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

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    Solutions Manual for Experimental Design Procedures for the Behavioral Sciences Roger E. Kirk

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

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    1 C H A P T E R 1 Research Strategies and the Control of Nuisance Variables 2. 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. Unacceptable d. Acceptable 4. c. (i) Amount of flurazepam (ii) Hypnotic suggestibility (iii) Gender, previous hypnotic experience d. (i) Three fixed ratio schedules of reinforcement (ii) Key pecking rate (iii) Age of pigeons, phase of estrous cycle 6. a. In an experiment, subjects are randomly assigned to the independent variable; in a quasi-experiment, subjects are not randomly assigned to the independent variable. b. Subjects were not randomly assigned to independent variable, which was adding or not adding fluoride to the water. 7. a. Obtain a sample of n children. For each child, randomize the order of presenting the three types of televised violence with the restriction that each type of violence is presented first, second, and third an equal number of times. b. Use a hidden camera to videotape children in a familiar environment as they watch television and note their facial expressions when various forms of violence are depicted. 8. e. Retrospective cohort study. The study involved a nonexperimental research strategy in which the subjects were classified on the basis of their earlier earnings during a six- month period. Multiple dependent variables were investigated, and these variables also occurred prior the beginning of the study. f. Retrospective cohort study. The study involved a nonexperimental research strategy in which the subjects were classified on the basis of the independent variable, which was appearing 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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    Chapter 1 Research Strategies and the Control of Nuisance Variables 2 dependent variable was measured at three different times on three different groups of cohorts. h. Retrospective cohort study. The study involved a nonexperimental research strategy in which 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 the independent and dependent variables were observed after the onset of the investigation. j. Retrospective cohort study. The study involved a nonexperimental research strategy in which men were identified who had or had not been exposed to chemicals used as fire retardants. The two samples of men were subsequently compared in terms of primary thyroid dysfunction. 9. c. History, compensatory rivalry by respondents receiving less desirable treatments, resentful demoralization of respondents receiving less desirable treatments d. Selection, selection-history effects e. Selection, selection-history effects, mortality f. History, selection, selection-history effects, mortality 10. c. Interaction of selection and treatment d. Interaction of selection and treatment 11. b. b, d, f, i c. b, d, f, i 12. a. Subjects were randomly sampled; residence was held constant. The age of the subjects was restricted. c. The city and gender of the drivers were held constant; age of the drivers and the length of time that they had driven a cab were restricted. d. The students within a matched pair were randomly assigned to the programs; the grade level was held constant. f. The sample from the Houston, TX, court was obtained by random sampling; the gender of 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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    3 C H A P T E R 2 Experimental Designs: An Oveview 2. d. (i) RB-3 design (ii) H 0 : μ .1 = μ .2 = μ .3 (iii) Y ij = μ + α j + π i + ε ij ( i = 1, . . . , 14; j = 1, . . . , 3) e. (i) t test for dependent samples (ii) H 0 : μ .1 ≤ μ .2 , where μ .1 and μ .2 denote the population means for English-Canadian and French-Canadian students, respectively. (iii) Y ij = μ + α j + π i + ε ij ( i = 1, . . . , 50; j = 1, 2) f. (i) CRF-62 design (ii) H 0 : μ 1. = μ 2. = . . . = μ 6. ; H 0 : μ .1 = μ .2 ; H 0 : μ jk – μ j ! k – μ ! j k + μ ! j ! k = 0 for all j and k (iii) Y ijk = μ + α j + β k + ( αβ ) jk + ε i ( jk ) ( i = 1, . . . , 50; j = 1, . . . , 6; k = 1, 2) g. (i) CR-3 design (ii) H 0 : μ 1 = μ 2 = μ 3 (iii) Y ij = μ + α j + ε i ( 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. An error effect is all effects not attributable to a treatment level or treatment combination. 4. b. A completely randomized design is the simplest design to lay out and analyze. The randomization procedures for the randomized block and Latin square designs are more complex than those for the completely randomized design, but the latter designs enable a researcher to isolate the effects of one nuisance variable or, in the case of the Latin square design, two nuisance variables. 5. c. a 1 b 1 , a 1 b 2 , a 1 b 3 , a 2 b 1 , a 2 b 2 , a 2 b 3 , a 3 b 1 , a 3 b 2 , a 3 b 3 d. a 1 b 1 , a 1 b 2 , a 2 b 1 , a 2 b 2 , a 3 b 1 , a 3 b 2 , a 4 b 1 , a 4 b 2 e. a 1 b 1 c 1 , a 1 b 1 c 2 , a 1 b 2 c 1 , a 1 b 2 c 2 , a 2 b 1 c 1 , a 2 b 1 c 2 , a 2 b 2 c 1 , a 2 b 2 c 2 , a 3 b 1 c 1 , a 3 b 1 c 2 , a 3 b 2 c 1 , a 3 b 2 c 2

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    Chapter 2 Experimental Designs: An Overview 4 6. d. CR-5 design with n = 6 Treat. Level Dep. Var. Group 1 ! " # Subject 1 ! Subject 6 a 1 ! a 1 Y 11 ! Y 61 Y . 1 Group 2 ! " # Subject 1 ! Subject 6 a 2 ! a 2 Y 12 ! Y 62 Y . 2 Group 3 ! " # Subject 1 ! Subject 6 a 3 ! a 3 Y 13 ! Y 63 Y . 3 Group 4 ! " # Subject 1 ! Subject 6 a 4 ! a 4 Y 14 ! Y 64 Y . 4 Group 5 ! " # Subject 1 ! Subject 6 a 5 ! a 5 Y 15 ! Y 65 Y . 5 e. t test for dependent samples with n = 7 Treat. Level Dep. Var. Treat. Level Dep. Var. Block 1 Block 2 Block 3 ! Block 7 a 1 a 1 a 1 ! a 1 Y 11 Y 21 Y 31 ! Y 71 a 2 a 2 a 2 ! a 2 Y 12 Y 22 Y 32 ! Y 7 2 Y . 1 Y . 2

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    Chapter 2 Experimental Designs: An Overview 5 f. RB-4 design with n = 6 Treat. Level Dep. Var. Treat. Level Dep. Var. Treat. Level Dep. Var. Treat. Level Dep. Var. Block 1 Block 2 Block 3 ! Block 6 a 1 a 1 a 1 ! a 1 Y 11 Y 21 Y 31 ! Y 61 a 2 a 2 a 2 ! a 2 Y 12 Y 22 Y 32 ! Y 62 a 3 a 3 a 3 ! a 3 Y 13 Y 23 Y 33 ! Y 63 a 4 a 4 a 4 ! a 4 Y 14 Y 24 Y 34 ! Y 64 Y 1 . Y 2 . Y 3 . ! Y 6 . Y . 1 Y . 2 Y . 3 Y . 4 g. CRF-222 design with n = 3 Treat. Comb. Dep. Var. Group 1 ! " # $ # Subject 1 Subject 2 Subject 3 a 1 b 1 c 1 a 1 b 1 c 1 a 1 b 1 c 1 Y 1111 Y 2111 Y 3111 Y .111 Group 2 ! " # $ # Subject 1 Subject 2 Subject 3 a 1 b 1 c 2 a 1 b 1 c 2 a 1 b 1 c 2 Y 1112 Y 2112 Y 3112 Y . 112 Group 3 ! " # $ # Subject 1 Subject 2 Subject 3 a 1 b 2 c 1 a 1 b 2 c 1 a 1 b 2 c 1 Y 1121 Y 2121 Y 3121 Y .121 ! ! ! Group 8 ! " # $ # Subject 1 Subject 2 Subject 3 a 2 b 2 c 2 a 2 b 2 c 2 a 2 b 2 c 2 Y 1222 Y 2222 Y 3222 Y . 222

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    Chapter 2 Experimental Designs: An Overview 6 h. LS-3 design with n = 3 Treat. Comb. Dep. Var. Group 1 ! " # $ # Subject 1 Subject 2 Subject 3 a 1 b 1 c 1 a 1 b 1 c 1 a 1 b 1 c 1 Y 1111 Y 2111 Y 3111 Y .111 Group 2 ! " # $ # Subject 1 Subject 2 Subject 3 a 1 b 2 c 3 a 1 b 2 c 3 a 1 b 2 c 3 Y 1123 Y 2123 Y 3123 Y . 123 Group 3 ! " # $ # Subject 1 Subject 2 Subject 3 a 1 b 3 c 2 a 1 b 3 c 2 a 1 b 3 c 2 Y 1132 Y 2132 Y 3132 Y . 132 Group 4 ! " # $ # Subject 1 Subject 2 Subject 3 a 2 b 1 c 2 a 2 b 1 c 2 a 2 b 1 c 2 Y 1212 Y 2212 Y 3212 Y . 212 ! ! ! Group 9 ! " # $ # Subject 1 Subject 2 Subject 3 a 3 b 3 c 1 a 3 b 3 c 1 a 3 b 3 c 1 Y 1331 Y 2331 Y 3331 Y . 331

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    Chapter 2 Experimental Designs: An Overview 7 8. d. RB-3 design with n = 14 Treat. Level Dep. Var. Treat. Level Dep. Var. Treat. Level Dep. Var. Block 1 Block 2 Block 3 ! Block 14 a 1 a 1 a 1 ! a 1 Y 11 Y 21 Y 31 ! Y 14, 1 a 2 a 2 a 2 ! a 2 Y 12 Y 22 Y 32 ! Y 14, 2 a 3 a 3 a 3 ! a 3 Y 13 Y 23 Y 33 ! Y 14, 3 Y 1 . Y 2 . Y 3 . ! Y 14 . Y . 1 Y . 2 Y . 3 e. t test for dependent samples with n 1 and n 2 = 50 Treat. Level Dep. Var. Treat. Level Dep. Var. Block 1 Block 2 Block 3 ! Block 50 a 1 a 1 a 1 ! a 1 Y 11 Y 21 Y 31 ! Y 50, 1 a 2 a 2 a 2 ! a 2 Y 12 Y 22 Y 32 ! Y 50, 2 Y . 1 Y . 2

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    Chapter 2 Experimental Designs: An Overview 8 f. CRF-62 design with n = 50 Treat. Comb. Dep. Var. Group 1 ! " # $ # Subject 1 ! Subject 50 a 1 b 1 ! a 1 b 1 Y 111 ! Y 50, 11 Y . 11 Group 2 ! " # $ # Subject 1 ! Subject 50 a 1 b 2 ! a 1 b 2 Y 112 ! Y 50, 12 Y . 12 Group 3 ! " # $ # Subject 1 ! Subject 50 a 2 b 1 ! a 2 b 1 Y 121 ! Y 50, 21 Y . 21 Group 4 ! " # $ # Subject 1 ! Subject 50 a 2 b 2 ! a 2 b 2 Y 122 ! Y 50, 22 Y . 22 ! ! ! Group 12 ! " # $ # Subject 1 ! Subject 50 a 6 b 2 ! a 6 b 2 Y 162 ! Y 50, 62 Y . 62

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    Chapter 2 Experimental Designs: An Overview 9 g. CR-3 design with n = 30 Treat. Level Dep. Var. Group 1 ! " # $ # Animal 1 ! Animal 30 a 1 ! a 1 Y 11 ! Y 30, 1 Y . 1 Group 2 ! " # $ # Animal 1 ! Animal 30 a 2 ! a 2 Y 12 ! Y 30, 2 Y . 2 Group 3 ! " # $ # Animal 1 ! Animal 30 a 3 ! a 3 Y 13 ! Y 30, 3 Y . 3 9. a. b. As the number of hours of deprivation increases, the difference in running time among the three reinforcement conditions decreases. 12. a. A scientific hypothesis is a testable supposition that is tentatively adopted to account for certain facts and to guide in the investigation of others. A statistical hypothesis is a statement about one or more parameters of a population or the functional form of a population. b. (i) Alternative hypothesis (ii) Null hypothesis 15. a. State the null and alternative hypotheses— H 0 : μ = 45, H 1 : μ ≠ 45. Specify the test statistic— t = ( Y ! μ 0 ) / ( ˆ " / n ) . Specify the sample size— n = 27, and the sampling distribution— t distribution. Specify the level of significance— α = .05. Obtain random 1 a 2 a 1 b 2 b 3 b 4 5 6 7 8 9 a 3 Running time (sec.) 10 hrs. 15 hrs. 20 hrs. Hours of deprivation 1 a 2 a 1 b 2 b 3 b 4 5 6 7 8 9 a 3 Running time (sec.) Small Medium Large Magnitude of reinforcement

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    Chapter 2 Experimental Designs: An Overview 10 samples of size n = 27, compute t , and make a decision. b. Reject the null hypothesis if t falls in either the lower or upper 2.5% of the sampling distribution of t ; otherwise, do not reject the null hypothesis. If the null hypothesis is rejected, conclude that the mean for children in the experimental program is not equal to the mean for ninth-graders who have been observed during the past several years; if the null hypothesis is not rejected, do not draw this conclusion. c. d. t = Y ! μ 0 ˆ " / n = 52.5 ! 45.0 15 / 27 = 7.5 2.89 = 2.60 , p = .015. The population mean for children in the experimental program was not equal to the mean for ninth-graders who have been observed during the past several years. The difference 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, 26 ˆ " n < μ < Y + t .05/2, 26 ˆ " n 52.5 ! 2.056(15) 27 < μ < 52.5 + 2.056(15) 27 46.6 < μ < 58.4 The researcher can be 95% confident that μ is greater than 46.6 or less than 58.4. The null hypothesis is not tenable. g. Y .05 = μ 0 + t .05/2, 26 ˆ ! n = 45 + 2.056(15) 27 = 50.935 t = Y .05 ! " μ ˆ # / n = 50.935 ! 52.5 15 / 27 = ! 1.565 2.887 = ! 0.54 TDIS(0.54,26,1) =.30 = ˆ ! ; 1 – ˆ ! =.70 Critical region ! = .025 Don't reject H 0 H 0 Reject t Critical region ! = .025 H 0 Reject f ( t )

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    Chapter 2 Experimental Designs: An Overview 11 h. True Situation μ = 45 ! μ = 52.5 Researcher’s μ = 45 Correct acceptance 1 – α = 1 – .05 = .95 Type II error ˆ ! = .30 Decision μ ≠ 45 Type I error α = .05 Correct rejection 1 – ˆ ! = 1 – .30 = .70 16. c. Correct rejection d. Correct acceptance e. Correct rejection f. Type I error 17. The power of an experiment can be increased by (1) adopting a lower level of significance, (2) increasing the size of the sample, (3) refining the experimental methodology so as to decrease the size of the population standard deviation, and (4) increasing the magnitude of the treatment effects considered worth detecting. Increasing the sample size is often the simplest way to increase power. The other ways of increasing power may lead to problems or may not be feasible. For example, the adoption of α > .05 may preclude the publication of the research. Refining the experimental methodology so as to decrease the size of the population standard deviation may be prohibitively expensive. Increasing the magnitude of the treatment effects considered worth detecting may not be appropriate. 18. a. State the null and alternative hypotheses— H 0 : μ 1 – μ 2 ≤ 0, H 1 : μ 1 – μ 2 > 0. Specify the test statistic— t = ( Y . 1 ! Y . 2 ) / ˆ " Pooled 2 1 n 1 + 1 n 2 # $ % & ' ( . Specify the sample size— n 1 = 24, n 2 = 23, and the sampling distribution— t distribution. Specify the level of significance— α = .05. Randomly assign N = 47 subjects to the two game types, compute t , and make a decision. b. Reject the null hypothesis if t falls in the upper 5% of the sampling distribution of t ; otherwise, do not reject the null hypothesis. If the null hypothesis is rejected, conclude that the risk-related cognitions of men who play racing video games is higher than that for the men who play the neutral games; if the null hypothesis is not rejected, do not draw this conclusion.

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    Chapter 2 Experimental Designs: An Overview 12 c. d. ! Pooled 2 = ( n 1 " 1) ! 1 2 + ( n 2 " 1) ! 2 2 ( n 1 " 1) + ( n 2 " 1) = (24 " 1)(1.3) 2 + (23 " 1)(1.2) 2 (24 " 1) + (23 " 1) = 1.568 t = ( Y . 1 ! Y . 2 ) / ˆ " Pooled 2 1 n 1 + 1 n 2 # $ % & ' ( = (7.54 ! 6.41) / 1.568 1 24 + 1 23 " # $ % & ' = 1.13 / 0.365 = 3.09 . The p value is less than .002. The mean risk-related cognitions for men who played the racing video games was higher than that for the men who played the neutral games. The difference between the means, 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 .05,45 ˆ " Pooled 2 1 n 1 + 1 n 2 # $ % & ' ( < μ 1 ! μ 2 (7.54 ! 6.41) ! 1.679 1.568 1 24 + 1 23 " # $ % & ' < μ 1 ! μ 2 0.52 < μ 1 – μ 2 The researcher can be 95% confident that μ 1 – μ 2 is greater than 0.52. The null hypothesis is not tenable. g. Y .05 = ! 0 + t .05,45 ˆ " Pooled 2 1 n 1 + 1 n 2 # $ % & ' ( = 0 + 1.679 1.568 1 24 + 1 23 ! " # $ % & = 0.613 t = Y .05 ! " # 0 ˆ $ Pooled 2 1 n 1 + 1 n 2 % & ' ( ) * = 0.613 ! 1.0 1.568 1 24 + 1 23 " # $ % & ' = ! 0.387 0.365 = ! 1.06 TDIS(1.06,45,1) =.15 = ˆ ! ; 1 – ˆ ! =.85 Critical region ! = .05 Don't reject H 0 H 0 Reject t f( t )

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    Chapter 2 Experimental Designs: An Overview 13 h. True Situation μ 1 – μ 2 = 0 ! μ 1 " ! μ 2 = 1.0 Researcher’s μ 1 – μ 2 ≤ 0 Correct acceptance 1 – α = 1 – .05 = .95 Type II error ˆ ! = .15 Decision μ 1 – μ 2 > 0 Type I error α = .05 Correct rejection 1 – ˆ ! = 1 – .15 = .85 19. c. p < .0005 d. p < .1048 20. c. t = 2.402 d. t = 3.601

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