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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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