Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

More documents

Recommendations

Info

182 CHAPTER 6 | ProbabilityFIGURE 6.18The relationship between the binomial distributionand the normal distribution. The binomialdistribution is a discrete histogram and the normaldistribution is a continuous, smooth curve.Each X value is represented by a bar in the histogramor a section of the normal distribution.0 1 2 3 4 5 6 7 8 9 10XTo gain maximum accuracy when using the normal approximation, you must rememberthat each X value in the binomial distribution actually corresponds to a bar in the histogram.In the histogram in Figure 6.18, for example, the score X = 6 is represented by a bar thatis bounded by real limits of 5.5 and 6.5. The actual probability of X = 6 is determined bythe area contained in this bar. To approximate this probability using the normal distribution,you should find the area that is contained between the two real limits. Similarly, ifyou are using the normal approximation to find the probability of obtaining a score greaterthan X = 6, you should use the area beyond the real limit boundary of 6.5. The followingexample demonstrates how the normal approximation to the binomial distribution is usedto compute probability values.EXAMPLE 6.13Suppose that you plan to test for ESP (extra-sensory perception) by asking people to predictthe suit of a card that is randomly selected from a complete deck. Before you beginyour test, however, you need to know what kind of performance is expected from peoplewho do not have ESP and are simply guessing. For these people, there are two possible outcomes,correct or incorrect, on each trial. Because there are four different suits, the probabilityof a correct prediction (assuming that there is no ESP) is p = 1 4 and the probabilityof an incorrect prediction is q = 3 4 . With a series of n = 48 trials, this situation meets thecriteria for the normal approximation to the binomial distribution:pn = 1 4 (48) = 12 qn = 3 (48) = 36 Both are greater than 10.4Caution: If the questionhad asked for the probabilityof 15 or morecorrect predictions, wewould find the areabeyond X 5 14.5. Readthe question carefully.Thus, the distribution of correct predictions will form a normal shaped distribution witha mean of m = pn = 12 and a standard deviation of s5Ïnpq = Ï9 5 3. We can use thisdistribution to determine probabilities for different levels of performance. For example, wecan calculate the probability that a person without ESP would guess correctly more than 15times in a series of 48 trials.Figure 6.19 shows the binomial distribution that we are considering. Because we wantthe probability of obtaining more than 15 correct predictions, we must find the shaded areain the tail of the distribution beyond X = 15.5. (Remember that a score of 15 correspondsto an interval from 14.5–15.5. We want scores beyond this interval.) The first step is to findthe z-score corresponding to X = 15.5.z 5 X 2ms515.5 2 1235 1.17Next, look up the probability in the unit normal table. In this case, we want the proportionin the tail beyond z = 1.17. The value from the table is p = 0.1210. This is the answerwe want. The probability of correctly predicting the suit of a card more than 15 times in aseries of 48 trials is only p = 0.1210 or 12.10%. Thus, it is very unlikely for an individualwithout ESP to guess correctly more than 15 out of 48 trials.■
SECTION 6.4 | Probability and the Binomial Distribution 183FIGURE 6.19The normal approximation of thebinomial distribution discussed inExample 6.13.X 515(14.5215.5)s 5 3m 5 12015.51.17XzLEARNING CHECK1. What is the standard deviation for a binomial distribution with p = q = 1 2 andn = 36?a. 3b. 9c. 12d. 182. For a binomial distribution with p = 1 4 , what is the probability that A will occurmore than 18 times in a series of 48 trials?a. 0.2514b. 0.0336c. 0.0228d. 0.01503. If you are simply guessing on a true/false test with 36 questions, what is theprobability that you will get 20 or more correct?a. 0.1587b. 0.2033c. 0.2514d. 0.3085ANSWERS1. A, 2. D, 3. D
Page 2 and 3:
EDITION10Statistics for theBehavior
Page 4 and 5:
Statistics for the Behavioral Scien
Page 7 and 8:
CONTENTSCHAPTER 1 Introduction to S
Page 9 and 10:
CONTENTSvii5.4 Using z-Scores to St
Page 11 and 12:
CONTENTSixCHAPTER 10 The t Test for
Page 13 and 14:
CONTENTSxiCHAPTER 15 Correlation 48
Page 15 and 16:
PREFACEMany students in the behavio
Page 17 and 18:
PREFACExv3. The former Chapter 19,
Page 19 and 20:
PREFACExviiTo the StudentA primary
Page 21:
ABOUT THE AUTHORSFREDERICK J GRAVET
Page 24 and 25:
PREVIEWBefore we begin our discussi
Page 26 and 27:
4 CHAPTER 1 | Introduction to Stati
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
10 CHAPTER 1 | Introduction to Stat
Page 34 and 35:
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
Page 46 and 47:
Page 48 and 49:
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
PREVIEWThere is some evidence that
Page 58 and 59:
36 CHAPTER 2 | Frequency Distributi
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
Page 89 and 90:
Central TendencyCHAPTER3Tools You W
Page 91 and 92:
SECTION 3.1 | Overview 69DEFINITION
Page 93 and 94:
SECTION 3.2 | The Mean 71research r
Page 95 and 96:
SECTION 3.2 | The Mean 73the distri
Page 97 and 98:
SECTION 3.2 | The Mean 75TABLE 3.1S
Page 99 and 100:
SECTION 3.2 | The Mean 77Table 3.2
Page 101 and 102:
SECTION 3.3 | The Median 793.3 The
Page 103 and 104:
SECTION 3.3 | The Median 81To find
Page 105 and 106:
SECTION 3.4 | The Mode 832. What is
Page 107 and 108:
SECTION 3.4 | The Mode 85FIGURE 3.7
Page 109 and 110:
SECTION 3.5 | Selecting a Measure o
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
SECTION 3.6 | Central Tendency and
Page 117 and 118:
FOCUS ON PROBLEM SOLVING 95of centr
Page 119 and 120:
PROBLEMS 976. A population of N = 1
Page 121 and 122:
VariabilityCHAPTER4Tools You Will N
Page 123 and 124:
SECTION 4.1 | Introduction to Varia
Page 125 and 126:
SECTION 4.2 | Defining Standard Dev
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
SECTION 4.3 | Measuring Variance an
Page 133 and 134:
SECTION 4.4 | Measuring Standard De
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
SECTION 4.5 | Sample Variance as an
Page 141 and 142:
SECTION 4.6 | More about Variance a
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
SUMMARY 1252. A population has a me
Page 149 and 150:
FOCUS ON PROBLEM SOLVING 127VAR0000
Page 151 and 152:
PROBLEMS 1299. For the following se
Page 153 and 154: z-Scores: Location of Scoresand Sta
Page 155 and 156: SECTION 5.1 | Introduction to z-Sco
Page 157 and 158: SECTION 5.2 | z-Scores and Location
Page 159 and 160: SECTION 5.2 | z-Scores and Location
Page 161 and 162: SECTION 5.3 | Other Relationships B
Page 163 and 164: SECTION 5.4 | Using z-Scores to Sta
Page 165 and 166: SECTION 5.4 | Using z-Scores to Sta
Page 167 and 168: SECTION 5.5 | Other Standardized Di
Page 169 and 170: SECTION 5.5 | Other Standardized Di
Page 171 and 172: SECTION 5.6 | Computing z-Scores fo
Page 173 and 174: SECTION 5.7 | Looking Ahead to Infe
Page 175 and 176: SUMMARY 153LEARNING CHECK1. In N =
Page 177 and 178: DEMONSTRATION 5.2 155sure that your
Page 179: PROBLEMS 15716. A distribution of e
Page 182 and 183: PREVIEWHow likely is it that you wi
Page 184 and 185: 162 CHAPTER 6 | Probabilitythe prob
Page 186 and 187: 164 CHAPTER 6 | Probability(Note: W
Page 188 and 189: 166 CHAPTER 6 | ProbabilityFIGURE 6
Page 190 and 191: 168 CHAPTER 6 | Probability■ The
Page 192 and 193: 170 CHAPTER 6 | ProbabilityFinding
Page 194 and 195: 172 CHAPTER 6 | Probabilityand exac
Page 196 and 197: 174 CHAPTER 6 | ProbabilityFinally,
Page 198 and 199: 176 CHAPTER 6 | ProbabilityXz-score
Page 200 and 201: 178 CHAPTER 6 | ProbabilityBOX 6.1
Page 202 and 203: 180 CHAPTER 6 | ProbabilityEXAMPLE
Page 206 and 207: 184 CHAPTER 6 | Probability6.5 Look
Page 208 and 209: 186 CHAPTER 6 | Probability2. For a
Page 210 and 211: 188 CHAPTER 6 | ProbabilityDEMONSTR
Page 212 and 213: 190 CHAPTER 6 | Probability6. Draw
Page 215 and 216: Probability and Samples: TheDistrib
Page 217 and 218: SECTION 7.1 | Samples, Populations,
Page 219 and 220: SECTION 7.1 | Samples, Populations,
Page 221 and 222: SECTION 7.2 | The Distribution of S
Page 229 and 230: SECTION 7.3 | Probability and the D
Page 231 and 232: SECTION 7.3 | Probability and the D
Page 233 and 234: SECTION 7.4 | More about Standard E
Page 235 and 236: SECTION 7.4 | More about Standard E
Page 241 and 242: FOCUS ON PROBLEM SOLVING 219SUMMARY
Page 243 and 244: PROBLEMS 221STEP 2Compute the z-sco
Page 245 and 246: Introduction toHypothesis TestingCH
Page 247 and 248: SECTION 8.1 | The Logic of Hypothes
Page 255 and 256:
SECTION 8.1 | The Logic of Hypothes
Page 257 and 258:
SECTION 8.1 | The Logic of Hypothes
Page 259 and 260:
SECTION 8.2 | Uncertainty and Error
Page 261 and 262:
SECTION 8.2 | Uncertainty and Error
Page 263 and 264:
SECTION 8.3 | More about Hypothesis
Page 265 and 266:
SECTION 8.3 | More about Hypothesis
Page 267 and 268:
SECTION 8.4 | Directional (One-Tail
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
SECTION 8.5 | Concerns about Hypoth
Page 275 and 276:
SECTION 8.5 | Concerns about Hypoth
Page 277 and 278:
SECTION 8.6 | Statistical Power 255
Page 279 and 280:
Page 281 and 282:
Page 283 and 284:
FOCUS ON PROBLEM SOLVING 2618. The
Page 285 and 286:
PROBLEMS 263In this distribution, o
Page 287 and 288:
PROBLEMS 26513. A random sample is
Page 289 and 290:
Introduction to the t StatisticCHAP
Page 291 and 292:
SECTION 9.1 | The t Statistic: An A
Page 293 and 294:
Page 295 and 296:
Page 297 and 298:
SECTION 9.2 | Hypothesis Tests with
Page 299 and 300:
SECTION 9.2 | Hypothesis Tests with
Page 301 and 302:
SECTION 9.3 | Measuring Effect Size
Page 303 and 304:
Page 305 and 306:
Page 307 and 308:
Page 309 and 310:
Page 311 and 312:
SECTION 9.4 | Directional Hypothese
Page 313 and 314:
SUMMARY 2913. A researcher rejects
Page 315 and 316:
DEMONSTRATION 9.1 293One-Sample Sta
Page 317 and 318:
PROBLEMS 295PROBLEMS1. Under what c
Page 319 and 320:
PROBLEMS 297b. Construct the 90% co
Page 321 and 322:
The t Test for TwoIndependent Sampl
Page 323 and 324:
SECTION 10.1 | Introduction to the
Page 325 and 326:
SECTION 10.2 | The Null Hypothesis
Page 327 and 328:
Page 329 and 330:
Page 331 and 332:
Page 333 and 334:
SECTION 10.3 | Hypothesis Tests wit
Page 335 and 336:
Page 337 and 338:
Page 339 and 340:
SECTION 10.4 | Effect Size and Conf
Page 341 and 342:
Page 343 and 344:
Page 345 and 346:
SECTION 10.5 | The Role of Sample V
Page 347 and 348:
KEY TERMS 325SUMMARY1. The independ
Page 349 and 350:
FOCUS ON PROBLEM SOLVING 327Group S
Page 351 and 352:
PROBLEMS 329The t Statistic Finally
Page 353 and 354:
PROBLEMS 331c. Write a sentence dem
Page 355:
PROBLEMS 33319. If other factors ar
Page 358 and 359:
PREVIEWIt’s the night before an e
Page 360 and 361:
338 CHAPTER 11 | The t Test for Two
Page 362 and 363:
Page 364 and 365:
Page 366 and 367:
Page 368 and 369:
Page 370 and 371:
Page 372 and 373:
Page 374 and 375:
Page 376 and 377:
Page 378 and 379:
Page 380 and 381:
Page 382 and 383:
Page 384 and 385:
Page 386 and 387:
Page 388 and 389:
PREVIEWYour job interview is tomorr
Page 390 and 391:
368 CHAPTER 12 | Introduction to An
Page 392 and 393:
Page 394 and 395:
Page 396 and 397:
Page 398 and 399:
Page 400 and 401:
Page 402 and 403:
Page 404 and 405:
Page 406 and 407:
Page 408 and 409:
Page 410 and 411:
Page 412 and 413:
Page 414 and 415:
Page 416 and 417:
Page 418 and 419:
Page 420 and 421:
Page 422 and 423:
Page 424 and 425:
Page 426 and 427:
Page 428 and 429:
Page 430 and 431:
Page 432 and 433:
Page 435 and 436:
Repeated-MeasuresAnalysis of Varian
Page 437 and 438:
SECTION 13.1 | Overview of the Repe
Page 439 and 440:
Page 441 and 442:
Page 443 and 444:
SECTION 13.2 | Hypothesis Testing a
Page 445 and 446:
Page 447 and 448:
Page 449 and 450:
Page 451 and 452:
SECTION 13.3 | More about the Repea
Page 453 and 454:
Page 455 and 456:
Page 457 and 458:
Page 459 and 460:
SPSS ® 4375. When the obtained F-r
Page 461 and 462:
DEMONSTRATION 13.1 439you must also
Page 463 and 464:
PROBLEMS 441PROBLEMS1. How does the
Page 465 and 466:
PROBLEMS 44313. The following summa
Page 467 and 468:
PROBLEMS 44523. The following data
Page 469 and 470:
Two-FactorAnalysis of Variance(Inde
Page 471 and 472:
SECTION 14.1 | An Overview of the T
Page 473 and 474:
Page 475 and 476:
Page 477 and 478:
Page 479 and 480:
Page 481 and 482:
SECTION 14.2 | An Example of the Tw
Page 483 and 484:
Page 485 and 486:
Page 487 and 488:
Page 489 and 490:
SECTION 14.3 | More about the Two-F
Page 491 and 492:
Page 493 and 494:
Page 495 and 496:
SUMMARY 473SUMMARY1. A research stu
Page 497 and 498:
FOCUS ON PROBLEM SOLVING 475Descrip
Page 499 and 500:
DEMONSTRATION 14.1 477STEP 2STAGE 1
Page 501 and 502:
PROBLEMS 479PROBLEMS1. Define each
Page 503 and 504:
PROBLEMS 48115. Research results in
Page 505:
PROBLEMS 483EasyFactorA TaskDifficu
Page 508 and 509:
PREVIEWA recent report describing t
Page 510 and 511:
488 CHAPTER 15 | CorrelationDEFINIT
Page 512 and 513:
490 CHAPTER 15 | CorrelationDEFINIT
Page 514 and 515:
492 CHAPTER 15 | CorrelationSubstit
Page 516 and 517:
494 CHAPTER 15 | Correlationeither
Page 518 and 519:
496 CHAPTER 15 | Correlationreliabl
Page 520 and 521:
498 CHAPTER 15 | Correlation60Numbe
Page 522 and 523:
500 CHAPTER 15 | CorrelationOne of
Page 524 and 525:
502 CHAPTER 15 | CorrelationBOX 15.
Page 526 and 527:
504 CHAPTER 15 | Correlation171615Z
Page 528 and 529:
506 CHAPTER 15 | Correlation3. What
Page 530 and 531:
508 CHAPTER 15 | Correlationon the
Page 532 and 533:
510 CHAPTER 15 | CorrelationLEARNIN
Page 534 and 535:
512 CHAPTER 15 | CorrelationScoresR
Page 536 and 537:
514 CHAPTER 15 | CorrelationThe pro
Page 538 and 539:
516 CHAPTER 15 | Correlationthat a
Page 540 and 541:
518 CHAPTER 15 | Correlationmeasure
Page 542 and 543:
520 CHAPTER 15 | CorrelationSUMMARY
Page 544 and 545:
522 CHAPTER 15 | CorrelationTo comp
Page 546 and 547:
524 CHAPTER 15 | CorrelationSTEP 2C
Page 548 and 549:
526 CHAPTER 15 | Correlation14. Ide
Page 551 and 552:
Introduction to RegressionCHAPTER16
Page 553 and 554:
SECTION 16.1 | Introduction to Line
Page 555 and 556:
Page 557 and 558:
Page 559 and 560:
Page 561 and 562:
SECTION 16.2 | The Standard Error o
Page 563 and 564:
Page 565 and 566:
Page 567 and 568:
SECTION 16.3 | Introduction to Mult
Page 569 and 570:
Page 571 and 572:
Page 573 and 574:
Page 575 and 576:
KEY TERMS 553a predicted portion an
Page 577 and 578:
DEMONSTRATION 16.1 555DEMONSTRATION
Page 579 and 580:
PROBLEMS 557Alzheimer’s disease.
Page 581 and 582:
The Chi-Square Statistic:Tests for
Page 583 and 584:
SECTION 17.1 | Introduction to Chi-
Page 585 and 586:
Page 587 and 588:
Page 589 and 590:
SECTION 17.2 | An Example of the Ch
Page 591 and 592:
Page 593 and 594:
Page 595 and 596:
SECTION 17.3 | The Chi-Square Test
Page 597 and 598:
Page 599 and 600:
Page 601 and 602:
Page 603 and 604:
Page 605 and 606:
SECTION 17.4 | Effect Size and Assu
Page 607 and 608:
SECTION 17.4 | Effect Size and Assu
Page 609 and 610:
SECTION 17.5 | Special Applications
Page 611 and 612:
SECTION 17.5 | Special Applications
Page 613 and 614:
SUMMARY 591With df = 2 and α = .05
Page 615 and 616:
SPSS ® SPSS ® 593General instruct
Page 617 and 618:
DEMONSTRATION 17.1 595FOCUS ON PROB
Page 619 and 620:
PROBLEMS 597Finally, we can add the
Page 621 and 622:
PROBLEMS 599response, a sample of 1
Page 623:
PROBLEMS 601a researcher obtains a
Page 626 and 627:
PREVIEWIn 1960, Gibson and Walk des
Page 628 and 629:
606 CHAPTER 18 | The Binomial Testp
Page 630 and 631:
608 CHAPTER 18 | The Binomial Test2
Page 632 and 633:
610 CHAPTER 18 | The Binomial Test
Page 634 and 635:
612 CHAPTER 18 | The Binomial Test
Page 636 and 637:
614 CHAPTER 18 | The Binomial TestT
Page 638 and 639:
616 CHAPTER 18 | The Binomial Testt
Page 640 and 641:
618 CHAPTER 18 | The Binomial TestB
Page 642 and 643:
Page 644 and 645:
Page 647 and 648:
Basic Mathematics ReviewAPPENDIXAPR
Page 649 and 650:
APPENDIX A | Basic Mathematics Revi
Page 651 and 652:
Page 653 and 654:
Page 655 and 656:
Page 657 and 658:
Page 659 and 660:
Page 661 and 662:
Page 663 and 664:
Page 665 and 666:
Page 667:
Page 670 and 671:
648 APPENDIX B | Statistical Tables
Page 672 and 673:
Page 674 and 675:
Page 676 and 677:
Page 678 and 679:
Page 680 and 681:
Page 682 and 683:
Page 684 and 685:
Page 686 and 687:
664 APPENDIX C | Solutions for Odd-
Page 688 and 689:
Page 690 and 691:
Page 692 and 693:
Page 694 and 695:
Page 696 and 697:
Page 698 and 699:
Page 700 and 701:
Page 702 and 703:
Page 704 and 705:
Page 706 and 707:
684 APPENDIX D | General Instructio
Page 709 and 710:
Hypothesis Tests for OrdinalData: M
Page 711 and 712:
APPENDIX E | Hypothesis Tests for O
Page 713 and 714:
Page 715 and 716:
Page 717 and 718:
Page 719 and 720:
Page 721:
Page 724 and 725:
702 Statistics Organizer: Finding t
Page 726 and 727:
Page 728 and 729:
Page 730 and 731:
Page 732 and 733:
Page 734 and 735:
Page 736 and 737:
Page 739 and 740:
ReferencesAckerman, R. (2011). Meta
Page 741 and 742:
REFERENCES 719Alzheimer’s disease
Page 743:
REFERENCES 721of aging and estrogen
Page 746 and 747:
724 NAME INDEXKaell, A., 622Kahn, K
Page 748 and 749:
726 SUBJECT INDEXConfidence interva
Page 750 and 751:
728 SUBJECT INDEXIndependent random
Page 752 and 753:
730 SUBJECT INDEXResearch studies,
Page 754:
732 SUBJECT INDEXTwo-factor ANOVA (
show all

Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?