The Statistical Imagination: Elementary Statistics for the Social Sciences

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  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2007-01-26
  • Publisher: McGraw-Hill Humanities/Social Sciences/Languages
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This basic social science statistics text uses illustrations and exercises for sociology, social work, political science, and criminal justice. Praised for a writing style that takes the anxiety out of statistics courses, the author explains basic statistical principles through a variety of engaging exercises, each designed to illuminate the unique theme of examining society both creatively and logically. In an effort to make the study of statistics relevant to students of the social sciences, the author encourages readers to interpret the results of calculations in the context of more substantive social issues, while continuing to value precise and accurate research. The text includes computer-based assignments with over 10 data sets for use with the free Student Version SPSS 15.0 CD-ROM that accompanies each new copy of the book. .

Table of Contents

Prefacep. X
The Statistical Imaginationp. 1
Introductionp. 1
The Statistical Imaginationp. 3
Linking the Statistical Imagination to the Sociological Imaginationp. 4
Statistical Norms and Social Normsp. 4
Statistical Ideals and Social Valuesp. 5
Statistics and Science: Tools for Proportional Thinkingp. 7
Descriptive and Inferential Statisticsp. 7
What Is Science?p. 8
Scientific Skepticism and the Statistical Imaginationp. 9
Conceiving of Datap. 10
The Research Processp. 13
Proportional Thinking: Calculating Proportions, Percentages, and Ratesp. 15
How to Succeed in This Course and Enjoy Itp. 20
Statistical Follies and Fallacies: The Problem of Small Denominatorsp. 21
Organizing Data to Minimize Statistical Errorp. 36
Introductionp. 36
Controlling Sampling Errorp. 37
Careful Statistical Estimation versus Hasty Guesstimationp. 40
Sampling Error and Its Management with Probability Theoryp. 41
Controlling Measurement Errorp. 42
Levels of Measurement: Careful Selection of Statistical Proceduresp. 42
Measurementp. 42
Nominal Variablesp. 43
Ordinal Variablesp. 44
Interval Variablesp. 44
Ratio Variablesp. 45
Improving the Level of Measurementp. 47
Distinguishing Level of Measurement and Unit of Measurep. 47
Coding and Counting Observationsp. 48
Frequency Distributionsp. 50
Standardizing Score Distributionsp. 51
Coding and Counting Interval/Ratio Datap. 52
Rounding Interval/Ratio Observationsp. 53
The Real Limits of Rounded Scoresp. 53
Proportional and Percentage Frequency Distributions for Interval/Ratio Variablesp. 55
Cumulative Percentage Frequency Distributionsp. 56
Percentiles and Quartilesp. 58
Grouping Interval/Ratio Datap. 60
Statistical Follies and Fallacies: The Importance of Having a Representative Samplep. 61
Charts and Graphs: A Picture Says a Thousand Wordsp. 78
Introduction: Pictorial Presentation of Datap. 78
Graphing and Table Construction Guidelinesp. 79
Graphing Nominal/Ordinal Datap. 80
Pie Chartsp. 80
Bar Chartsp. 83
Graphing Interval/Ratio Variablesp. 86
Histogramsp. 86
Polygons and Line Graphsp. 89
Using Graphs with Inferential Statistics and Research Applicationsp. 93
Statistical Follies and Fallacies: Graphical Distortionp. 94
Measuring Averagesp. 107
Introductionp. 107
The Meanp. 108
Proportional Thinking about the Meanp. 109
Potential Weaknesses of the Mean: Situations Where Reporting It Alone May Misleadp. 111
The Medianp. 112
Potential Weaknesses of the Median: Situations Where Reporting It Alone May Misleadp. 114
The Modep. 115
Potential Weaknesses of the Mode: Situations Where Reporting It Alone May Misleadp. 116
Central Tendency Statistics and the Appropriate Level of Measurementp. 117
Frequency Distribution Curves: Relationships Among the Mean, Median, and Modep. 118
The Normal Distributionp. 118
Skewed Distributionsp. 119
Using Sample Data to Estimate the Shape of a Score Distribution in a Populationp. 120
Organizing Data for Calculating Central Tendency Statisticsp. 122
Spreadsheet Format for Calculating Central Tendency Statisticsp. 122
Frequency Distribution Format for Calculating the Modep. 123
Statistical Follies and Fallacies: Mixing Subgroups in the Calculation of the Meanp. 124
Measuring Dispersion or Spread in a Distribution of Scoresp. 136
Introductionp. 136
The Rangep. 138
Limitations of the Range: Situations Where Reporting It Alone May Misleadp. 139
The Standard Deviationp. 139
Proportional and Linear Thinking about the Standard Deviationp. 140
Limitations of the Standard Deviationp. 145
The Standard Deviation as an Integral Part of Inferential Statisticsp. 147
Why Is It Called the "Standard" Deviation?p. 148
Standardized Scores (Z-Scores)p. 148
The Standard Deviation and the Normal Distributionp. 150
Tabular Presentation of Resultsp. 153
Statistical Follies and Fallacies: What Does It Indicate When the Standard Deviation Is Larger than the Mean?p. 154
Probability Theory and the Normal Probability Distributionp. 168
Introduction: The Human Urge to Predict the Futurep. 168
What Is a Probability?p. 170
Basic Rules of Probability Theoryp. 172
Probabilities Always Range Between 0 and 1p. 172
The Addition Rule for Alternative Eventsp. 172
Adjust for Joint Occurrencesp. 173
The Multiplication Rule for Compound Eventsp. 174
Account for Replacement with Compound Eventsp. 174
Using the Normal Curve as a Probability Distributionp. 176
Proportional Thinking about a Group of Cases and Single Casesp. 176
Partitioning Areas Under the Normal Curvep. 179
Sample Problems Using the Normal Curvep. 181
Computing Percentiles for Normally Distributed Populationsp. 191
The Normal Curve as a Tool for Proportional Thinkingp. 193
Statistical Follies and Fallacies: The Gambler's Fallacy: Independence of Probability Eventsp. 194
Using Probability Theory to Produce Sampling Distributionsp. 206
Introduction: Estimating Parametersp. 206
Point Estimatesp. 207
Predicting Sampling Errorp. 207
Sampling Distributionsp. 209
Sampling Distributions for Interval/Ratio Variablesp. 209
The Standard Errorp. 211
The Law of Large Numbersp. 212
The Central Limit Theoremp. 212
Sampling Distributions for Nominal Variablesp. 215
Rules Concerning a Sampling Distribution of Proportionsp. 218
Bean Counting as a Way of Grasping the Statistical Imaginationp. 219
Distinguishing Among Populations, Samples, and Sampling Distributionsp. 221
Statistical Follies and Fallacies: Treating a Point Estimate as Though It Were Absolutely Truep. 222
Parameter Estimation Using Confidence Intervalsp. 237
Introductionp. 237
Confidence Interval of a Population Meanp. 240
Calculating the Standard Error for a Confidence Interval of a Population Meanp. 241
Choosing the Critical Z-Score, Z[subscript Alpha]p. 242
Calculating the Error Termp. 243
Calculating the Confidence Intervalp. 243
The Five Steps for Computing a Confidence Interval of a Population Mean, Mu[subscript x]p. 245
Proper Interpretation of Confidence Intervalsp. 247
Common Misinterpretations of Confidence Intervalsp. 249
The Chosen Level of Confidence and the Precision of the Confidence Intervalp. 249
Sample Size and the Precision of the Confidence Intervalp. 250
Large-Sample Confidence Interval of a Population Proportionp. 252
Choosing a Sample Size for Polls, Surveys, and Research Studiesp. 256
Sample Size for a Confidence Interval of a Population Proportionp. 256
Statistical Follies and Fallacies: It Is Plus and Minus the Error Termp. 258
Hypothesis Testing I: The Six Steps of Statistical Inferencep. 267
Introduction: Scientific Theory and the Development of Testable Hypothesesp. 267
Making Empirical Predictionsp. 268
Statistical Inferencep. 269
The Importance of Sampling Distributions for Hypothesis Testingp. 272
The Six Steps of Statistical Inference for a Large Single-Sample Means Testp. 274
Test Preparationp. 276
The Six Stepsp. 276
Special Note on Symbolsp. 287
Understanding the Place of Probability Theory in Hypothesis Testingp. 287
A Focus on p-Valuesp. 287
The Level of Significance and Critical Regions of the Sampling Distribution Curvep. 288
The Level of Confidencep. 295
Study Hints: Organizing Problem Solutionsp. 295
Solution Boxes Using the Six Stepsp. 297
Interpreting Results When the Null Hypothesis Is Rejected: The Hypothetical Framework of Hypothesis Testingp. 301
Selecting Which Statistical Test to Usep. 301
Statistical Follies and Fallacies: Informed Common Sense: Going Beyond Common Sense by Observing Datap. 302
Hypothesis Testing II: Single-Sample Hypothesis Tests: Establishing the Representativeness of Samplesp. 315
Introductionp. 315
The Small Single-Sample Means Testp. 317
The "Students' t" Sampling Distributionp. 317
Selecting the Critical Probability Score, t[subscript Alpha], from the t-distribution Tablep. 321
Special Note on Symbolsp. 321
What Are Degrees of Freedom?p. 322
The Six Steps of Statistical Inference for a Small Single-Sample Means Testp. 324
Gaining a Sense of Proportion About the Dynamics of a Means Testp. 330
Relationships among Hypothesized Parameters, Observed Sample Statistics, Computed Test Statistics, p-Values, and Alpha Levelsp. 330
Using Single-Sample Hypothesis Tests to Establish Sample Representativenessp. 340
Target Values for Hypothesis Tests of Sample Representativenessp. 340
Large Single-Sample Proportions Testp. 344
The Six Steps of Statistical Inference for a Large Single-Sample Proportions Testp. 346
What to Do If a Sample Is Found Not to Be Representative?p. 349
Presentation of Data from Single-Sample Hypothesis Testsp. 350
A Confidence Interval of the Population Mean When n Is Smallp. 351
Statistical Follies and Fallacies: Issues of Sample Size and Sample Representativenessp. 353
Bivariate Relationships: t-Test for Comparing the Means of Two Groupsp. 368
Introduction: Bivariate Analysisp. 368
Difference of Means Testsp. 369
Joint Occurrences of Attributesp. 370
Correlationp. 371
Two-Group Difference of Means Test (t-Test) for Independent Samplesp. 371
The Standard Error and Sampling Distribution for the t-Test of the Difference Between Two Meansp. 374
The Six Steps of Statistical Inference for the Two-Group Difference of Means Testp. 378
When the Population Variances (or Standard Deviations) Appear Radically Differentp. 380
The Two-Group Difference of Means Test for Nonindependent or Matched-Pair Samplesp. 383
The Six Steps of Statistical Inference for the Two-Group Difference of Means Test for Nonindependent or Matched-Pair Samplesp. 388
Practical versus Statistical Significancep. 389
The Four Aspects of Statistical Relationshipsp. 390
Existence of a Relationshipp. 390
Direction of the Relationshipp. 390
Strength of the Relationship, Predictive Power, and Proportional Reduction in Errorp. 391
Practical Applications of the Relationshipp. 392
When to Apply the Various Aspects of Relationshipsp. 393
Relevant Aspects of a Relationship for Two-Group Difference of Means Testsp. 393
Statistical Follies and Fallacies: Fixating on Differences of Means While Ignoring Differences in Variancesp. 395
Analysis of Variance: Differences Among Means of Three or More Groupsp. 414
Introductionp. 414
Calculating Main Effectsp. 415
The General Linear Model: Testing the Statistical Significance of Main Effectsp. 418
Determining the Statistical Significance of Main Effects Using ANOVAp. 421
The F-Ratio Test Statisticp. 428
How the F-Ratio Turns Out When Group Means Are Not Significantly Differentp. 429
The F-Ratio as a Sampling Distributionp. 430
Relevant Aspects of a Relationship for ANOVAp. 432
Existence of the Relationshipp. 432
Direction of the Relationshipp. 432
Strength of the Relationshipp. 433
Practical Applications of the Relationshipp. 434
The Six Steps of Statistical Inference for One-Way ANOVAp. 437
Tabular Presentation of Resultsp. 442
Multivariate Applications of the General Linear Modelp. 442
Similarities Between the t-Test and the F-Ratio Testp. 443
Statistical Follies and Fallacies: Individualizing Group Findingsp. 444
Nominal Variables: The Chi-Square and Binomial Distributionsp. 464
Introduction: Proportional Thinking About Social Statusp. 464
Crosstab Tables: Comparing the Frequencies of Two Nominal/Ordinal Variablesp. 466
The Chi-Square Test: Focusing on the Frequencies of Joint Occurrencesp. 468
Calculating Expected Frequenciesp. 470
Differences Between Observed and Expected Cell Frequenciesp. 470
Degrees of Freedom for the Chi-Square Testp. 472
The Chi-Square Sampling Distribution and Its Critical Regionsp. 474
The Six Steps of Statistical Inference for the Chi-Square Testp. 475
Relevant Aspects of a Relationship for the Chi-Square Testp. 478
Using Chi-Square as a Difference of Proportions Testp. 479
Tabular Presentation of Datap. 481
Small Single-Sample Proportions Test: The Binomial Distributionp. 483
The Binomial Distribution Equationp. 484
Shortcut Formula for Expanding the Binomial Equationp. 486
The Six Steps of Statistical Inference for a Small Single-Sample Proportions Test: The Binomial Distribution Testp. 489
Statistical Follies and Fallacies: Low Statistical Power When the Sample Size Is Smallp. 492
Bivariate Correlation and Regression: Part 1: Concepts and Calculationsp. 509
Introduction: Improving Best Estimates of a Dependent Variablep. 509
A Correlation Between Two Interval/Ratio Variablesp. 510
Identifying a Linear Relationshipp. 511
Drawing the Scatterplotp. 513
Identifying a Linear Patternp. 513
Using the Linear Regression Equation to Measure the Effects of X on Yp. 516
Pearson's r Bivariate Correlation Coefficientp. 518
Computational Spreadsheet for Calculating Bivariate Correlation and Regression Statisticsp. 519
Characteristics of the Pearson's r Bivariate Correlation Coefficientp. 521
Understanding the Pearson's r Formulationp. 522
Regression Statisticsp. 524
The Regression Coefficient or Slope, bp. 525
The Y-intercept, ap. 525
Calculating the Terms of the Regression Line Formulap. 527
For the Especially Inquisitive: The Mathematical Relationship Between Pearson's r Correlation Coefficient and the Regression Coefficient, bp. 529
Statistical Follies and Fallacies The Failure to Observe a Scatterplot Before Calculating Pearson's rp. 531
Linear Equations Work Only with a Linear Pattern in the Scatterplotp. 531
Outlier Coordinates and the Attenuation and Inflation of Correlation Coefficientsp. 532
Bivariate Correlation and Regression: Part 2: Hypothesis Testing and Aspects of a Relationshipp. 552
Introduction: Hypothesis Test and Aspects of a Relationship Between Two Interval/Ratio Variablesp. 552
Organizing Data for the Hypothesis Testp. 553
The Six Steps of Statistical Inference and the Four Aspects of a Relationshipp. 555
Existence of a Relationshipp. 556
Direction of the Relationshipp. 561
Strength of the Relationshipp. 561
Practical Applications of the Relationshipp. 565
Careful Interpretation of Correlation and Regression Statisticsp. 567
Correlations Apply to a Population, Not to an Individualp. 567
Careful Interpretation of the Slope, bp. 568
Distinguishing Statistical Significance from Practical Significancep. 568
Tabular Presentation: Correlation Tablesp. 570
Statistical Follies and Fallacies: Correlation Does Not Always Indicate Causationp. 571
Review of Basic Mathematical Operationsp. 586
Statistical Probability Tablesp. 595
Statistical Table A-Random Number Tablep. 595
Statistical Table B-Normal Distribution Tablep. 596
Statistical Table C-t-Distribution Tablep. 598
Statistical Table D-Critical Values of the F-Ratio Distribution at the .05 Level of Significancep. 599
Statistical Table E-Critical Values of the F-Ratio Distribution at the .01 Level of Significancep. 600
Statistical Table F-q-Values of Range Tests at the .05 and .01 Levels of Significancep. 601
Statistical Table G-Critical Values of the Chi-Square Distributionp. 602
Answers to Selected Chapter Exercisesp. 603
Guide to SPSS for Windowsp. 620
Referencesp. 649
Indexp. 654
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