Preface | p. X |

The Statistical Imagination | p. 1 |

Introduction | p. 1 |

The Statistical Imagination | p. 3 |

Linking the Statistical Imagination to the Sociological Imagination | p. 4 |

Statistical Norms and Social Norms | p. 4 |

Statistical Ideals and Social Values | p. 5 |

Statistics and Science: Tools for Proportional Thinking | p. 7 |

Descriptive and Inferential Statistics | p. 7 |

What Is Science? | p. 8 |

Scientific Skepticism and the Statistical Imagination | p. 9 |

Conceiving of Data | p. 10 |

The Research Process | p. 13 |

Proportional Thinking: Calculating Proportions, Percentages, and Rates | p. 15 |

How to Succeed in This Course and Enjoy It | p. 20 |

Statistical Follies and Fallacies: The Problem of Small Denominators | p. 21 |

Organizing Data to Minimize Statistical Error | p. 36 |

Introduction | p. 36 |

Controlling Sampling Error | p. 37 |

Careful Statistical Estimation versus Hasty Guesstimation | p. 40 |

Sampling Error and Its Management with Probability Theory | p. 41 |

Controlling Measurement Error | p. 42 |

Levels of Measurement: Careful Selection of Statistical Procedures | p. 42 |

Measurement | p. 42 |

Nominal Variables | p. 43 |

Ordinal Variables | p. 44 |

Interval Variables | p. 44 |

Ratio Variables | p. 45 |

Improving the Level of Measurement | p. 47 |

Distinguishing Level of Measurement and Unit of Measure | p. 47 |

Coding and Counting Observations | p. 48 |

Frequency Distributions | p. 50 |

Standardizing Score Distributions | p. 51 |

Coding and Counting Interval/Ratio Data | p. 52 |

Rounding Interval/Ratio Observations | p. 53 |

The Real Limits of Rounded Scores | p. 53 |

Proportional and Percentage Frequency Distributions for Interval/Ratio Variables | p. 55 |

Cumulative Percentage Frequency Distributions | p. 56 |

Percentiles and Quartiles | p. 58 |

Grouping Interval/Ratio Data | p. 60 |

Statistical Follies and Fallacies: The Importance of Having a Representative Sample | p. 61 |

Charts and Graphs: A Picture Says a Thousand Words | p. 78 |

Introduction: Pictorial Presentation of Data | p. 78 |

Graphing and Table Construction Guidelines | p. 79 |

Graphing Nominal/Ordinal Data | p. 80 |

Pie Charts | p. 80 |

Bar Charts | p. 83 |

Graphing Interval/Ratio Variables | p. 86 |

Histograms | p. 86 |

Polygons and Line Graphs | p. 89 |

Using Graphs with Inferential Statistics and Research Applications | p. 93 |

Statistical Follies and Fallacies: Graphical Distortion | p. 94 |

Measuring Averages | p. 107 |

Introduction | p. 107 |

The Mean | p. 108 |

Proportional Thinking about the Mean | p. 109 |

Potential Weaknesses of the Mean: Situations Where Reporting It Alone May Mislead | p. 111 |

The Median | p. 112 |

Potential Weaknesses of the Median: Situations Where Reporting It Alone May Mislead | p. 114 |

The Mode | p. 115 |

Potential Weaknesses of the Mode: Situations Where Reporting It Alone May Mislead | p. 116 |

Central Tendency Statistics and the Appropriate Level of Measurement | p. 117 |

Frequency Distribution Curves: Relationships Among the Mean, Median, and Mode | p. 118 |

The Normal Distribution | p. 118 |

Skewed Distributions | p. 119 |

Using Sample Data to Estimate the Shape of a Score Distribution in a Population | p. 120 |

Organizing Data for Calculating Central Tendency Statistics | p. 122 |

Spreadsheet Format for Calculating Central Tendency Statistics | p. 122 |

Frequency Distribution Format for Calculating the Mode | p. 123 |

Statistical Follies and Fallacies: Mixing Subgroups in the Calculation of the Mean | p. 124 |

Measuring Dispersion or Spread in a Distribution of Scores | p. 136 |

Introduction | p. 136 |

The Range | p. 138 |

Limitations of the Range: Situations Where Reporting It Alone May Mislead | p. 139 |

The Standard Deviation | p. 139 |

Proportional and Linear Thinking about the Standard Deviation | p. 140 |

Limitations of the Standard Deviation | p. 145 |

The Standard Deviation as an Integral Part of Inferential Statistics | p. 147 |

Why Is It Called the "Standard" Deviation? | p. 148 |

Standardized Scores (Z-Scores) | p. 148 |

The Standard Deviation and the Normal Distribution | p. 150 |

Tabular Presentation of Results | p. 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 Distribution | p. 168 |

Introduction: The Human Urge to Predict the Future | p. 168 |

What Is a Probability? | p. 170 |

Basic Rules of Probability Theory | p. 172 |

Probabilities Always Range Between 0 and 1 | p. 172 |

The Addition Rule for Alternative Events | p. 172 |

Adjust for Joint Occurrences | p. 173 |

The Multiplication Rule for Compound Events | p. 174 |

Account for Replacement with Compound Events | p. 174 |

Using the Normal Curve as a Probability Distribution | p. 176 |

Proportional Thinking about a Group of Cases and Single Cases | p. 176 |

Partitioning Areas Under the Normal Curve | p. 179 |

Sample Problems Using the Normal Curve | p. 181 |

Computing Percentiles for Normally Distributed Populations | p. 191 |

The Normal Curve as a Tool for Proportional Thinking | p. 193 |

Statistical Follies and Fallacies: The Gambler's Fallacy: Independence of Probability Events | p. 194 |

Using Probability Theory to Produce Sampling Distributions | p. 206 |

Introduction: Estimating Parameters | p. 206 |

Point Estimates | p. 207 |

Predicting Sampling Error | p. 207 |

Sampling Distributions | p. 209 |

Sampling Distributions for Interval/Ratio Variables | p. 209 |

The Standard Error | p. 211 |

The Law of Large Numbers | p. 212 |

The Central Limit Theorem | p. 212 |

Sampling Distributions for Nominal Variables | p. 215 |

Rules Concerning a Sampling Distribution of Proportions | p. 218 |

Bean Counting as a Way of Grasping the Statistical Imagination | p. 219 |

Distinguishing Among Populations, Samples, and Sampling Distributions | p. 221 |

Statistical Follies and Fallacies: Treating a Point Estimate as Though It Were Absolutely True | p. 222 |

Parameter Estimation Using Confidence Intervals | p. 237 |

Introduction | p. 237 |

Confidence Interval of a Population Mean | p. 240 |

Calculating the Standard Error for a Confidence Interval of a Population Mean | p. 241 |

Choosing the Critical Z-Score, Z[subscript Alpha] | p. 242 |

Calculating the Error Term | p. 243 |

Calculating the Confidence Interval | p. 243 |

The Five Steps for Computing a Confidence Interval of a Population Mean, Mu[subscript x] | p. 245 |

Proper Interpretation of Confidence Intervals | p. 247 |

Common Misinterpretations of Confidence Intervals | p. 249 |

The Chosen Level of Confidence and the Precision of the Confidence Interval | p. 249 |

Sample Size and the Precision of the Confidence Interval | p. 250 |

Large-Sample Confidence Interval of a Population Proportion | p. 252 |

Choosing a Sample Size for Polls, Surveys, and Research Studies | p. 256 |

Sample Size for a Confidence Interval of a Population Proportion | p. 256 |

Statistical Follies and Fallacies: It Is Plus and Minus the Error Term | p. 258 |

Hypothesis Testing I: The Six Steps of Statistical Inference | p. 267 |

Introduction: Scientific Theory and the Development of Testable Hypotheses | p. 267 |

Making Empirical Predictions | p. 268 |

Statistical Inference | p. 269 |

The Importance of Sampling Distributions for Hypothesis Testing | p. 272 |

The Six Steps of Statistical Inference for a Large Single-Sample Means Test | p. 274 |

Test Preparation | p. 276 |

The Six Steps | p. 276 |

Special Note on Symbols | p. 287 |

Understanding the Place of Probability Theory in Hypothesis Testing | p. 287 |

A Focus on p-Values | p. 287 |

The Level of Significance and Critical Regions of the Sampling Distribution Curve | p. 288 |

The Level of Confidence | p. 295 |

Study Hints: Organizing Problem Solutions | p. 295 |

Solution Boxes Using the Six Steps | p. 297 |

Interpreting Results When the Null Hypothesis Is Rejected: The Hypothetical Framework of Hypothesis Testing | p. 301 |

Selecting Which Statistical Test to Use | p. 301 |

Statistical Follies and Fallacies: Informed Common Sense: Going Beyond Common Sense by Observing Data | p. 302 |

Hypothesis Testing II: Single-Sample Hypothesis Tests: Establishing the Representativeness of Samples | p. 315 |

Introduction | p. 315 |

The Small Single-Sample Means Test | p. 317 |

The "Students' t" Sampling Distribution | p. 317 |

Selecting the Critical Probability Score, t[subscript Alpha], from the t-distribution Table | p. 321 |

Special Note on Symbols | p. 321 |

What Are Degrees of Freedom? | p. 322 |

The Six Steps of Statistical Inference for a Small Single-Sample Means Test | p. 324 |

Gaining a Sense of Proportion About the Dynamics of a Means Test | p. 330 |

Relationships among Hypothesized Parameters, Observed Sample Statistics, Computed Test Statistics, p-Values, and Alpha Levels | p. 330 |

Using Single-Sample Hypothesis Tests to Establish Sample Representativeness | p. 340 |

Target Values for Hypothesis Tests of Sample Representativeness | p. 340 |

Large Single-Sample Proportions Test | p. 344 |

The Six Steps of Statistical Inference for a Large Single-Sample Proportions Test | p. 346 |

What to Do If a Sample Is Found Not to Be Representative? | p. 349 |

Presentation of Data from Single-Sample Hypothesis Tests | p. 350 |

A Confidence Interval of the Population Mean When n Is Small | p. 351 |

Statistical Follies and Fallacies: Issues of Sample Size and Sample Representativeness | p. 353 |

Bivariate Relationships: t-Test for Comparing the Means of Two Groups | p. 368 |

Introduction: Bivariate Analysis | p. 368 |

Difference of Means Tests | p. 369 |

Joint Occurrences of Attributes | p. 370 |

Correlation | p. 371 |

Two-Group Difference of Means Test (t-Test) for Independent Samples | p. 371 |

The Standard Error and Sampling Distribution for the t-Test of the Difference Between Two Means | p. 374 |

The Six Steps of Statistical Inference for the Two-Group Difference of Means Test | p. 378 |

When the Population Variances (or Standard Deviations) Appear Radically Different | p. 380 |

The Two-Group Difference of Means Test for Nonindependent or Matched-Pair Samples | p. 383 |

The Six Steps of Statistical Inference for the Two-Group Difference of Means Test for Nonindependent or Matched-Pair Samples | p. 388 |

Practical versus Statistical Significance | p. 389 |

The Four Aspects of Statistical Relationships | p. 390 |

Existence of a Relationship | p. 390 |

Direction of the Relationship | p. 390 |

Strength of the Relationship, Predictive Power, and Proportional Reduction in Error | p. 391 |

Practical Applications of the Relationship | p. 392 |

When to Apply the Various Aspects of Relationships | p. 393 |

Relevant Aspects of a Relationship for Two-Group Difference of Means Tests | p. 393 |

Statistical Follies and Fallacies: Fixating on Differences of Means While Ignoring Differences in Variances | p. 395 |

Analysis of Variance: Differences Among Means of Three or More Groups | p. 414 |

Introduction | p. 414 |

Calculating Main Effects | p. 415 |

The General Linear Model: Testing the Statistical Significance of Main Effects | p. 418 |

Determining the Statistical Significance of Main Effects Using ANOVA | p. 421 |

The F-Ratio Test Statistic | p. 428 |

How the F-Ratio Turns Out When Group Means Are Not Significantly Different | p. 429 |

The F-Ratio as a Sampling Distribution | p. 430 |

Relevant Aspects of a Relationship for ANOVA | p. 432 |

Existence of the Relationship | p. 432 |

Direction of the Relationship | p. 432 |

Strength of the Relationship | p. 433 |

Practical Applications of the Relationship | p. 434 |

The Six Steps of Statistical Inference for One-Way ANOVA | p. 437 |

Tabular Presentation of Results | p. 442 |

Multivariate Applications of the General Linear Model | p. 442 |

Similarities Between the t-Test and the F-Ratio Test | p. 443 |

Statistical Follies and Fallacies: Individualizing Group Findings | p. 444 |

Nominal Variables: The Chi-Square and Binomial Distributions | p. 464 |

Introduction: Proportional Thinking About Social Status | p. 464 |

Crosstab Tables: Comparing the Frequencies of Two Nominal/Ordinal Variables | p. 466 |

The Chi-Square Test: Focusing on the Frequencies of Joint Occurrences | p. 468 |

Calculating Expected Frequencies | p. 470 |

Differences Between Observed and Expected Cell Frequencies | p. 470 |

Degrees of Freedom for the Chi-Square Test | p. 472 |

The Chi-Square Sampling Distribution and Its Critical Regions | p. 474 |

The Six Steps of Statistical Inference for the Chi-Square Test | p. 475 |

Relevant Aspects of a Relationship for the Chi-Square Test | p. 478 |

Using Chi-Square as a Difference of Proportions Test | p. 479 |

Tabular Presentation of Data | p. 481 |

Small Single-Sample Proportions Test: The Binomial Distribution | p. 483 |

The Binomial Distribution Equation | p. 484 |

Shortcut Formula for Expanding the Binomial Equation | p. 486 |

The Six Steps of Statistical Inference for a Small Single-Sample Proportions Test: The Binomial Distribution Test | p. 489 |

Statistical Follies and Fallacies: Low Statistical Power When the Sample Size Is Small | p. 492 |

Bivariate Correlation and Regression: Part 1: Concepts and Calculations | p. 509 |

Introduction: Improving Best Estimates of a Dependent Variable | p. 509 |

A Correlation Between Two Interval/Ratio Variables | p. 510 |

Identifying a Linear Relationship | p. 511 |

Drawing the Scatterplot | p. 513 |

Identifying a Linear Pattern | p. 513 |

Using the Linear Regression Equation to Measure the Effects of X on Y | p. 516 |

Pearson's r Bivariate Correlation Coefficient | p. 518 |

Computational Spreadsheet for Calculating Bivariate Correlation and Regression Statistics | p. 519 |

Characteristics of the Pearson's r Bivariate Correlation Coefficient | p. 521 |

Understanding the Pearson's r Formulation | p. 522 |

Regression Statistics | p. 524 |

The Regression Coefficient or Slope, b | p. 525 |

The Y-intercept, a | p. 525 |

Calculating the Terms of the Regression Line Formula | p. 527 |

For the Especially Inquisitive: The Mathematical Relationship Between Pearson's r Correlation Coefficient and the Regression Coefficient, b | p. 529 |

Statistical Follies and Fallacies The Failure to Observe a Scatterplot Before Calculating Pearson's r | p. 531 |

Linear Equations Work Only with a Linear Pattern in the Scatterplot | p. 531 |

Outlier Coordinates and the Attenuation and Inflation of Correlation Coefficients | p. 532 |

Bivariate Correlation and Regression: Part 2: Hypothesis Testing and Aspects of a Relationship | p. 552 |

Introduction: Hypothesis Test and Aspects of a Relationship Between Two Interval/Ratio Variables | p. 552 |

Organizing Data for the Hypothesis Test | p. 553 |

The Six Steps of Statistical Inference and the Four Aspects of a Relationship | p. 555 |

Existence of a Relationship | p. 556 |

Direction of the Relationship | p. 561 |

Strength of the Relationship | p. 561 |

Practical Applications of the Relationship | p. 565 |

Careful Interpretation of Correlation and Regression Statistics | p. 567 |

Correlations Apply to a Population, Not to an Individual | p. 567 |

Careful Interpretation of the Slope, b | p. 568 |

Distinguishing Statistical Significance from Practical Significance | p. 568 |

Tabular Presentation: Correlation Tables | p. 570 |

Statistical Follies and Fallacies: Correlation Does Not Always Indicate Causation | p. 571 |

Review of Basic Mathematical Operations | p. 586 |

Statistical Probability Tables | p. 595 |

Statistical Table A-Random Number Table | p. 595 |

Statistical Table B-Normal Distribution Table | p. 596 |

Statistical Table C-t-Distribution Table | p. 598 |

Statistical Table D-Critical Values of the F-Ratio Distribution at the .05 Level of Significance | p. 599 |

Statistical Table E-Critical Values of the F-Ratio Distribution at the .01 Level of Significance | p. 600 |

Statistical Table F-q-Values of Range Tests at the .05 and .01 Levels of Significance | p. 601 |

Statistical Table G-Critical Values of the Chi-Square Distribution | p. 602 |

Answers to Selected Chapter Exercises | p. 603 |

Guide to SPSS for Windows | p. 620 |

References | p. 649 |

Index | p. 654 |

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