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

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392 CHAPTER 12 | Introduction to Analysis of Variance3. The populations from which the samples are selected must have equal variances(homogeneity of variance).Ordinarily, researchers are not overly concerned with the assumption of normality,especially when large samples are used, unless there are strong reasons to suspect theassumption has not been satisfied. The assumption of homogeneity of variance is an importantone. If a researcher suspects it has been violated, it can be tested by Hartley’s F-maxtest for homogeneity of variance (Chapter 10, p. 314).Finally, if you suspect that one of the assumptions for the independent-measuresANOVA has been violated, you can still proceed by transforming the original scoresto ranks and then using an alternative statistical analysis known as the Kruskal-Wallis test, which is designed specifically for ordinal data. The Kruskal-Wallis test ispresented in Appendix E. The Kruskal-Wallis test also can be useful if large samplevariance prevents the independent-measures ANOVA from producing a significantresult.LEARNING CHECK1. A researcher reports an F-ratio with df = 3, 36 for an independent-measures experiment.How many treatment conditions were compared in this experiment?a. 3b. 4c. 36d. 392. The following table shows the results of an analysis of variance comparingthree treatment conditions with a sample of n = 7 participants in each treatment.Note that several values are missing in the table. What is the missingvalue for SS total?a. 16b. 23c. 29d. 56Source SS df MSBetween 20 xx xx F = xxWithin xx xx 2Total xx xx3. A research report concludes that there are significant differences among treatments,with “F(2,27) = 8.62, p < .01, η 2 = 0.28.” If the same number of participants wasused in all of the treatment conditions, then how many individuals were in eachtreatment?a. 7b. 9c. 10d. cannot determine without additional informationANSWERS1. B, 2. D, 3. C
SECTION 12.5 | Post Hoc Tests 39312.5 Post Hoc TestsLEARNING OBJECTIVE9. Describe the circumstances in which posttests are necessary and explain what thetests accomplish.As noted earlier, the primary advantage of ANOVA (compared to t tests) is it allowsresearchers to test for significant mean differences when there are more than two treatmentconditions. ANOVA accomplishes this feat by comparing all the individual meandifferences simultaneously within a single test. Unfortunately, the process of combiningseveral mean differences into a single test statistic creates some difficulty when it is time tointerpret the outcome of the test. Specifically, when you obtain a significant F-ratio (rejectH 0), it simply indicates that somewhere among the entire set of mean differences there isat least one that is statistically significant. In other words, the overall F-ratio only tells youthat a significant difference exists; it does not tell exactly which means are significantlydifferent and which are not.In Example 12.2 we presented an independent-measures study using three samples tocompare three strategies for studying in preparation for a test: rereading the material to betested, answering prepared questions on the material, creating and answering your ownquestions. The three sample means were M 1= 5, M 2= 9, and M 3= 10. In this study thereare three mean differences:1. There is a 4-point difference between M 1and M 2.2. There is a 1-point difference between M 2and M 3.3. There is a 5-point difference between M 1and M 3.The ANOVA used to evaluate these data produced a significant F-ratio indicating that atleast one of the sample mean differences is large enough to satisfy the criterion of statisticalsignificance. In this example, the 5-point difference is the biggest of the three and,therefore, it must indicate a significant difference between the first treatment and the thirdtreatment (μ 1≠ μ 3). But what about the 4-point difference? Is it also large enough to besignificant? And what about the 1-point difference between M 2and M 3? Is it also significant?The purpose of post hoc tests is to answer these questions.DEFINITIONPost hoc tests (or posttests) are additional hypothesis tests that are done after anANOVA to determine exactly which mean differences are significant and which are not.As the name implies, post hoc tests are done after an ANOVA. More specifically, thesetests are done after ANOVA when1. You reject H 0and2. there are three or more treatments (k ≥ 3).Rejecting H 0indicates that at least one difference exists among the treatments. If there areonly two treatments, then there is no question about which means are different and, therefore,no need for posttests. However, with three or more treatments (k ≥ 3), the problem isto determine exactly which means are significantly different.■ Posttests and Type I ErrorsIn general, a post hoc test enables you to go back through the data and compare the individualtreatments two at a time. In statistical terms, this is called making pairwise comparisons.
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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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340 CHAPTER 11 | The t Test for Two
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PROBLEMS 44313. The following summa
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PROBLEMS 44523. The following data
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Two-FactorAnalysis of Variance(Inde
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SECTION 14.1 | An Overview of the T
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SECTION 14.2 | An Example of the Tw
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SECTION 14.3 | More about the Two-F
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SUMMARY 473SUMMARY1. A research stu
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FOCUS ON PROBLEM SOLVING 475Descrip
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DEMONSTRATION 14.1 477STEP 2STAGE 1
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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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490 CHAPTER 15 | CorrelationDEFINIT
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492 CHAPTER 15 | CorrelationSubstit
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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 17.3 | 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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