Solution Manual for Experimental Design: Procedures for the Behavioral Sciences , 4th Edition

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Solution Manual for Experimental Design: Procedures for the Behavioral Sciences , 4th Edition - Page 1 preview image

Solutions Manual forExperimentalDesignProcedures forthe BehavioralSciencesRoger E.Kirk

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iiiC O N T E N T SChapter 1Research Strategies and the Control of Nuisance Variables 1Chapter 2Experimental Design : An Overview 3Chapter 3Fundamental Assumptions in Analysis of Variance 14Chapter 4Completely Randomized Design 19Chapter 5Multiple Comparison Tests 27Chapter 6Trend Analysis 32Chapter 7General Linear Model Approach to ANOVA 41Chapter 8Randomized Block Designs 47Chapter 9Completely Randomized Factorial Design WithTwo Treatments 54Chapter 10Completely Randomized Factorial Design WithThree or More Treatments and Randomized BlockFactorial Design 61Chapter 11Hierarchical Designs 68Chapter 12Split-Plot Factorial Designs: Design WithGroup-Treatment Confounding 77Chapter 13Analysis of Covariance 86Chapter 14Latin Square and Related Designs 90Chapter 15Confounded Factorial Designs: Designs WithGroup-Interaction Confounding 94Chapter 16Fractional Factorial Designs: Designs With Treatment-Interaction Confounding 101

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1CHAPTER 1Research Strategiesand the Control ofNuisance Variables2.c.EU is a student; OU is a student.d.EU is a rat; OU is a rat.e.EU is a telephone number; OU is a respondent.3.c.Unacceptabled.Acceptable4.c.(i) Amount of flurazepam(ii)Hypnotic suggestibility(iii)Gender, previoushypnotic experienced.(i) Three fixed ratio schedules of reinforcement(ii)Key pecking rate(iii)Ageof pigeons, phase of estrous cycle6.a.In an experiment, subjects are randomly assigned to the independent variable; in aquasi-experiment, subjects are not randomly assigned to the independent variable.b.Subjects were not randomly assigned to independent variable, which was adding or notadding fluoride to the water.7.a.Obtain a sample ofnchildren. For each child, randomize the order of presenting thethree types of televised violence with the restriction that each type of violence ispresented first, second, and third an equal number of times.b.Use a hidden camera to videotape children in a familiar environment as they watchtelevision and note their facial expressions when various forms of violence aredepicted.8.e.Retrospective cohort study. The study involved a nonexperimental research strategy inwhich the subjects were classified on the basis of their earlier earnings during a six-month period. Multiple dependent variables were investigated, and these variables alsooccurred prior the beginning of the study.f.Retrospective cohort study. The study involved a nonexperimental research strategy inwhich the subjects were classified on the basis of the independent variable, which wasappearing or not appearing in the juvenile court in Houston, TX.g.Time-lag study. The study involved a nonexperimental research strategy in which the

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Chapter1Research Strategies and the Control of Nuisance Variables2dependent variable was measured at three different times on three different groups ofcohorts.h.Retrospective cohort study. The study involved a nonexperimental research strategy inwhich university records were used to identify students who were first-born, second-born, and so on, and their recreational activities.i.Prospective study. The study involved a nonexperimental research strategy in which theindependent and dependent variables were observed after the onset of the investigation.j.Retrospective cohort study. The study involved a nonexperimental research strategy inwhich men were identified who had or had not been exposed to chemicals used as fireretardants. The two samples of men were subsequently compared in terms of primarythyroid dysfunction.9.c.History, compensatory rivalry by respondents receiving less desirable treatments,resentful demoralization of respondents receiving less desirable treatmentsd.Selection, selection-history effectse.Selection, selection-history effects, mortalityf.History, selection, selection-history effects, mortality10.c.Interaction of selection and treatmentd.Interaction of selection and treatment11.b.b, d, f, ic.b, d, f, i12.a.Subjects were randomly sampled; residence was held constant. The age of the subjectswas restricted.c.The city and gender of the drivers were held constant; age of the drivers and the lengthof time that they had driven a cab were restricted.d.The students within a matched pair were randomly assigned to the programs; the gradelevel was held constant.f.The sample from the Houston, TX, court was obtained by random sampling; the genderof the subjects was held constant.g.The gender of the subjects was held constant.h.The gender of the subjects and the university that they attended were held constant.j.The gender of the subjects and the city in which they worked were held constant.

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3CHAPTER 2Experimental Designs:An Oveview2.d.(i) RB-3 design(ii)H0:μ.1=μ.2=μ.3(iii)Yij=μ+αj+πi+εij(i= 1,. . .,14;j= 1,. . ., 3)e.(i)ttest for dependent samples(ii)H0:μ.1≤μ.2, whereμ.1andμ.2denote thepopulation means for English-Canadian and French-Canadian students, respectively.(iii)Yij=μ+αj+πi+εij(i= 1,. . ., 50;j= 1, 2)f.(i) CRF-62 design(ii)H0:μ1.=μ2.=. . .=μ6.;H0:μ.1=μ.2;H0:μjk–μj!k–μ!j k+μ!j!k= 0 for alljandk(iii)Yijk=μ+αj+βk+ (αβ)jk+εi(jk)(i= 1,. . .,50;j= 1,. . ., 6;k= 1, 2)g.(i) CR-3 design(ii)H0:μ1=μ2=μ3(iii)Yij=μ+αj+εi(j)(i= 1,. . ., 30;j= 1,. . ., 3)3.a.The grand mean is the average value around which the treatment means vary.b.A treatment effect is the deviation of the grand mean from a treatment mean.c.Anerroreffectisalleffectsnotattributabletoatreatmentlevelortreatmentcombination.4.b.A completely randomized design is the simplest design to lay out and analyze. Therandomization procedures for the randomized block and Latin square designs are morecomplex than those for the completely randomized design, but the latter designs enablea researcher to isolate the effects of one nuisance variable or, in the case of the Latinsquare design, two nuisance variables.5.c.a1b1,a1b2,a1b3,a2b1,a2b2,a2b3,a3b1,a3b2,a3b3d.a1b1,a1b2,a2b1,a2b2,a3b1,a3b2,a4b1,a4b2e.a1b1c1,a1b1c2,a1b2c1,a1b2c2,a2b1c1,a2b1c2,a2b2c1,a2b2c2,a3b1c1,a3b1c2,a3b2c1,a3b2c2

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Chapter2Experimental Designs: An Overview46.d.CR-5 design withn= 6Treat.LevelDep.Var.Group1!"#Subject1!Subject6a1!a1Y11!Y61Y.1Group2!"#Subject1!Subject6a2!a2Y12!Y62Y.2Group3!"#Subject1!Subject6a3!a3Y13!Y63Y.3Group4!"#Subject1!Subject6a4!a4Y14!Y64Y.4Group5!"#Subject1!Subject6a5!a5Y15!Y65Y.5e.ttest for dependent samples withn= 7Treat.LevelDep.Var.Treat.LevelDep.Var.Block1Block2Block3!Block7a1a1a1!a1Y11Y21Y31!Y71a2a2a2!a2Y12Y22Y32!Y7 2Y.1Y.2

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Chapter2Experimental Designs: An Overview5f.RB-4 design withn= 6Treat.LevelDep.Var.Treat.LevelDep.Var.Treat.LevelDep.Var.Treat.LevelDep.Var.Block1Block2Block3!Block6a1a1a1!a1Y11Y21Y31!Y61a2a2a2!a2Y12Y22Y32!Y62a3a3a3!a3Y13Y23Y33!Y63a4a4a4!a4Y14Y24Y34!Y64Y1.Y2.Y3.!Y6.Y.1Y.2Y.3Y.4g.CRF-222 design withn= 3Treat.Comb.Dep.Var.Group1!"#$#Subject1Subject2Subject3a1b1c1a1b1c1a1b1c1Y1111Y2111Y3111Y.111Group2!"#$#Subject1Subject2Subject3a1b1c2a1b1c2a1b1c2Y1112Y2112Y3112Y.112Group3!"#$#Subject1Subject2Subject3a1b2c1a1b2c1a1b2c1Y1121Y2121Y3121Y.121!!!Group8!"#$#Subject1Subject2Subject3a2b2c2a2b2c2a2b2c2Y1222Y2222Y3222Y.222

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Chapter2Experimental Designs: An Overview6h.LS-3 design withn= 3Treat.Comb.Dep.Var.Group1!"#$#Subject1Subject2Subject3a1b1c1a1b1c1a1b1c1Y1111Y2111Y3111Y.111Group2!"#$#Subject1Subject2Subject3a1b2c3a1b2c3a1b2c3Y1123Y2123Y3123Y.123Group3!"#$#Subject1Subject2Subject3a1b3c2a1b3c2a1b3c2Y1132Y2132Y3132Y.132Group4!"#$#Subject1Subject2Subject3a2b1c2a2b1c2a2b1c2Y1212Y2212Y3212Y.212!!!Group9!"#$#Subject1Subject2Subject3a3b3c1a3b3c1a3b3c1Y1331Y2331Y3331Y.331

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Chapter2Experimental Designs: An Overview78.d.RB-3 design withn= 14Treat.LevelDep.Var.Treat.LevelDep.Var.Treat.LevelDep.Var.Block1Block2Block3!Block14a1a1a1!a1Y11Y21Y31!Y14, 1a2a2a2!a2Y12Y22Y32!Y14, 2a3a3a3!a3Y13Y23Y33!Y14, 3Y1.Y2.Y3.!Y14.Y.1Y.2Y.3e.ttest for dependent samples withn1andn2= 50Treat.LevelDep.Var.Treat.LevelDep.Var.Block1Block2Block3!Block50a1a1a1!a1Y11Y21Y31!Y50, 1a2a2a2!a2Y12Y22Y32!Y50, 2Y.1Y.2

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Chapter2Experimental Designs: An Overview8f.CRF-62 design withn= 50Treat.Comb.Dep.Var.Group1!"#$#Subject1!Subject50a1b1!a1b1Y111!Y50, 11Y.11Group2!"#$#Subject1!Subject50a1b2!a1b2Y112!Y50, 12Y.12Group3!"#$#Subject1!Subject50a2b1!a2b1Y121!Y50, 21Y.21Group4!"#$#Subject1!Subject50a2b2!a2b2Y122!Y50, 22Y.22!!!Group12!"#$#Subject1!Subject50a6b2!a6b2Y162!Y50, 62Y.62

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Chapter2Experimental Designs: An Overview9g.CR-3 design withn= 30Treat.LevelDep.Var.Group1!"#$#Animal1!Animal30a1!a1Y11!Y30,1Y.1Group2!"#$#Animal1!Animal30a2!a2Y12!Y30,2Y.2Group3!"#$#Animal1!Animal30a3!a3Y13!Y30,3Y.39.a.b.As the number of hours of deprivation increases, the difference in running time amongthe three reinforcement conditions decreases.12.a.A scientific hypothesis is a testable supposition that is tentatively adopted to accountfor certain facts and to guide in the investigation of others. A statistical hypothesis is astatement about one or more parameters of a population or the functional form of apopulation.b.(i) Alternative hypothesis(ii)Null hypothesis15.a.State the null and alternative hypotheses—H0:μ= 45,H1:μ≠45. Specify the teststatistic—t=(Y!μ0) / ( ˆ"/n). Specify the sample size—n= 27, and the samplingdistribution—tdistribution. Specify the level of significance—α= .05. Obtain random1a2a1b2b3b456789a3Running time (sec.)10 hrs.15 hrs.20 hrs.Hours of deprivation1a2a1b2b3b456789a3Running time (sec.)SmallMediumLargeMagnitude of reinforcement

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Chapter2Experimental Designs: An Overview10samples of sizen= 27, computet, and make a decision.b.Reject the null hypothesis iftfalls in either the lower or upper 2.5% of the samplingdistribution oft; otherwise, do not reject the null hypothesis. If the null hypothesis isrejected, conclude that the mean for children in the experimental program is not equalto the mean for ninth-graders who have been observed during the past several years; ifthe null hypothesis is not rejected, do not draw this conclusion.c.d.t=Y!μ0ˆ"/n=52.5!45.015 /27=7.52.89=2.60,p= .015.The population mean for children in the experimental program was not equal to themean for ninth-graders who have been observed during the past several years. Thedifference between children who did or did not participate in the experimental program,52.5 versus 45.0, was statistically significant,t(26) = 2.60,p= .015.e.d=52.5!45 / 15=0.5; this is a medium size effect.f.Y!t.05/2, 26ˆ"n< μ <Y+t.05/2, 26ˆ"n52.5!2.056(15)27< μ <52.5+2.056(15)2746.6 <μ< 58.4The researcher can be 95% confident thatμis greater than 46.6 or less than 58.4. Thenull hypothesis is not tenable.g.Y.05= μ0+t.05/2, 26ˆ!n=45+2.056(15)27=50.935t=Y.05!"μˆ#/n=50.935!52.515 /27=!1.5652.887=!0.54TDIS(0.54,26,1) =.30 =ˆ!; 1 –ˆ!=.70Critical region!= .025Don't rejectH0H0RejecttCritical region!= .025H0Rejectf(t)

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Chapter2Experimental Designs: An Overview11h.True Situationμ= 45!μ= 52.5Researcher’sμ= 45Correct acceptance1 –α= 1 – .05= .95Type II errorˆ!= .30Decisionμ≠45Type I errorα= .05Correct rejection1 –ˆ!= 1 – .30= .7016.c.Correct rejectiond.Correct acceptancee.Correct rejectionf.Type I error17.The power of an experiment can be increased by (1) adopting a lower level ofsignificance, (2) increasing the size of the sample, (3) refining the experimentalmethodology so as to decrease the size of the population standard deviation, and (4)increasingthemagnitudeofthetreatmenteffectsconsideredworthdetecting.Increasing the sample size is often the simplest way to increase power. The other waysof increasing power may lead to problems or may not be feasible. For example, theadoption ofα> .05 may preclude the publication of the research. Refining theexperimental methodology so as to decrease the size of the population standarddeviation may be prohibitively expensive. Increasing the magnitude of the treatmenteffects considered worth detecting may not be appropriate.18.a.State the null and alternative hypotheses—H0:μ1–μ2≤0,H1:μ1–μ2> 0. Specify thetest statistic—t=(Y.1!Y.2) /ˆ"Pooled21n1+1n2#$%&'(. Specify the sample size—n1= 24,n2= 23, and the sampling distribution—tdistribution. Specify the level of significance—α= .05. Randomly assignN= 47 subjects to the two game types, computet, and make adecision.b.Reject the null hypothesis iftfalls in the upper 5% of the sampling distribution oft;otherwise, do not reject the null hypothesis. If the null hypothesis is rejected, concludethat the risk-related cognitions of men who play racing video games is higher than thatfor the men who play the neutral games; if the null hypothesis is not rejected, do notdraw this conclusion.

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Chapter2Experimental Designs: An Overview12c.d.!Pooled2=(n1"1)!12+(n2"1)!22(n1"1)+(n2"1)=(24"1)(1.3)2+(23"1)(1.2)2(24"1)+(23"1)=1.568t=(Y.1!Y.2) /ˆ"Pooled21n1+1n2#$%&'(=(7.54!6.41) /1.568124+123"#$%&'=1.13 / 0.365=3.09. Thepvalue is less than .002.The mean risk-related cognitions for men who played the racing video games washigher than that for the men who played the neutral games. The difference between themeans, 7.54 versus 6.41, was statistically significant,t(45) = 3.09,p< .002.e.g=Y.1!Y.2/ ˆ"Pooled=7.54!6.41 / 1.25=0.90; this is a large effect.f.(Y.1!Y.2)!t.05,45ˆ"Pooled21n1+1n2#$%&'(< μ1!μ2(7.54!6.41)!1.6791.568124+123"#$%&'< μ1!μ20.52 <μ1–μ2The researcher can be 95% confident thatμ1–μ2is greater than 0.52. The nullhypothesis is not tenable.g.Y.05=!0+t.05,45ˆ"Pooled21n1+1n2#$%&'(=0+1.6791.568124+123!"#$%&=0.613t=Y.05!"#0ˆ$Pooled21n1+1n2%&'()*=0.613!1.01.568124+123"#$%&'=!0.3870.365=!1.06TDIS(1.06,45,1) =.15 =ˆ!; 1 –ˆ!=.85Critical region!= .05Don't rejectH0H0Rejecttf(t)

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Chapter2Experimental Designs: An Overview13h.True Situationμ1–μ2= 0!μ1"!μ2=1.0Researcher’sμ1–μ2≤0Correct acceptance1 –α= 1 – .05= .95Type II errorˆ!= .15Decisionμ1–μ2> 0Type I errorα= .05Correct rejection1 –ˆ!= 1 – .15= .8519.c.p< .0005d.p< .104820.c.t= 2.402d.t= 3.601

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