and civil courts. He has briefed various leaders here and abroad, including President Clinton, Attorney General Reno and Princess Anne of Great Britain. Finally, Fox was honored in 2007 by the Massachusetts Committee against the Death Penalty with the Hugo Adam Bedau Award for excellence in capital punishment scholarship and by Northeastern University with the 2008 Klein Lectureship.

Preface	p. xi
Why the Social Researcher Uses Statistics	p. 1
The Nature of Social Research	p. 1
Why Test Hypotheses?	p. 3
The Stages of Social Research	p. 4
Using Series of Numbers to Do Social Research	p. 5
The Functions of Statistics	p. 12
Summary	p. 18
Questions and Problems	p. 18
Looking at the Larger Picture: A Student Survey	p. 21
Description	p. 23
Organizing the Data	p. 25
Frequency Distributions of Nominal Data	p. 25
Comparing Distributions	p. 26
Proportions and Percentages	p. 26
Simple Frequency Distributions of Ordinal and Interval Data	p. 28
Grouped Frequency Distributions of Interval Data	p. 29
Cumulative Distributions	p. 31
Dealing with Decimal Data	p. 33
Flexible Class Intervals	p. 35
Cross-Tabulations	p. 37
Graphic Presentations	p. 43
Summary	p. 50
Questions and Problems	p. 51
Measures of Central Tendency	p. 58
The Mode	p. 58
The Median	p. 59
The Mean	p. 60
Taking One Step at a Time	p. 62
Comparing the Mode, Median, and Mean	p. 62
Step-by-Step Illustration: Mode, Median, and Mean	p. 63
Summary	p. 67
Questions and Problems	p. 68
Measures of Variability	p. 72
The Range	p. 73
The Variance and the Standard Deviation	p. 74
Step-by-Step Illustration: Standard Deviation	p. 75
The Raw-Score Formula for Variance and Standard Deviation	p. 76
Step-by-Step Illustration: Variance and Standard Deviation Using Raw Scores	p. 77
The Meaning of the Standard Deviation	p. 78
Comparing Measures of Variability	p. 81
Summary	p. 82
Questions and Problems	p. 82
Looking at the Larger Picture: Describing Data	p. 85
From Description to Decision Making	p. 89
Probability and the Normal Curve	p. 91
Probability	p. 92
Probability Distributions	p. 93
The Normal Curve as a Probability Distribution	p. 96
Characteristics of the Normal Curve	p. 97
The Model and the Reality of the Normal Curve	p. 97
The Area under the Normal Curve	p. 99
Standard Scores and the Normal Curve	p. 105
Finding Probability under the Normal Curve	p. 107
Step-by-Step Illustration: Probability under the Normal Curve	p. 108
Step-by-Step Illustration: Finding Scores from Probability Based on the Normal Curve	p. 113
Summary	p. 114
Questions and Problems	p. 114
Samples and Populations	p. 118
Random Sampling	p. 119
Sampling Error	p. 120
Sampling Distribution of Means	p. 121
Standard Error of the Mean	p. 128
Confidence Intervals	p. 129
The t Distribution	p. 133
Step-by-Step Illustration: Confidence Interval Using t	p. 138
Estimating Proportions	p. 140
Step-by-Step Illustration: Confidence Interval for Proportions	p. 141
Summary	p. 142
Questions and Problems	p. 143
Looking at the Larger Picture: Generalizing from Samples to Populations	p. 146
Decision Making	p. 149
Testing Differences between Means	p. 151
The Null Hypothesis: No Difference between Means	p. 153
The Research Hypothesis: A Difference between Means	p. 154
Sampling Distribution of Differences between Means	p. 154
Testing Hypotheses with the Distribution of Differences between Means	p. 158
Levels of Significance	p. 162
Standard Error of the Difference between Means	p. 166
Testing the Difference between Means	p. 167
Step-by-Step Illustration: Test of Difference between Means	p. 169
Comparing Dependent Samples	p. 171
Step-by-Step Illustration: Test of Difference between Means for Same Sample Measured Twice	p. 172
Step-by-Step Illustration: Test of Difference between Means for Matched Samples	p. 175
Two Sample Test of Proportions	p. 177
Step-by-Step Illustration: Test of Difference between Proportions	p. 177
Requirements for Testing the Difference between Means	p. 179
Summary	p. 180
Questions and Problems	p. 181
Analysis of Variance	p. 191
The Logic of Analysis of Variance	p. 192
The Sum of Squares	p. 194
A Research Illustration	p. 195
Mean Square	p. 200
The F Ratio	p. 201
Step-by-Step Illustration: Analysis of Variance	p. 204
Requirements for Using the F Ratio	p. 208
Summary	p. 208
Questions and Problems	p. 209
Nonparametric Tests of Significance	p. 215
One-Way Chi-Square Test	p. 216
Step-by-Step Illustration: One-Way Chi-Square	p. 219
Two-Way Chi-Square Test	p. 220
Step-by-Step Illustration: Two-Way Chi-Square Test of Significance	p. 226
Step-by-Step Illustration: Comparing Several Groups	p. 230
The Median Test	p. 236
Step-by-Step Illustration: Median Test	p. 236
Summary	p. 239
Questions and Problems	p. 239
Looking at the Larger Picture: Testing for Differences	p. 248
From Decision Making to Association	p. 251
Correlation	p. 253
Strength of Correlation	p. 253
Direction of Correlation	p. 254
Curvilinear Correlation	p. 255
The Correlation Coefficient	p. 256
Pearson's Correlation Coefficient	p. 257
Step-by-Step Illustration: Pearson's Correlation Coefficient	p. 263
Summary	p. 265
Questions and Problems	p. 266
Regression Analysis	p. 272
The Regression Model	p. 273
Interpreting the Regression Line	p. 278
Regression and Pearson's Correlation	p. 280
Step-by-Step Illustration: Regression Analysis	p. 281
Summary	p. 283
Questions and Problems	p. 283
Nonparametric Measures of Correlation	p. 290
Spearman's Rank-Order Correlation Coefficient	p. 290
Step-by-Step Illustration: Spearman's Rank-Order Correlation Coefficient	p. 295
Goodman's and Kruskal's Gamma	p. 298
Step-by-Step Illustration: Goodman's and Kruskal's Gamma	p. 299
Correlation Coefficient for Nominal Data Arranged in a 2 × 2 Table	p. 302
Correlation Coefficients for Nominal Data in Larger than 2 × 2 Tables	p. 304
Summary	p. 307
Questions and Problems	p. 307
Looking at the Larger Picture: Measuring Association	p. 315
Applying Statistics	p. 317
Choosing Statistical Procedures for Research Problems	p. 319
Research Situations	p. 323
Research Solutions	p. 340
Appendixes	p. 349
Instructions for Using ABCalc	p. 351
A Review of Some Fundamentals of Mathematics	p. 355
Tables	p. 360
List of Formulas	p. 372
Answers to Problems	p. 377
Index	p. 383
Table of Contents provided by Ingram. All Rights Reserved.

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Elementary Statistics in Social Research Essentials

Summary

Author Biography

Table of Contents

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