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

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434 CHAPTER 13 | Repeated-Measures Analysis of VarianceTreatmentParticipant I II DA 3 5 2B 4 14 10C 5 7 2D 4 6 2M D= 4SS D= 48The Repeated-Measures t Test The null hypothesis for the t test states that for thegeneral population there is no mean difference between the two treatment conditions.H 0: μ D= 0With n = 4 participants, the test has df = 3 and the critical boundaries for a two-tailed testwith α = .05 are t = ±3.182.For these data, the sample mean difference is M D= 4, the variance for the differencescores is s 2 = 16, and the standard error is SMD= 2 points. These values produce a t statistic oft 5 M D 2m DS MD5 4 2 025 2.00The t value is not in the critical region so we fail to reject H 0and conclude that there is nosignificant difference between the two treatments.The Repeated-Measures ANOVA Now we will reorganize the data into a formatthat is compatible with a repeated-measures ANOVA. Notice that the ANOVAuses the original scores (not the difference scores) and requires the P totals for eachparticipant.TreatmentParticipant I II PA 3 5 8 G = 48B 4 14 18 ΣX 2 = 372C 5 7 12 N = 8D 4 6 10Again, the null hypothesis states that for the general population there is no mean differencebetween the two treatment conditions.H 0: μ 1– μ 2= 0For this study, df between treatments= 1, df within treatments= 6, df between subjects= 3, which producedf error= (6 – 3) = 3. Thus, the F-ratio has df = 1, 3 and the critical value for α = .05 isF = 10.13. Note that the denominator of the F-ratio has the same df value as the t statistic(df = 3) and that the critical value for F is equal to the squared critical value fort (10.13 = 3.182 2 ).
SECTION 13.3 | More about the Repeated-Measures Design 435For these data, SS total= 84,SS within= 52SS between treatments= (84 – 52) = 32SS between subjects= 28SS error= (52 – 28) = 24The two variances in the F-ratio areMS between treatments5 SS between treatmentsdf between treatments5 32 1 5 32and MS error5 SS errordf error5 24 3 5 8and the F-ratio is F 5 MS between treatmentsMS error5 32 8 5 4.00Notice that the F-ratio and the t statistic are related by the equation F = t 2 (4 = 2 2 ). TheF-ratio (like the t statistic) is not in the critical region so, once again, we fail to reject H 0and conclude that there is no significant difference between the two treatments. ■LEARNING CHECK1. Under what circumstances would a study using a repeated-measures ANOVAhave a distinct advantage over a study using an independent-measuresANOVA?a. When there are many participants available and individual differencesare large.b. When there are few participants available and individual differencesare large.c. When there are many participants available and individual differencesare small.d. When there are few participants available and individual differences aresmall.2. A repeated-measures ANOVA produced an F-ratio of F = 9.00 with df = 1, 14. Ifthe same data were analyzed with a repeated-measures t test, what value would beobtained for the t statistic?a. 3b. 9c. 81d. Cannot determine without more information.ANSWERS1. B, 2. A
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EDITION10Statistics for theBehavior
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Statistics for the Behavioral Scien
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CONTENTSCHAPTER 1 Introduction to S
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CONTENTSvii5.4 Using z-Scores to St
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CONTENTSixCHAPTER 10 The t Test for
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CONTENTSxiCHAPTER 15 Correlation 48
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PREFACEMany students in the behavio
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PREFACExv3. The former Chapter 19,
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PREFACExviiTo the StudentA primary
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ABOUT THE AUTHORSFREDERICK J GRAVET
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PREVIEWBefore we begin our discussi
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4 CHAPTER 1 | Introduction to Stati
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10 CHAPTER 1 | Introduction to Stat
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PREVIEWThere is some evidence that
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36 CHAPTER 2 | Frequency Distributi
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Central TendencyCHAPTER3Tools You W
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SECTION 3.1 | Overview 69DEFINITION
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SECTION 3.2 | The Mean 71research r
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SECTION 3.2 | The Mean 73the distri
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SECTION 3.2 | The Mean 75TABLE 3.1S
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SECTION 3.2 | The Mean 77Table 3.2
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SECTION 3.3 | The Median 793.3 The
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SECTION 3.3 | The Median 81To find
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SECTION 3.4 | The Mode 832. What is
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SECTION 3.4 | The Mode 85FIGURE 3.7
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SECTION 3.5 | Selecting a Measure o
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SECTION 3.6 | Central Tendency and
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FOCUS ON PROBLEM SOLVING 95of centr
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PROBLEMS 976. A population of N = 1
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VariabilityCHAPTER4Tools You Will N
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SECTION 4.1 | Introduction to Varia
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SECTION 4.2 | Defining Standard Dev
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SECTION 4.3 | Measuring Variance an
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SECTION 4.4 | Measuring Standard De
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SECTION 4.5 | Sample Variance as an
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SECTION 4.6 | More about Variance a
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SUMMARY 1252. A population has a me
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FOCUS ON PROBLEM SOLVING 127VAR0000
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PROBLEMS 1299. For the following se
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z-Scores: Location of Scoresand Sta
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SECTION 5.1 | Introduction to z-Sco
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SECTION 5.2 | z-Scores and Location
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SECTION 5.2 | z-Scores and Location
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SECTION 5.3 | Other Relationships B
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SECTION 5.4 | Using z-Scores to Sta
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SECTION 5.4 | Using z-Scores to Sta
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SECTION 5.5 | Other Standardized Di
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SECTION 5.5 | Other Standardized Di
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SECTION 5.6 | Computing z-Scores fo
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SECTION 5.7 | Looking Ahead to Infe
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SUMMARY 153LEARNING CHECK1. In N =
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DEMONSTRATION 5.2 155sure that your
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PROBLEMS 15716. A distribution of e
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PREVIEWHow likely is it that you wi
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162 CHAPTER 6 | Probabilitythe prob
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164 CHAPTER 6 | Probability(Note: W
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166 CHAPTER 6 | ProbabilityFIGURE 6
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168 CHAPTER 6 | Probability■ The
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170 CHAPTER 6 | ProbabilityFinding
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172 CHAPTER 6 | Probabilityand exac
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174 CHAPTER 6 | ProbabilityFinally,
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176 CHAPTER 6 | ProbabilityXz-score
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178 CHAPTER 6 | ProbabilityBOX 6.1
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180 CHAPTER 6 | ProbabilityEXAMPLE
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182 CHAPTER 6 | ProbabilityFIGURE 6
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184 CHAPTER 6 | Probability6.5 Look
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186 CHAPTER 6 | Probability2. For a
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188 CHAPTER 6 | ProbabilityDEMONSTR
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190 CHAPTER 6 | Probability6. Draw
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Probability and Samples: TheDistrib
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SECTION 7.1 | Samples, Populations,
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SECTION 7.1 | Samples, Populations,
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SECTION 7.2 | The Distribution of S
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SECTION 7.3 | Probability and the D
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SECTION 7.3 | Probability and the D
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SECTION 7.4 | More about Standard E
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SECTION 7.4 | More about Standard E
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FOCUS ON PROBLEM SOLVING 219SUMMARY
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PROBLEMS 221STEP 2Compute the z-sco
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Introduction toHypothesis TestingCH
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SECTION 8.1 | The Logic of Hypothes
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SECTION 8.2 | Uncertainty and Error
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SECTION 8.2 | Uncertainty and Error
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SECTION 8.3 | More about Hypothesis
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SECTION 8.3 | More about Hypothesis
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SECTION 8.4 | Directional (One-Tail
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SECTION 8.5 | Concerns about Hypoth
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SECTION 8.5 | Concerns about Hypoth
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SECTION 8.6 | Statistical Power 255
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FOCUS ON PROBLEM SOLVING 2618. The
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PROBLEMS 263In this distribution, o
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PROBLEMS 26513. A random sample is
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Introduction to the t StatisticCHAP
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SECTION 9.1 | The t Statistic: An A
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SECTION 9.2 | Hypothesis Tests with
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SECTION 9.2 | Hypothesis Tests with
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SECTION 9.3 | Measuring Effect Size
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SECTION 9.4 | Directional Hypothese
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SUMMARY 2913. A researcher rejects
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DEMONSTRATION 9.1 293One-Sample Sta
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PROBLEMS 295PROBLEMS1. Under what c
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PROBLEMS 297b. Construct the 90% co
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The t Test for TwoIndependent Sampl
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SECTION 10.1 | Introduction to the
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SECTION 10.2 | The Null Hypothesis
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SECTION 10.3 | Hypothesis Tests wit
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SECTION 10.4 | Effect Size and Conf
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SECTION 10.5 | The Role of Sample V
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KEY TERMS 325SUMMARY1. The independ
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FOCUS ON PROBLEM SOLVING 327Group S
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PROBLEMS 329The t Statistic Finally
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PROBLEMS 331c. Write a sentence dem
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PROBLEMS 33319. If other factors ar
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PREVIEWIt’s the night before an e
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338 CHAPTER 11 | The t Test for Two
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PREVIEWYour job interview is tomorr
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368 CHAPTER 12 | Introduction to An
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PREVIEWA recent report describing t
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488 CHAPTER 15 | CorrelationDEFINIT
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494 CHAPTER 15 | Correlationeither
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496 CHAPTER 15 | Correlationreliabl
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498 CHAPTER 15 | Correlation60Numbe
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500 CHAPTER 15 | CorrelationOne of
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502 CHAPTER 15 | CorrelationBOX 15.
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504 CHAPTER 15 | Correlation171615Z
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506 CHAPTER 15 | Correlation3. What
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508 CHAPTER 15 | Correlationon the
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510 CHAPTER 15 | CorrelationLEARNIN
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512 CHAPTER 15 | CorrelationScoresR
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514 CHAPTER 15 | CorrelationThe pro
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516 CHAPTER 15 | Correlationthat a
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518 CHAPTER 15 | Correlationmeasure
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520 CHAPTER 15 | CorrelationSUMMARY
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522 CHAPTER 15 | CorrelationTo comp
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524 CHAPTER 15 | CorrelationSTEP 2C
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526 CHAPTER 15 | Correlation14. Ide
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Introduction to RegressionCHAPTER16
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SECTION 16.1 | Introduction to Line
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SECTION 16.2 | The Standard Error o
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SECTION 16.3 | Introduction to Mult
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KEY TERMS 553a predicted portion an
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DEMONSTRATION 16.1 555DEMONSTRATION
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PROBLEMS 557Alzheimer’s disease.
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The Chi-Square Statistic:Tests for
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SECTION 17.1 | Introduction to Chi-
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SECTION 17.2 | An Example of the Ch
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SECTION 17.4 | Effect Size and Assu
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SECTION 17.4 | Effect Size and Assu
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SECTION 17.5 | Special Applications
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SECTION 17.5 | Special Applications
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SUMMARY 591With df = 2 and α = .05
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SPSS ® SPSS ® 593General instruct
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DEMONSTRATION 17.1 595FOCUS ON PROB
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PROBLEMS 597Finally, we can add the
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PROBLEMS 599response, a sample of 1
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PROBLEMS 601a researcher obtains a
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PREVIEWIn 1960, Gibson and Walk des
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606 CHAPTER 18 | The Binomial Testp
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608 CHAPTER 18 | The Binomial Test2
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610 CHAPTER 18 | The Binomial Test
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612 CHAPTER 18 | The Binomial Test
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614 CHAPTER 18 | The Binomial TestT
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616 CHAPTER 18 | The Binomial Testt
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618 CHAPTER 18 | The Binomial TestB
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Basic Mathematics ReviewAPPENDIXAPR
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APPENDIX A | Basic Mathematics Revi
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648 APPENDIX B | Statistical Tables
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664 APPENDIX C | Solutions for Odd-
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684 APPENDIX D | General Instructio
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Hypothesis Tests for OrdinalData: M
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APPENDIX E | Hypothesis Tests for O
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702 Statistics Organizer: Finding t
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ReferencesAckerman, R. (2011). Meta
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REFERENCES 719Alzheimer’s disease
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REFERENCES 721of aging and estrogen
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724 NAME INDEXKaell, A., 622Kahn, K
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726 SUBJECT INDEXConfidence interva
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728 SUBJECT INDEXIndependent random
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730 SUBJECT INDEXResearch studies,
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732 SUBJECT INDEXTwo-factor ANOVA (
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Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

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