# Solution Manual for Introductory Statistics for the Behavioral Sciences 7th Edition by Joan Welkowitz

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#### Solution Manual for Introductory Statistics for the Behavioral Sciences 7th Edition by Joan Welkowitz

A comprehensive and user-friendly introduction to statistics for behavioral science students—revised and updated

Refined over seven editions by master teachers, this book gives instructors and students alike clear examples and carefully crafted exercises to support the teaching and learning of statistics for both manipulating and consuming data.

One of the most popular and respected statistics texts in the behavioral sciences, the Seventh Edition of Introductory Statistics for the Behavioral Sciences has been fully revised. The new edition presents all the topics students in the behavioral sciences need in a uniquely accessible and easy-to-understand format, aiding in the comprehension and implementation of the statistical analyses most commonly used in the behavioral sciences.

Preface xv
Acknowledgments xix
Glossary of Symbols xxi
Part I Descriptive Statistics 1
Chapter 1 Introduction 3
Why Study Statistics? 4
Descriptive and Inferential Statistics 5
Populations, Samples, Parameters, and Statistics 6
Measurement Scales 7
Independent and Dependent Variables 10
Summation Notation 12
Ihno’s Study 16
Summary 18
Exercises 19
Thought Questions 23
Computer Exercises 23
Bridge to SPSS 24
Chapter 2 Frequency Distributions and Graphs 26
The Purpose of Descriptive Statistics 27
Regular Frequency Distributions 28
Cumulative Frequency Distributions 30
Grouped Frequency Distributions 31
Real and Apparent Limits 33
Interpreting a Raw Score 34
Definition of Percentile Rank and Percentile 34
Computational Procedures 35
Deciles, Quartiles, and the Median 38
Graphic Representations 39
Shapes of Frequency Distributions 43
Summary 45
Exercises 47
Thought Questions 49
Computer Exercises 49
Bridge to SPSS 50
Chapter 3 Measures of Central Tendency and Variability 53
Introduction 54
The Mode 56
The Median 56
The Mean 58
The Concept of Variability 62
The Range 65
The Standard Deviation and Variance 66
Summary 73
Exercises 75
Thought Questions 76
Computer Exercises 77
Bridge to SPSS 78
Chapter 4 Standardized Scores and the Normal Distribution 81
Interpreting a Raw Score Revisited 82
Rules for Changing μ and σ 84
Standard Scores (z Scores) 85
T Scores, SAT Scores, and IQ Scores 88
The Normal Distribution 90
Table of the Standard Normal Distribution 93
Illustrative Examples 95
Summary 101
Exercises 103
Thought Questions 105
Computer Exercises 106
Bridge to SPSS 106
Part II Basic Inferential Statistics 109
Chapter 5 Introduction to Statistical Inference 111
Introduction 113
The Goals of Inferential Statistics 114
Sampling Distributions 114
The Standard Error of the Mean 119
The z Score for Sample Means 122
Null Hypothesis Testing 124
Assumptions Required by the Statistical Test for the Mean of a Single Population 132
Summary 133
Exercises 135
Thought Questions 137
Computer Exercises 138
Bridge to SPSS 138
Appendix: The Null Hypothesis Testing Controversy 139
Chapter 6 The One-Sample t Test and Interval Estimation 142
Introduction 143
The Statistical Test for the Mean of a Single Population When σ Is Not Known: The t Distributions 144
Interval Estimation 148
The Standard Error of a Proportion 152
Summary 155
Exercises 156
Thought Questions 157
Computer Exercises 158
Bridge to SPSS 158
Chapter 7 Testing Hypotheses About the Difference Between the Means of Two Populations 160
The Standard Error of the Difference 162
Estimating the Standard Error of the Difference 166
The t Test for Two Sample Means 167
Confidence Intervals for μ1 − μ2 172
The Assumptions Underlying the Proper Use of the t Test for Two Sample Means 175
Measuring the Size of an Effect 176
The t Test for Matched Samples 178
Summary 185
Exercises 187
Thought Questions 190
Computer Exercises 191
Bridge to SPSS 191
Chapter 8 Nonparametric Tests for the Difference Between Two Means 194
Introduction 195
The Difference Between the Locations of Two Independent Samples: The Rank-Sum Test 199
The Difference Between the Locations of Two Matched Samples: The Wilcoxon Test 205
Summary 210
Exercises 212
Thought Questions 215
Computer Exercises 216
Bridge to SPSS 216
Chapter 9 Linear Correlation 218
Introduction 219
Describing the Linear Relationship Between Two Variables 222
Interpreting the Magnitude of a Pearson r 229
When Is It Important That Pearson’s r Be Large? 234
Testing the Significance of the Correlation Coefficient 236
The Relationship Between Two Ranked Variables: The Spearman Rank-Order Correlation Coefficient 239
Summary 242
Exercises 244
Thought Questions 247
Computer Exercises 248
Bridge to SPSS 248
Appendix: Equivalence of the Various Formulas for r 251
Chapter 10 Prediction and Linear Regression 253
Introduction 254
Using Linear Regression to Make Predictions 254
Measuring Prediction Error: The Standard Error of Estimate 263
The Connection Between Correlation and the t Test 265
Estimating the Proportion of Variance Accounted for in the Population 271
Summary 273
Exercises 275
Thought Questions 277
Computer Exercises 277
Bridge to SPSS 278
Chapter 11 Introduction to Power Analysis 281
Introduction 282
Concepts of Power Analysis 283
The Significance Test of the Mean of a Single Population 285
The Significance Test of the Proportion of a Single Population 290
The Significance Test of a Pearson r 292
Testing the Difference Between Independent Means 293
Testing the Difference Between the Means of Two Matched Populations 297
Choosing a Value for d for a Power Analysis Involving Independent Means 299
Using Power Analysis Concepts to Interpret the Results of Null Hypothesis Tests 301
Summary 304
Exercises 306
Thought Questions 308
Computer Exercises 309
Bridge to SPSS 310
Part III Analysis of Variance Methods 313
Chapter 12 One-Way Analysis of Variance 315
Introduction 317
The General Logic of ANOVA 318
Computational Procedures 321
Testing the F Ratio for Statistical Significance 326
Calculating the One-Way ANOVA From Means and Standard Deviations 328
Comparing the One-Way ANOVA With the t Test 329
A Simplified ANOVA Formula for Equal Sample Sizes 330
Effect Size for the One-Way ANOVA 331
Some Comments on the Use of ANOVA 333
A Nonparametric Alternative to the One-Way ANOVA: The Kruskal-Wallis H Test 336
Summary 339
Exercises 343
Thought Questions 346
Computer Exercises 346
Bridge to SPSS 346
Appendix: Proof That the Total Sum of Squares Is Equal to the Sum of the Between-Group and the Within-Group Sum of Squares 348
Chapter 13 Multiple Comparisons 349
Introduction 350
Fisher’s Protected t Tests and the Least Significant Difference (LSD) 351
Tukey’s Honestly Significant Difference (HSD) 355
Other Multiple Comparison Procedures 360
Planned and Complex Comparisons 362
Nonparametric Multiple Comparisons: The Protected Rank-Sum Test 365
Summary 366
Exercises 368
Thought Questions 369
Computer Exercises 370
Bridge to SPSS 370
Chapter 14 Introduction to Factorial Design: Two-Way Analysis of Variance 372
Introduction 373
Computational Procedures 374
The Meaning of Interaction 384
Following Up a Significant Interaction 387
Measuring Effect Size in a Factorial ANOVA 390
Summary 392
Exercises 395
Thought Questions 398
Computer Exercises 399
Bridge to SPSS 399
Chapter 15 Repeated-Measures ANOVA 402
Introduction 403
Calculating the One-Way RM ANOVA 403
Rationale for the RM ANOVA Error Term 408
Assumptions and Other Considerations Involving the RM ANOVA 408
The RM Versus RB Design: An Introduction to the Issues of Experimental Design 411
The Two-Way Mixed Design 415
Summary 423
Exercises 428
Thought Questions 430
Computer Exercises 430
Bridge to SPSS 431
Part IV Nonparametric Statistics for Categorical Data 435
Chapter 16 Probability of Discrete Events and the Binomial Distribution 437
Introduction 438
Probability 439
The Binomial Distribution 442
The Sign Test for Matched Samples 448
Summary 450
Exercises 451
Thought Questions 453
Computer Exercises 453
Bridge to SPSS 454
Chapter 17 Chi-Square Tests 457
Chi Square and the Goodness of Fit: One-Variable Problems 458
Chi Square as a Test of Independence: Two-Variable Problems 464
Measures of Strength of Association in Two-Variable Tables 470
Summary 472
Exercises 474
Thought Questions 476
Computer Exercises 477
Bridge to SPSS 478
Appendix 481
Statistical Tables 483