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# Statistics for Psychology

**by**Aron, Arthur Ph.D.; Aron, Elaine N., Ph.D.; Coups, Elliot Ph.D.

5th

### 9780136010579

0136010571

Hardcover

3/9/2008

Pearson

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## Summary

The top-selling Statistics for Psychology, Fifth Edition, emphasizes meaning and concepts, not just symbols and numbers. Everything is explained in direct, simple language. Definitional formulas are used throughout to provide a concise symbolic summary of the logic of each particular procedure. Each procedure is taught both verbally and numerically-an important step in permanently establishing a concept in a student's mind. Thoroughly up to date and well written, Statistics for Psychology engages the reader and helps students understand statistics. Book jacket.

## Table of Contents

Preface to the Instructor | p. xi |

Introduction to the Student | p. xvi |

Displaying the Order in a Group of Numbers Using Tables and Graphs | p. 1 |

The Two Branches of Statistical Methods | p. 2 |

Some Basic Concepts | p. 3 |

Important Trivia for Poetic Statistics Students | p. 6 |

Frequency Tables | p. 7 |

Histograms | p. 10 |

Math Anxiety, Statistics Anxiety, and You: A Message for Those of You Who Are Truly Worried About This Course | p. 12 |

Shapes of Frequency Distributions | p. 15 |

Controversy: Misleading Graphs | p. 19 |

Frequency Tables and Histograms in Research Articles | p. 21 |

Summary | p. 23 |

Key Terms | p. 24 |

Example Worked-Out Problems | p. 24 |

Practice Problems | p. 25 |

Using SPSS | p. 29 |

Chapter Note | p. 32 |

Central Tendency and Variability | p. 33 |

Central Tendency | p. 34 |

Variability | p. 43 |

The Sheer Joy (Yes, Joy) of Statistical Analysis | p. 51 |

Controversy: The Tyranny of the Mean | p. 52 |

Gender, Ethnicity, and Math Performance | p. 53 |

Central Tendency and Variability in Research Articles | p. 55 |

Summary | p. 57 |

Key Terms | p. 57 |

Example Worked-Out Problems | p. 57 |

Practice Problems | p. 59 |

Using SPSS | p. 62 |

Chapter Notes | p. 65 |

Some Key Ingredients for Inferential Statistics: Z Scores, the Normal Curve, Sample versus Population, and Probability | p. 67 |

Z Scores | p. 68 |

The Normal Curve | p. 73 |

de Moivre, the Eccentric Stranger Who Invented the Normal Curve | p. 74 |

Sample and Population | p. 83 |

Surveys, Polls, and 1948's Costly "Free Sample" | p. 86 |

Probability | p. 88 |

Pascal Begins Probability Theory at the Gambling Table, Then Learns to Bet on God | p. 89 |

Controversies: Is the Normal Curve Really So Normal? and Using Nonrandom Samples | p. 93 |

Z Scores, Normal Curves, Samples and Populations, and Probabilities in Research Articles | p. 95 |

Advanced Topics: Probability Rules and Conditional Probabilities | p. 96 |

Summary | p. 97 |

Key Terms | p. 98 |

Example Worked-Out Problems | p. 99 |

Practice Problems | p. 102 |

Using SPSS | p. 105 |

Chapter Notes | p. 106 |

Introduction to Hypothesis Testing | p. 107 |

A Hypothesis-Testing Example | p. 108 |

The Core Logic of Hypothesis Testing | p. 109 |

The Hypothesis-Testing Process | p. 110 |

One-Tailed and Two-Tailed Hypothesis Tests | p. 119 |

Controversy: Should Significance Tests Be Banned? | p. 124 |

Jacob Cohen, the Ultimate New Yorker: Funny, Pushy, Brilliant, and Kind | p. 126 |

Hypothesis Tests in Research Articles | p. 127 |

Summary | p. 128 |

Key Terms | p. 129 |

Example Worked-Out Problems | p. 129 |

Practice Problems | p. 131 |

Chapter Notes | p. 136 |

Hypothesis Tests with Means of Samples | p. 137 |

The Distribution of Means | p. 138 |

Hypothesis Testing with a Distribution of Means: The Z Test | p. 146 |

More About Polls: Sampling Errors and Errors in Thinking About Samples | p. 147 |

Controversy: Marginal Significance | p. 153 |

Hypothesis Tests About Means of Samples (Z Tests) and Standard Errors in Research Articles | p. 154 |

Advanced Topic: Estimation, Standard Errors, and Confidence Intervals | p. 156 |

Advanced Topic Controversy: Confidence Intervals versus Significance Tests | p. 162 |

Advanced Topic: Confidence Intervals in Research Articles | p. 163 |

Summary | p. 163 |

Key Terms | p. 164 |

Example Worked-Out Problems | p. 164 |

Practice Problems | p. 167 |

Chapter Notes | p. 173 |

Making Sense of Statistical Significance: Decision Errors, Effect Size, and Statistical Power | p. 175 |

Decision Errors | p. 175 |

Effect Size | p. 179 |

Effect Sizes for Relaxation and Meditation: A Restful Meta-Analysis | p. 184 |

Statistical Power | p. 187 |

What Determines the Power of a Study? | p. 191 |

The Power of Typical Psychology Experiments | p. 199 |

The Role of Power When Planning a Study | p. 203 |

The Role of Power When Interpreting the Results of a Study | p. 205 |

Controversy: Statistical Significance versus Effect Size | p. 208 |

Decision Errors, Effect Size, and Power in Research Articles | p. 210 |

Advanced Topic: Figuring Statistical Power | p. 212 |

Summary | p. 214 |

Key Terms | p. 215 |

Example Worked-Out Problems | p. 215 |

Practice Problems | p. 217 |

Chapter Note | p. 221 |

Introduction to t Tests: Single Sample and Dependent Means | p. 222 |

The t Test for a Single Sample | p. 223 |

William S. Gosset, Alias "Student": Not a Mathematician, But a Practical Man | p. 224 |

The t Test for Dependent Means | p. 236 |

Assumptions of the t Test for a Single Sample and the t Test for Dependent Means | p. 247 |

Effect Size and Power for the t Test for Dependent Means | p. 247 |

Controversy: Advantages and Disadvantages of Repeated-Measures Designs | p. 250 |

The Power of Studies Using Difference Scores: How the Lanarkshire Milk Experiment Could Have Been Milked for More | p. 251 |

Single Sample t Tests and Dependent Means t Tests in Research Articles | p. 252 |

Summary | p. 253 |

Key Terms | p. 254 |

Example Worked-Out Problems | p. 254 |

Practice Problems | p. 258 |

Using SPSS | p. 265 |

Chapter Notes | p. 268 |

The t Test for Independent Means | p. 270 |

The Distribution of Differences Between Means | p. 271 |

Hypothesis Testing with a t Test for Independent Means | p. 278 |

Assumptions of the t Test for Independent Means | p. 286 |

Monte Carlo Methods: When Mathematics Becomes Just an Experiment, and Statistics Depend on a Game of Chance | p. 286 |

Effect Size and Power for the t Test for Independent Means | p. 288 |

Review and Comparison of the Three Kinds of t Tests | p. 290 |

Controversy: The Problem of Too Many t Tests | p. 291 |

The t Test for Independent Means in Research Articles | p. 292 |

Advanced Topic: Power for the t Test for Independent Means When Sample Sizes Are Not Equal | p. 293 |

Summary | p. 294 |

Key Terms | p. 295 |

Example Worked-Out Problems | p. 295 |

Practice Problems | p. 298 |

Using SPSS | p. 305 |

Chapter Notes | p. 309 |

Introduction to the Analysis of Variance | p. 310 |

Basic Logic of the Analysis of Variance | p. 311 |

Sir Ronald Fisher, Caustic Genius of Statistics | p. 317 |

Carrying Out an Analysis of Variance | p. 319 |

Hypothesis Testing with the Analysis of Variance | p. 327 |

Assumptions in the Analysis of Variance | p. 331 |

Planned Contrasts | p. 334 |

Post Hoc Comparisons | p. 337 |

Effect Size and Power for the Analysis of Variance | p. 339 |

Controversy: Omnibus Tests versus Planned Contrasts | p. 343 |

Analyses of Variance in Research Articles | p. 344 |

Advanced Topic: The Structural Model in the Analysis of Variance | p. 345 |

Principles of the Structural Model | p. 345 |

Summary | p. 351 |

Key Terms | p. 352 |

Example Worked-Out Problems | p. 353 |

Practice Problems | p. 357 |

Using SPSS | p. 364 |

Chapter Notes | p. 368 |

Factorial Analysis of Variance | p. 370 |

Basic Logic of Factorial Designs and Interaction Effects | p. 371 |

Recognizing and Interpreting Interaction Effects | p. 376 |

Basic Logic of the Two-Way Analysis of Variance | p. 386 |

Personality and Situational Influences on Behavior: An Interaction Effect | p. 387 |

Assumptions in the Factorial Analysis of Variance | p. 389 |

Extensions and Special Cases of the Analysis of Variance | p. 389 |

Controversy: Dichotomizing Numeric Variables | p. 391 |

Factorial Analysis of Variance in Research Articles | p. 393 |

Advanced Topic: Figuring a Two-Way Analysis of Variance | p. 395 |

Advanced Topic: Power and Effect Size in the Factorial Analysis of Variance | p. 406 |

Summary | p. 410 |

Key Terms | p. 411 |

Example Worked-Out Problems | p. 412 |

Practice Problems | p. 415 |

Using SPSS | p. 426 |

Chapter Notes | p. 431 |

Correlation | p. 432 |

Graphing Correlations: The Scatter Diagram | p. 434 |

Patterns of Correlation | p. 437 |

The Correlation Coefficient | p. 443 |

Galton: Gentleman Genius | p. 446 |

Significance of a Correlation Coefficient | p. 452 |

Correlation and Causality | p. 456 |

Issues in Interpreting the Correlation Coefficient | p. 458 |

Illusory Correlation: When You Know Perfectly Well That If It's Big, It's Fat-and You Are Perfectly Wrong | p. 460 |

Effect Size and Power for the Correlation Coefficient | p. 464 |

Controversy: What Is a Large Correlation? | p. 466 |

Correlation in Research Articles | p. 467 |

Summary | p. 469 |

Key Terms | p. 471 |

Example Worked-Out Problems | p. 471 |

Practice Problems | p. 474 |

Using SPSS | p. 482 |

Chapter Notes | p. 485 |

Prediction | p. 487 |

Predictor (X) and Criterion (Y) Variables | p. 488 |

The Linear Prediction Rule | p. 488 |

The Regression Line | p. 492 |

Finding the Best Linear Prediction Rule | p. 496 |

The Least Squared Error Principle | p. 498 |

Issues in Prediction | p. 503 |

Multiple Regression | p. 506 |

Limitations of Prediction | p. 508 |

Controversy: Unstandardized and Standardized Regression Coefficients; Comparing Predictors | p. 509 |

Clinical versus Statistical Prediction | p. 510 |

Prediction in Research Articles | p. 511 |

Advanced Topic: Error and Proportionate Reduction in Error | p. 514 |

Summary | p. 518 |

Key Terms | p. 519 |

Example Worked-Out Problems | p. 519 |

Practice Problems | p. 524 |

Using SPSS | p. 532 |

Chapter Notes | p. 535 |

Chi-Square Tests | p. 536 |

Karl Pearson, Inventor of Chi-Square and Center of Controversy | p. 537 |

The Chi-Square Statistic and the Chi-Square Test for Goodness of Fit | p. 538 |

The Chi-Square Test for Independence | p. 546 |

Assumptions for Chi-Square Tests | p. 554 |

Effect Size and Power for Chi-Square Tests for Independence | p. 554 |

Controversy: The Minimum Expected Frequency | p. 558 |

Chi-Square Tests in Research Articles | p. 559 |

Summary | p. 560 |

Key Terms | p. 561 |

Example Worked-Out Problems | p. 561 |

Practice Problems | p. 565 |

Using SPSS | p. 572 |

Chapter Notes | p. 576 |

Strategies When Population Distributions Are Not Normal: Data Transformations and Rank-Order Tests | p. 577 |

Assumptions in the Standard Hypothesis-Testing Procedures | p. 578 |

Data Transformations | p. 580 |

Rank-Order Tests | p. 585 |

Comparison of Methods | p. 589 |

Controversy: Computer-Intensive Methods | p. 591 |

Where Do Random Numbers Come From? | p. 594 |

Data Transformations and Rank-Order Tests in Research Articles | p. 595 |

Summary | p. 596 |

Key Terms | p. 597 |

Example Worked-Out Problems | p. 597 |

Practice Problems | p. 597 |

Using SPSS | p. 602 |

Chapter Notes | p. 609 |

The General Linear Model and Making Sense of Advanced Statistical Procedures in Research Articles | p. 611 |

The General Linear Model | p. 612 |

Two Women Make a Point About Gender and Statistics | p. 616 |

Partial Correlation | p. 617 |

Reliability | p. 618 |

Multilevel Modeling | p. 620 |

Factor Analysis | p. 622 |

Causal Modeling | p. 625 |

The Golden Age of Statistics: Four Guys Around London | p. 627 |

Procedures That Compare Groups | p. 634 |

Analysis of Covariance (ANCOVA) | p. 634 |

Multivariate Analysis of Variance (MANOVA) and Multivariate Analysis of Covariance (MANCOVA) | p. 635 |

Overview of Statistical Techniques | p. 636 |

Controversy: Should Statistics Be Controversial? | p. 637 |

The Forced Partnership of Fisher and Pearson | p. 638 |

How to Read Results Using Unfamiliar Statistical Techniques | p. 639 |

Summary | p. 641 |

Key Terms | p. 642 |

Practice Problems | p. 642 |

Using SPSS | p. 654 |

Chapter Notes | p. 662 |

Tables | p. 664 |

Answers to Set I Practice Problems | p. 673 |

Glossary | p. 701 |

Glossary of Symbols | p. 708 |

References | p. 710 |

Index | p. 719 |

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