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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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The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.