Explaining psychological statistics: Barry H. Cohen
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Hoboken
Wiley
2013
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| Edition: | 4. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXIX, 817 S. graph. Darst. |
| ISBN: | 9781118436608 |
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| 245 | 1 | 0 | |a Explaining psychological statistics |b Barry H. Cohen |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Hoboken |b Wiley |c 2013 | |
| 300 | |a XXIX, 817 S. |b graph. Darst. | ||
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| _version_ | 1804150711975411712 |
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| adam_text | PREFACE TO THE FOURTH EDITION
ACKNOWLEDGMENTS
XXIII
XXIX
CONTENTS
PYVRT ONE
DESCRIPTIVE STATISTICS
INTRODUCTION TO PSYCHOLOGICAL STATISTICS
A.
B.
C.
CONCEPTUAL FOUNDATION
WHAT IS (ARE) STATISTICS?
STATISTICS AND RESEARCH
VARIABLES AND CONSTANTS
SCALES OF MEASUREMENT
PARAMETRIC VERSUS NONPARAMETRIC STATISTICS
LIKERT SCALES AND THE MEASUREMENT CONTROVERSY
CONTINUOUS VERSUS DISCRETE VARIABLES
SCALES VERSUS VARIABLES VERSUS UNDERLYING CONSTRUCTS
INDEPENDENT VERSUS DEPENDENT VARIABLES
EXPERIMENTAL VERSUS OBSERVATIONAL RESEARCH
POPULATIONS VERSUS SAMPLES
STATISTICAL FORMULAS
SUMMARY
EXERCISES
BASIC STATISTICAL PROCEDURES
VARIABLES WITH SUBSCRIPTS
THE SUMMATION SIGN
PROPERTIES OF THE SUMMATION SIGN
ROUNDING OFF NUMBERS
SUMMARY
EXERCISES
ANALYSIS BY SPSS
IHNO S DATA
VARIABLE VIEW
DATA CODING
MISSING VALUES
COMPUTING NEW VARIABLES
READING EXCEL FILES INTO SPSS
EXERCISES
1
1
1
1
2
2
3
6
7
8
8
9
10
11
12
12
13
14
M
15
1 6
18
19
20
21
21
22
23
23
2A
2A
25
FREQUENCY TABLES, GRAPHS, AND DISTRIBUTIONS
A. CONCEPTUAL FOUNDATION
FREQUENCY DISTRIBUTIONS
THE CUMULATIVE FREQUENCY DISTRIBUTION
THE RELATIVE FREQUENCY AND CUMULATIVE RELATIVE
FREQUENCY DISTRIBUTIONS
27
27
27
28
29
CONTENTS
THE CUMULATIVE PERCENTAGE DISTRIBUTION 29
PERCENTILES 30
GRAPHS 30
REAL VERSUS THEORETICAL DISTRIBUTIONS 34
SUMMARY 35
EXERCISES 37
B. BASIC STATISTICAL PROCEDURES 38
GROUPED FREQUENCY DISTRIBUTIONS 38
APPARENT VERSUS REAL LIMITS 39
CONSTRUCTING CLASS INTERVALS 39
CHOOSING THE CLASS INTERVAL WIDTH 39
CHOOSING THE LIMITS OF THE LOWEST INTERVAL 40
RELATIVE AND CUMULATIVE FREQUENCY DISTRIBUTIONS 41
CUMULATIVE PERCENTAGE DISTRIBUTION 41
ESTIMATING PERCENTILES AND PERCENTILE RANKS
BY LINEAR INTERPOLATION 42
GRAPHING A GROUPED FREQUENCY DISTRIBUTION 43
GUIDELINES FOR DRAWING GRAPHS OF FREQUENCY DISTRIBUTIONS 44
SUMMARY 46
EXERCISES 47
C. ANALYSIS BY SPSS 48
CREATING FREQUENCY DISTRIBUTIONS 48
PERCENTILE RANKS AND MISSING VALUES 50
GRAPHING YOUR DISTRIBUTION 50
OBTAINING PERCENTILES 52
THE SPLIT FILE FUNCTION 52
STEM-AND-LEAF PLOTS 53
EXERCISES 55
MEASURES OF CENTRAL TENDENCY AND VARIABILITY 57
A. CONCEPTUAL FOUNDATION 57
MEASURES OF CENTRAL TENDENCY 57
MEASURES OF VARIABILITY 61
SKEWED DISTRIBUTIONS 69
SUMMARY 73
EXERCISES 75
B. BASIC STATISTICAL PROCEDURES 76
FORMULAS FOR THE MEAN 76
COMPUTATIONAL FORMULAS FOR THE VARIANCE AND
STANDARD DEVIATION 77
OBTAINING THE STANDARD DEVIATION DIRECTLY FROM
YOUR CALCULATOR 80
PROPERTIES OF THE MEAN 81
PROPERTIES OF THE STANDARD DEVIATION 83
MEASURING SKEWNESS 84
MEASURING KURTOSIS 85
SUMMARY 87
EXERCISES 88
C. ANALYSIS BY SPSS 89
SUMMARY STATISTICS 89
USING EXPLORE TO OBTAIN ADDITIONAL STATISTICS 90
BOXPLOTS 91
SELECTING CASES 94
EXERCISES 96
KEY FORMULAS 96
CONTENTS
STANDARDIZED SCORES AND THE NORMAL DISTRIBUTION 99
A. CONCEPTUAL FOUNDATION 99
Z SCORES 99
FINDING A RAW SCORE FROM A Z SCORE 101
SETS OF Z SCORES 101
PROPERTIES OF Z SCORES 102
SAT, T, AND IQ SCORES 103
THE NORMAL DISTRIBUTION 104
INTRODUCING PROBABILITY: SMOOTH DISTRIBUTIONS VERSUS
DISCRETE EVENTS 106
REAL DISTRIBUTIONS VERSUS THE NORMAL DISTRIBUTION 107
Z SCORES AS A RESEARCH TOOL 108
SAMPLING DISTRIBUTION OF THE MEAN 109
STANDARD ERROR OF THE MEAN 110
SAMPLING DISTRIBUTION VERSUS POPULATION DISTRIBUTION 111
SUMMARY 112
EXERCISES 113
B. BASIC STATISTICAL PROCEDURES 115
FINDING PERCENTILE RANKS 115
FINDING THE AREA BETWEEN TWO Z SCORES 116
FINDING THE RAW SCORES CORRESPONDING TO A GIVEN AREA 118
AREAS IN THE MIDDLE OF A DISTRIBUTION 119
FROM SCORE TO PROPORTION AND PROPORTION TO SCORE 119
DESCRIBING GROUPS 120
PROBABILITY RULES 122
SUMMARY 125
ADVANCED MATERIAL: THE MATHEMATICS OF THE
NORMAL DISTRIBUTION 127
EXERCISES 128
C. ANALYSIS BY SPSS 130
CREATING Z SCORES 130
OBTAINING STANDARD ERRORS 130
OBTAINING AREAS OF THE NORMAL DISTRIBUTION 131
DATA TRANSFORMATIONS 131
EXERCISES 132
KEY FORMULAS 132
ONE- AND TWO-SAMPLE HYPOTHESIS TESTS 135
INTRODUCTION TO HYPOTHESIS TESTING: THE
ONE-SAMPLE Z TEST 135
A. CONCEPTUAL FOUNDATION 135
SELECTING A GROUP OF SUBJECTS 135
THE NEED FOR HYPOTHESIS TESTING 136
THE LOGIC OF NULL HYPOTHESIS TESTING 137
THE NULL HYPOTHESIS DISTRIBUTION 137
THE NULL HYPOTHESIS DISTRIBUTION FOR THE ONE-SAMPLE CASE 138
Z SCORES AND THE NULL HYPOTHESIS DISTRIBUTION 139
STATISTICAL DECISIONS 140
CONTENTS
THE Z SCORE AS TEST STATISTIC 141
TYPE I AND TYPE II ERRORS 142
THE TRADE-OFF BETWEEN TYPE I AND TYPE II ERRORS 143
ONE-TAILED VERSUS TWO-TAILED TESTS 144
SUMMARY 147
EXERCISES 147
B. BASIC STATISTICAL PROCEDURES 148
STEP 1: STATE THE HYPOTHESIS 149
STEP 2: SELECT THE STATISTICAL TEST AND THE SIGNIFICANCE LEVEL 150
STEP 3: SELECT THE SAMPLE AND COLLECT THE DATA 150
STEP 4: FIND THE REGION OF REJECTION 151
STEP 5: CALCULATE THE TEST STATISTIC 152
STEP 6: MAKE THE STATISTICAL DECISION 153
INTERPRETING THE RESULTS 154
ASSUMPTIONS UNDERLYING THE ONE-SAMPLE Z TEST 155
VARIETIES OF THE ONE-SAMPLE TEST 157
WHY THE ONE-SAMPLE TEST IS RARELY PERFORMED 158
PUBLISHING THE RESULTS OF ONE-SAMPLE TESTS 159
SUMMARY 160
EXERCISES 162
ADVANCED MATERIAL: CORRECTING NULL HYPOTHESIS
TESTING FALLACIES 163
ADVANCED EXERCISES 168
C. ANALYSIS BY SPSS 169
THE ONE-SAMPLE Z TEST 169
TESTING THE NORMALITY ASSUMPTION 170
EXERCISES 171
KEY FORMULAS 172
INTERVAL ESTIMATION AND THE T DISTRIBUTION 173
A. CONCEPTUAL FOUNDATION 173
THE MEAN OF THE NULL HYPOTHESIS DISTRIBUTION 174
WHEN THE POPULATION STANDARD DEVIATION IS NOT KNOWN 174
CALCULATING A SIMPLE EXAMPLE 175
THE T DISTRIBUTION 175
DEGREES OF FREEDOM AND THE T DISTRIBUTION 177
CRITICAL VALUES OF THE T DISTRIBUTION 178
CALCULATING THE ONE-SAMPLE T TEST 179
SAMPLE SIZE AND THE ONE-SAMPLE T TEST 179
USES FOR THE ONE-SAMPLE T TEST 180
CAUTIONS CONCERNING THE ONE-SAMPLE T TEST 180
ESTIMATING THE POPULATION MEAN 182
SUMMARY 183
EXERCISES 184
ADVANCED MATERIAL: A NOTE ABOUT ESTIMATORS 185
B. BASIC STATISTICAL PROCEDURES 185
STEP 1: SELECT THE SAMPLE SIZE 186
STEP 2: SELECT THE LEVEL OF CONFIDENCE 186
STEP 3: SELECT THE RANDOM SAMPLE AND COLLECT THE DATA 186
STEP 4: CALCULATE THE LIMITS OF THE INTERVAL 186
RELATIONSHIP BETWEEN INTERVAL ESTIMATION AND NULL
HYPOTHESIS TESTING 190
CONTENTS
ASSUMPTIONS UNDERLYING THE ONE-SAMPLE T TEST AND THE
CONFIDENCE INTERVAL FOR THE POPULATION MEAN 191
USE OF THE CONFIDENCE INTERVAL FOR THE POPULATION MEAN 193
PUBLISHING THE RESULTS OF ONE-SAMPLE T TESTS 194
SUMMARY 194
EXERCISES 195
C. ANALYSIS BY SPSS 196
PERFORMING A ONE-SAMPLE T TEST 196
CONFIDENCE INTERVALS FOR THE POPULATION MEAN 198
BOOTSTRAPPING 198
EXERCISES 200
KEY FORMULAS 200
THE T TEST FOR TWO INDEPENDENT SAMPLE MEANS 203
A. CONCEPTUAL FOUNDATION 203
NULL HYPOTHESIS DISTRIBUTION FOR THE DIFFERENCES
OF TWO SAMPLE MEANS 204
STANDARD ERROR OF THE DIFFERENCE 205
FORMULA FOR COMPARING THE MEANS OF TWO SAMPLES 206
NULL HYPOTHESIS FOR THE TWO-SAMPLE CASE 207
THE Z TEST FOR TWO LARGE SAMPLES 208
SEPARATE-VARIANCES T TEST 209
THE POOLED-VARIANCES ESTIMATE 209
THE POOLED-VARIANCES T TEST 210
FORMULA FOR EQUAL SAMPLE SIZES 211
CALCULATING THE TWO-SAMPLE T TEST 211
INTERPRETING THE CALCULATED T 212
LIMITATIONS OF STATISTICAL CONCLUSIONS 213
SUMMARY 213
EXERCISES 214
B. BASIC STATISTICAL PROCEDURES 215
STEP 1: STATE THE HYPOTHESES 215
STEP 2: SELECT THE STATISTICAL TEST AND THE SIGNIFICANCE LEVEL 216
STEP 3: SELECT THE SAMPLES AND COLLECT THE DATA 216
STEP 4: FIND THE REGION OF REJECTION 217
STEP 5: CALCULATE THE TEST STATISTIC 217
STEP 6: MAKE THE STATISTICAL DECISION 218
INTERPRETING THE RESULTS 218
CONFIDENCE INTERVALS FOR THE DIFFERENCE BETWEEN TWO
POPULATION MEANS 219
ASSUMPTIONS OF THE T TEST FOR TWO INDEPENDENT SAMPLES 221
HOV TESTS AND THE SEPARATE-VARIANCES T TEST 223
RANDOM ASSIGNMENT AND THE SEPARATE-VARIANCES T TEST 224
WHEN TO USE THE TWO-SAMPLE T TEST 225
WHEN TO CONSTRUCT CONFIDENCE INTERVALS 226
HETEROGENEITY OF VARIANCE AS AN EXPERIMENTAL RESULT 226
PUBLISHING THE RESULTS OF THE TWO-SAMPLE T TEST 226
SUMMARY 227
EXERCISES 228
ADVANCED MATERIAL: FINDING THE DEGREES OF FREEDOM
FOR THE SEPARATE-VARIANCES T TEST 230
ADVANCED EXERCISES 231
?DI CONTENTS
C. ANALYSIS BY SPSS 232
PERFORMING THE TWO-INDEPENDENT-SAMPLES T TEST 232
CONFIDENCE INTERVAL FOR THE DIFFERENCE OF TWO POPULATION MEANS 233
BOOTSTRAPPING 233
EXERCISES 233
KEY FORMULAS 234
STATISTICAL POWER AND EFFECT SIZE 237
A. CONCEPTUAL FOUNDATION 237
THE ALTERNATIVE HYPOTHESIS DISTRIBUTION 237
THE EXPECTED T VALUE (DELTA) 239
THE EFFECT SIZE 241
POWER ANALYSIS 242
THE INTERPRETATION OF T VALUES 243
ESTIMATING EFFECT SIZE 244
MANIPULATING POWER 246
SUMMARY 246
EXERCISES 247
B. BASIC STATISTICAL PROCEDURES 248
USING POWER TABLES 248
THE RELATIONSHIP BETWEEN ALPHA AND POWER 249
POWER ANALYSIS WITH FIXED SAMPLE SIZES 250
SAMPLE SIZE DETERMINATION 251
THE CASE OF UNEQUAL SAMPLE SIZES 252
THE POWER OF A ONE-SAMPLE TEST 253
CONSTRUCTING CONFIDENCE INTERVALS FOR EFFECT SIZES 254
CALCULATING POWER RETROSPECTIVELY 255
META-ANALYSIS 256
SUMMARY 257
EXERCISES 258
ADVANCED MATERIAL: WHEN IS NULL HYPOTHESIS TESTING USEFUL? 259
C. ANALYSIS BY SPSS 265
POWER CALCULATIONS IN SPSS 265
G*POWER 3 267
EXERCISES 268
KEY FORMULAS 269
PART
HYPOTHESIS TESTS INVOLVING TWO MEASURES
ON EACH SUBJECT 271
LINEAR CORRELATION 271
A. CONCEPTUAL FOUNDATION 271
PERFECT CORRELATION 271
NEGATIVE CORRELATION 272
THE CORRELATION COEFFICIENT 272
LINEAR TRANSFORMATIONS 274
CONTENTS ?CI!I
GRAPHING THE CORRELATION 274
DEALING WITH CURVILINEAR RELATIONSHIPS 275
PROBLEMS IN GENERALIZING FROM SAMPLE CORRELATIONS 277
CORRELATION DOES NOT IMPLY CAUSATION 279
TRUE EXPERIMENTS INVOLVING CORRELATION 280
SUMMARY 280
EXERCISES 281
B. BASIC STATISTICAL PROCEDURES 283
THE COVARIANCE 283
THE UNBIASED COVARIANCE 284
AN EXAMPLE OF CALCULATING PEARSON S R 284
WHICH FORMULA TO USE 285
TESTING PEARSON S R FOR SIGNIFICANCE 285
UNDERSTANDING THE DEGREES OF FREEDOM 287
ASSUMPTIONS ASSOCIATED WITH PEARSON S R 288
USES OF THE PEARSON CORRELATION COEFFICIENT 289
PUBLISHING THE RESULTS OF CORRELATIONAL STUDIES 290
THE POWER ASSOCIATED WITH CORRELATIONAL TESTS 291
SUMMARY 293
EXERCISES 294
C. ANALYSIS BY SPSS 296
CREATING SCATTERPLOTS 296
COMPUTING PEARSON S R 296
THE LISTWISE OPTION 298
USING THE SYNTAX WINDOW FOR MORE OPTIONS 298
USING THE KEYWORD WITH TO REDUCE THE SIZE
OF YOUR CORRELATION MATRIX 299
BOOTSTRAPPING 300
EXERCISES 301
KEY FORMULAS 302
LINEAR REGRESSION 303
A. CONCEPTUAL FOUNDATION 303
PERFECT PREDICTIONS 303
PREDICTING WITH Z SCORES 304
CALCULATING AN EXAMPLE 304
REGRESSION TOWARD THE MEAN 305
GRAPHING REGRESSION IN TERMS OF Z SCORES 305
THE RAW-SCORE REGRESSION FORMULA 306
THE SLOPE AND THE Y INTERCEPT 307
PREDICTIONS BASED ON RAW SCORES 308
INTERPRETING THE Y INTERCEPT 309
QUANTIFYING THE ERRORS AROUND THE REGRESSION LINE 309
THE VARIANCE OF THE ESTIMATE 310
EXPLAINED AND UNEXPLAINED VARIANCE 311
THE COEFFICIENT OF DETERMINATION 312
THE COEFFICIENT OF NONDETERMINATION 312
CALCULATING THE VARIANCE OF THE ESTIMATE 312
SUMMARY 313
EXERCISES 313
B. BASIC STATISTICAL PROCEDURES 314
LIFE INSURANCE RATES 314
REGRESSION IN TERMS OF SAMPLE STATISTICS 315
?CIV CONTENTS
FINDING THE REGRESSION EQUATION 315
MAKING PREDICTIONS 316
USING SAMPLE STATISTICS TO ESTIMATE THE VARIANCE
OF THE ESTIMATE 316
STANDARD ERROR OF THE ESTIMATE 317
TESTING THE REGRESSION SLOPE FOR SIGNIFICANCE 318
ASSUMPTIONS UNDERLYING LINEAR REGRESSION 319
REGRESSING X ON Y 319
ALTERNATIVE FORMULA FOR THE REGRESSION SLOPE 320
WHEN TO USE LINEAR REGRESSION 320
THE POINT-BISERIAL CORRELATION COEFFICIENT 322
CALCULATING R
PB
323
DERIVING R
PB
FROM A T VALUE 324
INTERPRETING R
PB
324
STRENGTH OF ASSOCIATION IN THE POPULATION (OMEGA SQUARED) 325
BISERIAL R 327
SUMMARY 327
EXERCISES 328
C. ANALYSIS BY SPSS 330
COMPUTING A LINEAR REGRESSION ANALYSIS 330
BOOTSTRAPPING 333
POINT-BISERIAL CORRELATIONS 333
EXERCISES 333
KEY FORMULAS 334
THE MATCHED T TEST 337
A. CONCEPTUAL FOUNDATION 337
BEFORE-AFTER DESIGN 337
THE DIRECT-DIFFERENCE METHOD 338
THE MATCHED T TEST AS A FUNCTION OF LINEAR CORRELATION 339
REDUCTION IN DEGREES OF FREEDOM 341
DRAWBACK OF THE BEFORE-AFTER DESIGN 341
OTHER REPEATED-MEASURES DESIGNS 341
MATCHED-PAIRS DESIGN 342
CORRELATED OR DEPENDENT SAMPLES 343
WHEN NOT TO USE THE MATCHED T TEST 343
SUMMARY 344
EXERCISES 345
B. BASIC STATISTICAL PROCEDURES 346
STEP 1: STATE THE HYPOTHESES 346
STEP 2: SELECT THE STATISTICAL TEST AND THE SIGNIFICANCE LEVEL 346
STEP 3: SELECT THE SAMPLES AND COLLECT THE DATA 346
STEP 4: FIND THE REGION OF REJECTION 347
STEP 5: CALCULATE THE TEST STATISTIC 347
STEP 6: MAKE THE STATISTICAL DECISION 348
USING THE CORRELATION FORMULA FOR THE MATCHED T TEST 348
THE CONFIDENCE INTERVAL FOR THE DIFFERENCE OF TWO
POPULATION MEANS 349
EFFECT SIZE FOR THE MATCHED T TEST 350
POWER OF THE MATCHED T TEST 352
ASSUMPTIONS OF THE MATCHED T TEST 353
THE VARIETIES OF DESIGNS CALLING FOR THE MATCHED T TEST
PUBLISHING THE RESULTS OF A MATCHED T TEST
SUMMARY
EXERCISES
ADVANCED MATERIAL: DISPLAYING THE RESULTS FROM
A MATCHED T TEST
C. ANALYSIS BY SPSS
PERFORMING A MATCHED-PAIRS T TEST
BOOTSTRAPPING
EXERCISES
KEY FORMULAS
CONTENTS
353
355
356
357
359
360
360
362
362
362
PY RT FOWL*
ANALYSIS OF VARIANCE WITHOUT REPEATED MEASURES 365
ONE-WAY INDEPENDENT
ANOVA 365
A. CONCEPTUAL FOUNDATION 365
TRANSFORMING THE T TEST INTO ANOVA 366
EXPANDING THE DENOMINATOR 367
EXPANDING THE NUMERATOR 368
THE F RATIO 368
THE F RATIO AS A RATIO OF TWO POPULATION VARIANCE ESTIMATES 368
DEGREES OF FREEDOM AND THE F DISTRIBUTION 369
THE SHAPE OF THE F DISTRIBUTION 370
ANOVA AS A ONE-TAILED TEST 371
USING TABLES OF F VALUES 371
AN EXAMPLE WITH THREE EQUAL-SIZED GROUPS 371
CALCULATING A SIMPLE ANOVA 372
INTERPRETING THE F RATIO 373
ADVANTAGES OF THE ONE-WAY ANOVA 375
SUMMARY 375
EXERCISES 376
B. BASIC STATISTICAL PROCEDURES 377
AN ANOVA EXAMPLE WITH UNEQUAL SAMPLE SIZES 377
STEP 1: STATE THE HYPOTHESES 377
STEP 2: SELECT THE STATISTICAL TEST AND THE SIGNIFICANCE LEVEL 378
STEP 3: SELECT THE SAMPLES AND COLLECT THE DATA 378
STEP 4: FIND THE REGION OF REJECTION 378
STEP 5: CALCULATE THE TEST STATISTIC 379
STEP 6: MAKE THE STATISTICAL DECISION 380
INTERPRETING SIGNIFICANT RESULTS 381
THE SUMS OF SQUARES APPROACH 381
THE PROPORTION OF VARIANCE ACCOUNTED FOR IN AN ANOVA 383
ASSUMPTIONS OF THE ONE-WAY ANOVA FOR INDEPENDENT GROUPS 385
TESTING HOMOGENEITY OF VARIANCE 386
THE BROWN-FORSYTHE AND WELCH TESTS 388
POWER AND EFFECT SIZE FOR ANOVA 388
VARIETIES OF THE ONE-WAY ANOVA 392
PUBLISHING THE RESULTS OF A ONE-WAY ANOVA 394
SUMMARY 396
EXERCISES 398
CONTENTS
C. ANALYSIS BY SPSS 401
PERFORMING A ONE-WAY ANOVA 401
REPORTING EFFECT SIZE FOR A ONE-WAY ANOVA 402
EXERCISES 403
KEY FORMULAS 403
MULTIPLE COMPARISONS 407
A. CONCEPTUAL FOUNDATION 407
THE NUMBER OF POSSIBLE T TESTS 407
EXPERIMENTWISE ALPHA 408
COMPLEX AND PLANNED COMPARISONS 409
FISHER S PROTECTED T TESTS 409
COMPLETE VERSUS PARTIAL NULL HYPOTHESES 411
TUKEY S HSD TEST 412
THE STUDENTIZED RANGE STATISTIC 412
ADVANTAGES AND DISADVANTAGES OF TUKEY S TEST 413
OTHER PROCEDURES FOR POST HOC PAIRWISE COMPARISONS 414
THE ADVANTAGE OF PLANNING AHEAD 416
BONFERRONI T, OR DUNN S TEST 416
SUMMARY 417
EXERCISES 418
B. BASIC STATISTICAL PROCEDURES 419
CALCULATING PROTECTED T TESTS 419
CALCULATING FISHER S LSD 420
CALCULATING TUKEY S HSD 421
THE HARMONIC MEAN REVISITED 422
INTERPRETING THE RESULTS OF POST HOC PAIRWISE COMPARISONS 422
CONFIDENCE INTERVALS FOR POST HOC PAIRWISE COMPARISONS 423
TUKEY S HSD VERSUS ANOVA 424
THE MODIFIED LSD (FISHER-HAYTER) TEST 424
WHICH PAIRWISE COMPARISON PROCEDURE SHOULD YOU USE? 425
COMPLEX COMPARISONS 425
SCHEFFE S TEST 429
ORTHOGONAL CONTRASTS 430
MODIFIED BONFERRONI TESTS 432
THE ANALYSIS OF TREND COMPONENTS 433
SUMMARY 440
EXERCISES 442
C. ANALYSIS BY SPSS 444
MULTIPLE COMPARISONS 444
CONTRASTS 446
EXERCISES 448
KEY FORMULAS 448
TWO-WAY
ANOVA 451
A. CONCEPTUAL FOUNDATION 451
CALCULATING A SIMPLE ONE-WAY ANOVA 451
ADDING A SECOND FACTOR 452
REGROUPING THE SUMS OF SQUARES 453
NEW TERMINOLOGY 453
CONTENTS
CALCULATING THE TWO-WAY ANOVA 454
CALCULATING MS
W
455
CALCULATING THE MAIN EFFECT OF THE DRUG TREATMENT FACTOR 455
CALCULATING THE MAIN EFFECT OF THE GENDER FACTOR 455
GRAPHING THE CELL MEANS 456
THE GENERAL LINEAR MODEL 457
CALCULATING THE VARIABILITY DUE TO INTERACTION 458
TYPES OF INTERACTIONS 459
SEPARATING INTERACTIONS FROM CELL MEANS 462
THE F RATIO IN A TWO-WAY ANOVA 463
ADVANTAGES OF THE TWO-WAY DESIGN 463
SUMMARY 465
EXERCISES 466
B. BASIC STATISTICAL PROCEDURES 467
STEP 1: STATE THE NULL HYPOTHESIS 467
STEP 2: SELECT THE STATISTICAL TEST AND THE SIGNIFICANCE LEVEL 467
STEP 3: SELECT THE SAMPLES AND COLLECT THE DATA 468
STEP 4: FIND THE REGIONS OF REJECTION 468
STEP 5: CALCULATE THE TEST STATISTICS 469
STEP 6: MAKE THE STATISTICAL DECISIONS 472
THE SUMMARY TABLE FOR A TWO-WAY ANOVA 472
INTERPRETING THE RESULTS 473
POST HOC COMPARISONS FOR THE SIGNIFICANT MAIN EFFECTS 474
EFFECT SIZES IN THE TWO-WAY ANOVA 475
POST HOC COMPARISONS FOR A SIGNIFICANT INTERACTION 477
INTERACTION OF TREND COMPONENTS 481
ASSUMPTIONS OF THE TWO-WAY ANOVA 481
ADVANTAGES OF THE TWO-WAY ANOVA WITH TWO
EXPERIMENTAL FACTORS 482
ADVANTAGES OF THE TWO-WAY ANOVA WITH ONE
GROUPING FACTOR 483
ADVANTAGES OF THE TWO-WAY ANOVA WITH TWO
GROUPING FACTORS 483
PUBLISHING THE RESULTS OF A TWO-WAY ANOVA 484
THE TWO-WAY ANOVA FOR UNBALANCED DESIGNS 485
SUMMARY 487
EXERCISES 489
C. ANALYSIS BY SPSS 493
PERFORMING A TWO-WAY ANOVA 493
OPTIONS FOR UNIVARIATE ANOVA 495
SIMPLE MAIN EFFECTS 496
EXERCISES 498
KEY FORMULAS 498
PART FL VC
ANALYSIS OF VARIANCE WITH REPEATED MEASURES 501
CKAPTEI* 15 .
REPEATED MEASURES
ANOVA 501
A. CONCEPTUAL FOUNDATION 501
CALCULATION OF AN INDEPENDENT-GROUPS ANOVA 501
THE ONE-WAY RM ANOVA AS A TWO-WAY INDEPENDENT ANOVA 502
CALCULATING THE SS COMPONENTS OF THE RM ANOVA 503
CONTENTS
COMPARING THE INDEPENDENT ANOVA WITH THE RM ANOVA 504
THE ADVANTAGE OF THE RM ANOVA 505
PICTURING THE SUBJECT BY TREATMENT INTERACTION 506
COMPARING THE RM ANOVA TO A MATCHED T TEST 506
DEALING WITH ORDER EFFECTS 508
DIFFERENTIAL CARRYOVER EFFECTS 509
THE RANDOMIZED-BLOCKS DESIGN 509
SUMMARY 510
EXERCISES 511
B. BASIC STATISTICAL PROCEDURES 512
STEP 1: STATE THE HYPOTHESES 513
STEP 2: SELECT THE STATISTICAL TEST AND THE SIGNIFICANCE LEVEL 513
STEP 3: SELECT THE SAMPLES AND COLLECT THE DATA 513
STEP 4: FIND THE REGION OF REJECTION 513
STEP 5: CALCULATE THE TEST STATISTIC 514
STEP 6: MAKE THE STATISTICAL DECISION 515
INTERPRETING THE RESULTS 515
THE RESIDUAL COMPONENT 516
THE EFFECT SIZE OF AN RM ANOVA 517
POWER OF THE RM ANOVA 519
ASSUMPTIONS OF THE RM ANOVA 520
DEALING WITH A LACK OF SPHERICITY 522
POST HOC COMPARISONS 523
VARIETIES OF REPEATED-MEASURES AND RANDOMIZED-BLOCKS
DESIGNS 524
COUNTERBALANCING 526
TREND ANALYSIS WITH REPEATED MEASURES 528
PUBLISHING THE RESULTS OF AN RM ANOVA 529
SUMMARY 531
EXERCISES 532
ADVANCED MATERIAL: USING MANOVA TO TEST
REPEATED MEASURES 535
C. ANALYSIS BY SPSS 536
PERFORMING A ONE-WAY RM ANOVA 536
PLOTS AND CONTRASTS 540
OPTIONS 540
EXERCISES 542
KEY FORMULAS 542
TWO-WAY MIXED-DESIGN
ANOVA 545
A. CONCEPTUAL FOUNDATION 545
THE ONE-WAY RM ANOVA REVISITED 546
CONVERTING THE ONE-WAY RM ANOVA TO A
MIXED-DESIGN ANOVA 547
TWO-WAY INTERACTION IN THE MIXED-DESIGN ANOVA 550
SUMMARIZING THE MIXED-DESIGN ANOVA 551
INTERPRETING THE RESULTS 552
THE VARIETIES OF MIXED DESIGNS 552
SUMMARY 554
EXERCISES 555
B. BASIC STATISTICAL PROCEDURES 555
STEP 1: STATE THE HYPOTHESES 556
STEP 2: SELECT THE STATISTICAL TEST AND THE SIGNIFICANCE LEVEL 556
CONTENTS
STEP 3: SELECT THE SAMPLES AND COLLECT THE DATA 556
STEP 4: FIND THE REGIONS OF REJECTION 557
STEP 5: CALCULATE THE TEST STATISTICS 558
STEP 6: MAKE THE STATISTICAL DECISIONS 561
INTERPRETING THE RESULTS 561
ALTERNATIVE BREAKDOWN OF THE SS COMPONENTS OF A
MIXED-DESIGN ANOVA 562
ESTIMATING EFFECT SIZES FOR A MIXED DESIGN 563
PUBLISHING THE RESULTS OF A MIXED ANOVA 563
ASSUMPTIONS OF THE MIXED-DESIGN ANOVA 564
A SPECIAL CASE: THE BEFORE-AFTER MIXED DESIGN 565
POST HOC COMPARISONS 566
AN EXCERPT FROM THE PSYCHOLOGICAL LITERATURE 569
INTERACTIONS INVOLVING TRENDS 570
REMOVING ERROR VARIANCE FROM COUNTERBALANCED
DESIGNS 571
SUMMARY 572
EXERCISES 574
C. ANALYSIS BY SPSS 578
PERFORMING A TWO-WAY MIXED-DESIGN ANOVA 578
PLOTS 579
POST HOC TESTS 580
OPTIONS: HOMOGENEITY TESTS 580
SIMPLE MAIN EFFECTS 5 81
EXERCISES 582
KEY FORMULAS 582
MULTIPLE REGRESSION AND ITS CONNECTION TO
ANOVA 585
MULTIPLE REGRESSION 585
A. CONCEPTUAL FOUNDATION 585
UNCORRELATED PREDICTORS 586
THE STANDARDIZED REGRESSION EQUATION 587
MORE THAN TWO MUTUALLY UNCORRELATED PREDICTORS 587
THE SIGN OF CORRELATIONS 588
TWO CORRELATED PREDICTORS 588
THE BETA WEIGHTS 589
COMPLETELY REDUNDANT PREDICTORS 591
PARTIAL REGRESSION SLOPES 591
DEGREES OF FREEDOM 593
SEMIPARTIAL CORRELATIONS 593
CALCULATING THE SEMIPARTIAL CORRELATION 594
SUPPRESSOR VARIABLES 595
COMPLEMENTARY VARIABLES 596
THE RAW-SCORE PREDICTION FORMULA 597
PARTIAL CORRELATION 598
FINDING THE BEST PREDICTION EQUATION 600
HIERARCHICAL (THEORY-BASED) REGRESSION 601
SUMMARY 602
EXERCISES 603
CONTENTS
B. BASIC STATISTICAL PROCEDURES 605
THE SIGNIFICANCE TEST FOR MULTIPLE R 605
TESTS FOR THE SIGNIFICANCE OF INDIVIDUAL PREDICTORS 606
METHODS FOR VARIABLE SELECTION 607
PROBLEMS ASSOCIATED WITH HAVING MANY PREDICTORS 611
TOO FEW PREDICTORS 615
MINIMAL SAMPLE SIZE 615
BASIC ASSUMPTIONS OF MULTIPLE REGRESSION 616
REGRESSION WITH DICHOTOMOUS PREDICTORS 618
MULTIPLE REGRESSION AS A RESEARCH TOOL: VARIABLE ORDERING 619
PUBLISHING THE RESULTS OF MULTIPLE REGRESSION 621
SUMMARY 622
EXERCISES 623
OPTIONAL EXERCISE 626
ADVANCED MATERIAL 626
C. ANALYSIS BY SPSS 632
PERFORMING A MULTIPLE REGRESSION ANALYSIS 632
STATISTICS, PLOTS, SAVE, AND OPTIONS 634
STEPWISE REGRESSION 635
HIERARCHICAL REGRESSION 636
EXERCISES 636
KEY FORMULAS 637
THE REGRESSION APPROACH TO
ANOVA 639
A. CONCEPTUAL FOUNDATION 639
DUMMY CODING 640
THE REGRESSION PLANE 640
EFFECT CODING 641
THE GENERAL LINEAR MODEL 642
EQUIVALENCE OF TESTING ANOVA AND R
2
642
TWO-WAY ANOVA AS REGRESSION 643
THE GLM FOR HIGHER-ORDER ANOVA 645
ANALYZING UNBALANCED DESIGNS 646
METHODS FOR CONTROLLING ERROR VARIANCE 649
SUMMARY 650
EXERCISES 652
B. BASIC STATISTICAL PROCEDURES 653
SIMPLE ANCOVA AS MULTIPLE REGRESSION 653
THE LINEAR REGRESSION APPROACH TO ANCOVA 656
POST HOC COMPARISONS 663
PERFORMING ANCOVA BY MULTIPLE REGRESSION 664
POWER AND EFFECT SIZE 665
THE ASSUMPTIONS OF ANCOVA 665
ADDITIONAL CONSIDERATIONS 666
FACTORIAL ANCOVA 667
USING TWO OR MORE COVARIATES 668
ALTERNATIVES TO ANCOVA 668
USING ANCOVA WITH INTACT GROUPS 670
SUMMARY 671
EXERCISES 673
C. ANALYSIS BY SPSS 675
DUMMY CODING 675
EFFECT CODING 677
CONTENTS
TWO-WAY ANOVA BY REGRESSION 677
ANALYSIS OF COVARIANCE 678
ANALYSIS OF COVARIANCE BY MULTIPLE REGRESSION 681
EXERCISES 682
KEY FORMULAS 682
NONPARAMETRIC STATISTICS 685
THE BINOMIAL DISTRIBUTION 685
A. CONCEPTUAL FOUNDATION 685
THE ORIGIN OF THE BINOMIAL DISTRIBUTION 686
THE BINOMIAL DISTRIBUTION WITH N = 4 687
THE BINOMIAL DISTRIBUTION WITH N = 12 688
WHEN THE BINOMIAL DISTRIBUTION IS NOT SYMMETRICAL 689
THE Z TEST FOR PROPORTIONS 691
THE CLASSICAL APPROACH TO PROBABILITY 692
THE RULES OF PROBABILITY APPLIED TO DISCRETE VARIABLES 693
THE EMPIRICAL APPROACH TO PROBABILITY 694
SUMMARY 695
EXERCISES 696
B. BASIC STATISTICAL PROCEDURES 697
STEP 1: STATE THE HYPOTHESES 697
STEP 2: SELECT THE STATISTICAL TEST AND THE SIGNIFICANCE LEVEL 697
STEP 3: SELECT THE SAMPLES AND COLLECT THE DATA 698
STEP 4: FIND THE REGION OF REJECTION 698
STEP 5: CALCULATE THE TEST STATISTIC 698
STEP 6: MAKE THE STATISTICAL DECISION 699
INTERPRETING THE RESULTS 699
ASSUMPTIONS OF THE SIGN TEST 699
THE GAMBLER S FALLACY 700
WHEN TO USE THE BINOMIAL DISTRIBUTION FOR NULL
HYPOTHESIS TESTING 700
SUMMARY 702
EXERCISES 703
ADVANCED MATERIAL: PERMUTATIONS AND COMBINATIONS 704
CONSTRUCTING THE BINOMIAL DISTRIBUTION 705
C. ANALYSIS BY SPSS 706
PERFORMING A BINOMIAL TEST 706
OPTIONS FOR THE BINOMIAL TEST 708
THE SIGN TEST 709
EXERCISES 710
KEY FORMULAS 711
CHI-SQUARE TESTS 713
A. CONCEPTUAL FOUNDATION 713
THE MULTINOMIAL DISTRIBUTION 713
THE CHI-SQUARE DISTRIBUTION 714
EXPECTED AND OBSERVED FREQUENCIES 714
CONTENTS
THE CHI-SQUARE STATISTIC 715
CRITICAL VALUES OF CHI-SQUARE 715
TAILS OF THE CHI-SQUARE DISTRIBUTION 716
EXPECTED FREQUENCIES BASED ON NO PREFERENCE 717
THE VARIETIES OF ONE-WAY CHI-SQUARE TESTS 718
SUMMARY 720
EXERCISES 720
B. BASIC STATISTICAL PROCEDURES 721
TWO-VARIABLE CONTINGENCY TABLES 721
PEARSON S CHI-SQUARE TEST OF ASSOCIATION 722
AN EXAMPLE OF HYPOTHESIS TESTING WITH CATEGORICAL DATA 722
THE SIMPLEST CASE: 2X2 TABLES 726
MEASURING STRENGTH OF ASSOCIATION 726
ASSUMPTIONS OF THE CHI-SQUARE TEST 729
SOME USES FOR THE CHI-SQUARE TEST FOR INDEPENDENCE 730
PUBLISHING THE RESULTS OF A CHI-SQUARE TEST 731
SUMMARY 732
EXERCISES 733
ADVANCED MATERIAL 735
C. ANALYSIS BY SPSS 737
PERFORMING A ONE-WAY CHI-SQUARE TEST 737
PERFORMING A TWO-WAY CHI-SQUARE TEST 739
EXERCISES 741
KEY FORMULAS 741
STATISTICAL TABLES 743
A. 1. AREAS UNDER THE STANDARD NORMAL DISTRIBUTION 743
A.2. CRITICAL VALUES OF THE T DISTRIBUTION 746
A. 3. POWER AS A FUNCTION OF 5 AND SIGNIFICANCE CRITERION (A) 747
A.4. 8 AS A FUNCTION OF SIGNIFICANCE CRITERION (A) AND POWER 748
A.5. CRITICAL VALUES OF PEARSON S R (DF = N - 2) 749
A.6. TABLE OF FISHER S TRANSFORMATION OF R TO Z 750
A.7. CRITICAL VALUES OF THE F DISTRIBUTION FOR A = .05 751
A.8. CRITICAL VALUES OF THE F DISTRIBUTION FOR A = .025 752
A.9. CRITICAL VALUES OF THE F DISTRIBUTION FOR A = .01 753
A. 10. POWER OF ANOVA (A = .05) 754
A. 11. CRITICAL VALUES OF THE STUDENTIZED RANGE
STATISTIC (Q) FOR A = .05 755
A.12. ORTHOGONAL POLYNOMIAL TREND COEFFICIENTS 756
A.13. PROBABILITIES OF THE BINOMIAL DISTRIBUTION FOR P = .5 757
A. 14. CRITICAL VALUES OF THE %
2
DISTRIBUTION 758
ANSWERS TO SELECTED EXERCISES
IN SECTIONS A AND B 759
DATA FROM IHNO S EXPERIMENT 777
REFERENCES 781
INDEX 787
|
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| author | Cohen, Barry H. 1949- |
| author_GND | (DE-588)173670857 |
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| bvnumber | BV041255039 |
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| discipline | Soziologie Psychologie |
| edition | 4. ed. |
| format | Book |
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| genre_facet | Einführung |
| id | DE-604.BV041255039 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:43:16Z |
| institution | BVB |
| isbn | 9781118436608 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026229000 |
| oclc_num | 869849873 |
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| owner_facet | DE-188 DE-473 DE-BY-UBG |
| physical | XXIX, 817 S. graph. Darst. |
| publishDate | 2013 |
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| publisher | Wiley |
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| spelling | Cohen, Barry H. 1949- Verfasser (DE-588)173670857 aut Explaining psychological statistics Barry H. Cohen 4. ed. Hoboken Wiley 2013 XXIX, 817 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistik (DE-588)4056995-0 gnd rswk-swf Psychologie (DE-588)4047704-6 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Statistik (DE-588)4056995-0 s Psychologie (DE-588)4047704-6 s DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026229000&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cohen, Barry H. 1949- Explaining psychological statistics Barry H. Cohen Statistik (DE-588)4056995-0 gnd Psychologie (DE-588)4047704-6 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4047704-6 (DE-588)4151278-9 |
| title | Explaining psychological statistics Barry H. Cohen |
| title_auth | Explaining psychological statistics Barry H. Cohen |
| title_exact_search | Explaining psychological statistics Barry H. Cohen |
| title_full | Explaining psychological statistics Barry H. Cohen |
| title_fullStr | Explaining psychological statistics Barry H. Cohen |
| title_full_unstemmed | Explaining psychological statistics Barry H. Cohen |
| title_short | Explaining psychological statistics |
| title_sort | explaining psychological statistics barry h cohen |
| title_sub | Barry H. Cohen |
| topic | Statistik (DE-588)4056995-0 gnd Psychologie (DE-588)4047704-6 gnd |
| topic_facet | Statistik Psychologie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026229000&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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