Basic Statistics for the Behavioral Sciences, 6th Edition

Front Cover......Page 1
Title Page......Page 6
Copyright......Page 7
Contents......Page 11
Preface......Page 25
What Do Researchers Do with Statistics?......Page 34
What If I’m Not Very Good at Statistics?......Page 35
All Right, So How Do I Learn Statistics?......Page 36
Basic Statistical Notation......Page 37
Transforming Scores......Page 39
Creating Graphs......Page 40
CHAPTER SUMMARY......Page 42
APPLICATION QUESTIONS......Page 43
THE LOGIC OF RESEARCH......Page 45
Samples and Populations......Page 46
Obtaining Data by Measuring Variables......Page 47
Understanding Relationships......Page 48
A QUICK REVIEW......Page 51
Descriptive Statistics......Page 53
Statistics versus Parameters......Page 54
Experiments......Page 55
Correlational Studies......Page 58
A Word about Causality......Page 59
The Four Types of Measurement Scales......Page 60
Continuous versus Discrete Scales......Page 61
A QUICK REVIEW......Page 62
PUTTING IT ALL TOGETHER......Page 63
CHAPTER SUMMARY......Page 64
REVIEW QUESTIONS......Page 65
APPLICATION QUESTIONS......Page 66
NEW STATISTICAL NOTATION......Page 69
Presenting Simple Frequency in a Table......Page 70
Graphing a Simple Frequency Distribution......Page 71
The Normal Distribution......Page 75
Other Common Frequency Polygons......Page 76
Labeling Frequency Distributions......Page 78
A QUICK REVIEW......Page 79
RELATIVE FREQUENCY AND THE NORMAL CURVE......Page 80
Presenting Relative Frequency in a Table or Graph......Page 81
Finding Relative Frequency Using the Normal Curve......Page 82
COMPUTING CUMULATIVE FREQUENCY AND PERCENTILE......Page 84
Computing Percentiles......Page 85
Finding Percentile Using the Area Under the Normal Curve......Page 86
A WORD ABOUT GROUPED FREQUENCY DISTRIBUTIONS......Page 87
CHAPTER SUMMARY......Page 88
REVIEW QUESTIONS......Page 89
APPLICATION QUESTIONS......Page 90
INTEGRATION QUESTIONS......Page 91
SUMMARY OF FORMULAS......Page 92
NEW STATISTICAL NOTATION......Page 93
WHAT IS CENTRAL TENDENCY?......Page 94
THE MODE......Page 95
THE MEDIAN......Page 96
THE MEAN......Page 98
Uses of the Mean......Page 99
Comparing the Mean, Median, and Mode......Page 100
DEVIATIONS AROUND THE MEAN......Page 102
Using the Mean to Predict Scores......Page 104
DESCRIBING THE POPULATION MEAN......Page 105
Summarizing an Experiment......Page 106
Graphing the Results of an Experiment......Page 108
A QUICK REVIEW......Page 110
Inferring the Relationship in the Population......Page 111
CHAPTER SUMMARY......Page 112
REVIEW QUESTIONS......Page 113
APPLICATION QUESTIONS......Page 114
INTEGRATION QUESTIONS......Page 115
SUMMARY OF FORMULAS......Page 116
NEW STATISTICAL NOTATION......Page 117
WHY IS IT IMPORTANT TO KNOW ABOUT MEASURES OF VARIABILITY?......Page 118
A QUICK REVIEW......Page 119
UNDERSTANDING THE VARIANCE AND STANDARD DEVIATION......Page 120
The Sample Variance......Page 121
The Sample Standard Deviation......Page 122
A QUICK REVIEW......Page 125
Computing the Sample Variance......Page 126
A QUICK REVIEW......Page 127
THE POPULATION VARIANCE AND THE POPULATION STANDARD DEVIATION......Page 128
Estimating the Population Variance and Population Standard Deviation......Page 129
Computing the Estimated Population Variance and Standard Deviation......Page 131
A QUICK REVIEW......Page 132
APPLYING THE VARIANCE AND STANDARD DEVIATION TO RESEARCH......Page 133
Variability and Strength of a Relationship......Page 134
Variability and Errors in Prediction......Page 135
STATISTICS IN PUBLISHED RESEARCH: REPORTING VARIABILITY......Page 136
CHAPTER SUMMARY......Page 137
REVIEW QUESTIONS......Page 138
APPLICATION QUESTIONS......Page 139
INTEGRATION QUESTIONS......Page 140
SUMMARY OF FORMULAS......Page 141
NEW STATISTICAL NOTATION......Page 142
UNDERSTANDING z-SCORES......Page 143
Computing z-Scores......Page 145
Computing a Raw Score When z Is Known......Page 146
A QUICK REVIEW......Page 147
INTERPRETING z-SCORES USING THE z-DISTRIBUTION......Page 148
USING z-SCORES TO COMPARE DIFFERENT VARIABLES......Page 149
USING z-SCORES TO DETERMINE THE RELATIVE FREQUENCY OF RAW SCORES......Page 150
The Standard Normal Curve......Page 151
Using the z-Table......Page 153
STATISTICS IN PUBLISHED RESEARCH: USING z-SCORES......Page 156
The Sampling Distribution of Means......Page 157
The Standard Error of the Mean......Page 159
Computing a z-Score for a Sample Mean......Page 160
Describing the Relative Frequency of Sample Means......Page 161
Summary of Describing a Sample Mean with a z-Score......Page 162
CHAPTER SUMMARY......Page 163
REVIEW QUESTIONS......Page 164
APPLICATION QUESTIONS......Page 165
INTEGRATION QUESTIONS......Page 166
SUMMARY OF FORMULAS......Page 167
NEW STATISTICAL NOTATION......Page 168
UNDERSTANDING CORRELATIONAL RESEARCH......Page 169
Drawing Conclusions from Correlational Research......Page 170
Plotting Correlational Data: The Scatterplot......Page 171
Linear Relationships......Page 172
Nonlinear Relationships......Page 174
STRENGTH OF THE RELATIONSHIP......Page 175
Perfect Association......Page 176
Intermediate Association......Page 177
Zero Association......Page 179
THE PEARSON CORRELATION COEFFICIENT......Page 180
A QUICK REVIEW......Page 183
THE SPEARMAN RANK-ORDER CORRELATION COEFFICIENT......Page 184
THE RESTRICTION OF RANGE PROBLEM......Page 186
STATISTICS IN PUBLISHED RESEARCH: CORRELATION COEFFICIENTS......Page 187
CHAPTER SUMMARY......Page 188
REVIEW QUESTIONS......Page 189
APPLICATION QUESTIONS......Page 190
SUMMARY OF FORMULAS......Page 192
NEW STATISTICAL NOTATION......Page 193
UNDERSTANDING LINEAR REGRESSION......Page 194
THE LINEAR REGRESSION EQUATION......Page 196
Computing the Slope......Page 197
Plotting the Regression Line......Page 199
Computing Predicted Y Scores......Page 200
DESCRIBING THE ERRORS IN PREDICTION......Page 201
Computing the Variance of the Y Scores around Y¿......Page 202
Computing the Standard Error of the Estimate......Page 203
Interpreting the Standard Error of the Estimate......Page 204
The Strength of a Relationship and Prediction Error......Page 206
COMPUTING THE PROPORTION OF VARIANCE ACCOUNTED FOR......Page 207
Using r to Compute the Proportion of Variance Accounted For......Page 209
Applying the Proportion of Variance Accounted For......Page 210
A QUICK REVIEW......Page 211
PUTTING IT ALL TOGETHER......Page 212
CHAPTER SUMMARY......Page 213
APPLICATION QUESTIONS......Page 214
INTEGRATION QUESTIONS......Page 216
SUMMARY OF FORMULAS......Page 217
NEW STATISTICAL NOTATION......Page 218
THE LOGIC OF PROBABILITY......Page 219
Factors Affecting the Probability of an Event......Page 221
OBTAINING PROBABILITY FROM THE STANDARD NORMAL CURVE......Page 222
Determining the Probability of Individual Scores......Page 223
Determining the Probability of Sample Means......Page 224
A QUICK REVIEW......Page 225
RANDOM SAMPLING AND SAMPLING ERROR......Page 226
DECIDING WHETHER A SAMPLE REPRESENTS A POPULATION......Page 227
A QUICK REVIEW......Page 229
Setting Up the Sampling Distribution......Page 230
Identifying the Critical Value......Page 231
Deciding if the Sample Represents the Population......Page 232
Other Ways to Set up the Sampling Distribution......Page 233
PUTTING IT ALL TOGETHER......Page 235
KEY TERMS......Page 236
APPLICATION QUESTIONS......Page 237
INTEGRATION QUESTIONS......Page 238
SUMMARY OF FORMULAS......Page 239
NEW STATISTICAL NOTATION......Page 240
THE ROLE OF INFERENTIAL STATISTICS IN RESEARCH......Page 241
Creating the Experimental Hypotheses......Page 242
Designing a One-Sample Experiment......Page 243
Creating the Statistical Hypotheses......Page 244
The Logic of Statistical Hypothesis Testing......Page 246
Setting Up the Sampling Distribution for a Two-Tailed Test......Page 248
Computing z......Page 249
Comparing the Obtained z to the Critical Value......Page 250
INTERPRETING SIGNIFICANT RESULTS......Page 251
INTERPRETING NONSIGNIFICANT RESULTS......Page 252
SUMMARY OF THE z-TEST......Page 253
The One-Tailed Test for Increasing Scores......Page 254
A QUICK REVIEW......Page 256
Type I Errors: Rejecting H0 When H0 Is True......Page 257
Type II Errors: Retaining H0 When H0 Is False......Page 259
Comparing Type I and Type II Errors......Page 260
Power......Page 261
PUTTING IT ALL TOGETHER......Page 262
CHAPTER SUMMARY......Page 263
APPLICATION QUESTIONS......Page 264
SUMMARY OF FORMULAS......Page 266
WHY IS IT IMPORTANT TO KNOW ABOUT t-TESTS?......Page 267
PERFORMING THE ONE-SAMPLE t-TEST......Page 268
Computing tobt......Page 269
A QUICK REVIEW......Page 270
The t-Distribution and Degrees of Freedom......Page 271
Interpreting the t-Test......Page 273
The One-Tailed t-Test......Page 274
A QUICK REVIEW......Page 275
ESTIMATING BY COMPUTING A CONFIDENCE INTERVAL......Page 276
Computing the Confidence Interval......Page 277
STATISTICS IN PUBLISHED RESEARCH: REPORTING THE t-TEST......Page 279
Testing the Pearson r......Page 280
Testing the Spearman rS......Page 285
MAXIMIZING THE POWER OF STATISTICAL TESTS......Page 286
CHAPTER SUMMARY......Page 288
REVIEW QUESTIONS......Page 289
APPLICATION QUESTIONS......Page 290
INTEGRATION QUESTIONS......Page 291
SUMMARY OF FORMULAS......Page 292
NEW STATISTICAL NOTATION......Page 293
UNDERSTANDING THE TWO-SAMPLE EXPERIMENT......Page 294
Statistical Hypotheses for the Independent-Samples t-Test......Page 295
The Sampling Distribution for the Independent-Samples t-Test......Page 296
Computing the Independent-Samples t-Test......Page 297
Interpreting the Independent-Samples t-Test......Page 300
Confidence Interval for the Difference between Two s......Page 301
Performing One-Tailed Tests with Independent Samples......Page 302
A QUICK REVIEW......Page 303
THE RELATED-SAMPLES t-TEST......Page 304
The Logic of Hypotheses Testing in the Related-Samples t-Test......Page 305
STATISTICAL HYPOTHESES FOR THE RELATED-SAMPLES t-TEST......Page 306
Computing the Related-Samples t-Test......Page 307
Interpreting the Related-Samples t-Test......Page 308
Performing One-Tailed Tests with Related Samples......Page 310
A QUICK REVIEW......Page 311
Graphing the Results of a Two-Sample Experiment......Page 312
Measuring Effect Size in the Two-Sample Experiment......Page 313
STATISTICS IN PUBLISHED RESEARCH: THE TWO-SAMPLE EXPERIMENT......Page 316
CHAPTER SUMMARY......Page 317
REVIEW QUESTIONS......Page 318
APPLICATION QUESTIONS......Page 319
INTEGRATION QUESTIONS......Page 321
SUMMARY OF FORMULAS......Page 322
NEW STATISTICAL NOTATION......Page 323
AN OVERVIEW OF ANOVA......Page 324
How ANOVA Controls the Experiment-Wise Error Rate......Page 325
The Order of Operations in ANOVA: The F Statistic and Post Hoc Comparisons......Page 326
UNDERSTANDING THE ANOVA......Page 327
The Mean Square between Groups......Page 328
Comparing the Mean Squares: The Logic of the F-Ratio......Page 329
The Theoretical Components of the F-ratio......Page 331
PERFORMING THE ANOVA......Page 332
Computing the Fobt......Page 333
Interpreting Fobt......Page 337
PERFORMING POST HOC COMPARISONS......Page 339
Tukey’s HSD Multiple Comparisons Test......Page 340
SUMMARY OF STEPS IN PERFORMING A ONE-WAY ANOVA......Page 342
The Confidence Interval for Each Population......Page 343
Describing Effect Size in the ANOVA......Page 344
Using the SPSS Appendix......Page 345
CHAPTER SUMMARY......Page 346
APPLICATION QUESTIONS......Page 347
INTEGRATION QUESTIONS......Page 349
SUMMARY OF FORMULAS......Page 350
NEW STATISTICAL NOTATION......Page 351
UNDERSTANDING THE TWO-WAY DESIGN......Page 352
OVERVIEW OF THE TWO-WAY, BETWEEN-SUBJECTS ANOVA......Page 353
The Main Effect of Factor A......Page 354
The Main Effect of Factor B......Page 356
Interaction Effects......Page 357
A QUICK REVIEW......Page 359
COMPUTING THE TWO-WAY ANOVA......Page 360
Computing the Sums and Means......Page 361
Computing the Sums of Squares......Page 362
Computing the Mean Squares......Page 365
Computing F......Page 367
Interpreting Each F......Page 368
Graphing and Post Hoc Comparisons with Main Effects......Page 369
Graphing the Interaction Effect......Page 371
Performing Post Hoc Comparisons on the Interaction Effect......Page 372
Interpreting the Overall Results of the Experiment......Page 374
Describing the Effect Size: Eta Squared......Page 375
SUMMARY OF THE STEPS IN PERFORMING A TWO-WAY ANOVA......Page 376
CHAPTER SUMMARY......Page 377
REVIEW QUESTIONS......Page 378
APPLICATION QUESTIONS......Page 379
INTEGRATION QUESTIONS......Page 381
SUMMARY OF FORMULAS......Page 382
WHY IS IT IMPORTANT TO KNOW ABOUT NONPARAMETRIC PROCEDURES?......Page 384
ONE-WAY CHI SQUARE......Page 385
Hypotheses and Assumptions of the One-Way Chi Square......Page 386
Computing the One-Way Chi Square......Page 387
Interpreting the One-Way Chi Square......Page 388
Testing Other Hypotheses with the One-Way Chi Square......Page 389
THE TWO-WAY CHI SQUARE......Page 390
Computing the Two-Way Chi Square......Page 392
A QUICK REVIEW......Page 393
Describing the Relationship in a Two-Way Chi Square......Page 394
STATISTICS IN PUBLISHED RESEARCH: REPORTING CHI SQUARE......Page 395
The Logic of Nonparametric Procedures for Ranked Data......Page 396
Choosing a Nonparametric Procedure......Page 397
Tests for Two Independent Samples: The Mann–Whitney U Test and the Rank Sums Test......Page 398
The Wilcoxon T Test for Two Related Samples......Page 401
The Kruskal–Wallis H Test......Page 402
The Friedman Test  2......Page 404
CHAPTER SUMMARY......Page 406
APPLICATION QUESTIONS......Page 407
INTEGRATION QUESTIONS......Page 410
SUMMARY OF FORMULAS......Page 411
A.1 CREATING GROUPED FREQUENCY DISTRIBUTIONS......Page 412
A.2 PERFORMING LINEAR INTERPOLATION......Page 414
A.3 THE ONE-WAY, WITHIN-SUBJECTS ANALYSIS OF VARIANCE......Page 417
B.1 ENTERING DATA......Page 425
B.2 FREQUENCY DISTRIBUTIONS AND PERCENTILE......Page 428
B.3 CENTRAL TENDENCY, VARIABILITY, AND z-SCORES......Page 430
B.4 CORRELATION COEFFICIENTS AND THE LINEAR REGRESSION EQUATION......Page 432
B.5 THE ONE-SAMPLE t-TEST AND SIGNIFICANCE TESTING OF CORRELATION COEFFICIENTS......Page 435
B.6 TWO-SAMPLE t-TESTS......Page 437
B.7 THE ONE-WAY, BETWEEN-SUBJECTS ANOVA......Page 440
B.8 THE TWO-WAY, BETWEEN-SUBJECTS ANOVA......Page 442
B.9 CHI SQUARE PROCEDURES......Page 444
B.10 NONPARAMETRIC TESTS FOR RANKED SCORES......Page 447
B.11 THE ONE-WAY, WITHIN-SUBJECTS ANOVA......Page 449
C: Statistical Tables......Page 451
TABLE 1 PROPORTIONS OF AREA UNDER THE STANDARD NORMAL CURVE: THE z-TABLES......Page 452
TABLE 2 CRITICAL VALUES OF t: THE t-TABLES......Page 456
TABLE 3 CRITICAL VALUES OF THE PEARSON CORRELATION COEFFICIENT: THE r-TABLES......Page 457
TABLE 4 CRITICAL VALUES OF THE SPEARMAN RANK-ORDER CORRELATION COEFFICIENT: THE rS-TABLES......Page 458
TABLE 5 CRITICAL VALUES OF F: THE F-TABLES......Page 459
TABLE 6 VALUES OF STUDENTIZED RANGE STATISTIC, qK......Page 462
TABLE 7 CRITICAL VALUES OF CHI SQUARE: THE X2-TABLES......Page 464
TABLE 8 CRITICAL VALUES OF THE MANN–WHITNEY U......Page 465
TABLE 9 CRITICAL VALUES OF THE WILCOXON T......Page 469
D: Answers to Odd-Numbered Questions......Page 471
GLOSSARY......Page 486
INDEX......Page 494