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

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428 CHAPTER 13 | Repeated-Measures Analysis of VarianceFor the study in Example 13.1, the report could state:The means and variances for the three strategies are shown in Table 1. A repeatedmeasuresanalysis of variance indicated significant mean differences in the participants’test scores for the three study strategies, F (2, 10) = 19.09, p < .01, η 2= 0.79.TABLE 1Test scores using three different study strategiesRereadAnswer PreparedQuestionsCreate andAnswer QuestionsM 5.00 9.00 10.00SD 2.19 2.61 2.45■ Post Hoc Tests with Repeated MeasuresRecall that ANOVA provides an overall test of significance for the mean differences betweentreatments. When the null hypothesis is rejected, it indicates only that there is a differencebetween at least two of the treatment means. If k = 2, it is obvious which two treatmentsare different. However, when k is greater than 2, the situation becomes more complex. Todetermine exactly which differences are significant, the researcher must follow the ANOVAwith post hoc tests. In Chapter 12, we used Tukey’s HSD and the Scheffé test to make thesemultiple comparisons among treatment means. These two procedures attempt to control theoverall alpha level by making adjustments for the number of potential comparisons.For a repeated-measures ANOVA, Tukey’s HSD and the Scheffé test can be used inthe exact same manner as was done for the independent-measures ANOVA, provided thatyou substitute MS errorin place of MS within treatmentsin the formulas and use df errorin place ofdf within treatmentswhen locating the critical value in a statistical table.■ Assumptions of the Repeated-Measures ANOVAThe basic assumptions for the repeated-measures ANOVA are identical to those requiredfor the independent-measures ANOVA.1. The observations within each treatment condition must be independent(see p. 244).2. The population distribution within each treatment must be normal. (As before, theassumption of normality is important only with small samples.)3. The variances of the population distributions for each treatment should beequivalent.For the repeated-measures ANOVA, there is an additional assumption, called homogeneityof covariance. Basically, it refers to the requirement that the relative standing of eachsubject be maintained in each treatment condition. This assumption is violated if the effectof the treatment is not consistent for all of the subjects or if order effects exist for some,but not other, subjects. This issue is very complex and is beyond the scope of this book.However, methods do exist for dealing with violations of this assumption (for a discussion,see Keppel, 1973).If there is reason to suspect that one of the assumptions for the repeated-measuresANOVA has been violated, an alternative analysis known as the Friedman test is presentedin Appendix E. The Friedman test requires that the original scores be transformed intoranks before evaluating the differences between treatment conditions.
SECTION 13.3 | More about the Repeated-Measures Design 429LEARNING CHECK1. Which of the following accurately describes the two stages of a repeated-measuresanalysis of variance?a. The first stage is identical to the independent-measures analysis and the secondstage removes individual differences from the numerator of the F-ratio.b. The first stage is identical to the independent-measures analysis and the secondstage removes individual differences from the denominator of the F-ratio.c. The first stage removes individual differences from the numerator of the F-ratioand the second stage is identical to the independent-measures analysis.d. The first stage removes individual differences from the denominator of theF-ratio and the second stage is identical to the independent-measures analysis.2. For the repeated-measures ANOVA, SS erroris found by _____.a. SS total– SS between treatmentsb. SS between treatments– SS withinc. SS between treatments– SS between subjectsd. SS within– SS between subjects3. A researcher uses a repeated-measures ANOVA to test for mean differences amongthree treatment conditions using a sample of n = 10 participants. What are the dfvalues for the F-ratio from this analysis?a. 3, 9b. 2, 9c. 3, 18d. 2, 184. The results of a repeated-measures ANOVA are reported as follows, F(2, 24) =1.12, p > .05. How many individuals participated in the study?a. 25b. 13c. 12d. 7ANSWERS1. B, 2. D, 3. D, 4. B13.3 More about the Repeated-Measures DesignLEARNING OBJECTIVES6. Describe the general advantages and disadvantages of repeated-measures vs.independent-measures designs and identify the circumstances in which each ismore appropriate.7. Explain the relationship between the repeated-measures t test and a repeatedmeasuresANOVA when evaluating the difference between two means from arepeated-measures design.■ Advantages and Disadvantages of the Repeated-Measures DesignWhen we first encountered the repeated-measure design (Chapter 11), we noted thatthis type of research study has certain advantages and disadvantages compared to the
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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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PROBLEMS 479PROBLEMS1. Define each
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PROBLEMS 48115. Research results in
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PROBLEMS 483EasyFactorA TaskDifficu
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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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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 17.3 | The Chi-Square Test
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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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