Week 8 Homework 10. If an experiment is conducted with 5 conditions and 6 subjects in each condition, what are dfn and dfe? 17. The following data are from a hypothetical study on the effects of age and time on scores on a test of reading comprehension. Compute the analysis of variance summary table. Treatment Effects of a Drug on Cognitive Functioning in Children with Mental Retardation and ADHD for questions 28 and 29 OVERVIEW This study investigated the cognitive effects of stimulant medication in children with mental retardation and Attention-Deficit/Hyperactivity Disorder. This case study shows the data for the Delay of Gratification (DOG) task. Children were given various dosages of a drug, methylphenidate (MPH) and then completed this task as part of a larger battery of tests. The order of doses was counterbalancedso that each dose appeared equally often in each position. For example, six children received the lowest dose first, six received it second, etc. The children were on each dose one week before testing. This task, adapted from the preschool delay task of the Gordon Diagnostic System (Gordon, 1983), measures the ability to suppress or delay impulsive behavioral responses. Children were told that a star would appear on the computer screen if they waited \"long enough\" to press a response key. If a child responded sooner in less than four seconds after their previous response, they did not earn a star, and the 4-second counter restarted. The DOG differentiates children with and without ADHD of normal intelligence (e.g., Mayes et al., 2001), and is sensitive to MPH treatment in these children (Hall & Kataria, 1992). QUESTIONS TO ANSWER Does higher dosage lead to higher cognitive performance (measured by the number of correct responses to the DOG task)? DESIGN ISSUES This is a repeated-measures design because each participant performed the task after each dosage. DESCRIPTIONS OF VARIABLES VARIABLE DESCRIPTION d0 d15 d30 d60 Number of correct responses after taking a placebo Number of correct responses after taking .15 mg/kg of the drug Number of correct responses after taking .30 mg/kg of the drug Number of correct responses after taking .60 mg/kg of the drug 28. (AT) The dataset ADHD Treatment has four scores per subject. a. Is the design between-subjects or within-subjects? b. Create an ANOVA summary table. 29. (AT) Using the Anger Expression Index from the Angry Moods study as the dependent variable, perform a 2x2 ANOVA with gender and sports participation as the two factors. Do athletes and non-athletes differ significantly in how much anger they express? Do the genders differ significantly in Anger Expression Index? Is the effect of sports participation significantly different for the two genders? Use the following information to answer the next three exercises. Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses. = S2 = Northeast 16.3 16.1 16.4 16.5 ________ ________ South 16.9 16.5 16.4 16.2 ________ ________ West 16.4 16.5 16.6 16.1 ________ ________ Central 16.2 16.6 16.5 16.4 ________ ________ H0: 1 = 2 = 3 = 4 = 5 H: At least any two of the group means 1, 2, ..., 5 are not equal. 61. degrees of freedom - numerator: df(num) = _________ 63. F statistic = ________ East 17.1 17.2 16.6 16.8 ________ ________ 69. A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same. CNN 45 12 18 38 23 35 FOX 15 43 68 50 31 22 LOCAL 72 37 56 60 51 Suppose that Table 13.24 shows the results of a study. Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05. 71. Are the mean number of times a month a person eats out the same for whites, blacks, Hispanics and Asians? Suppose that Table 13.26 shows the results of a study. WHITE 6 8 2 4 6 BLACK 4 1 5 2 HISPANIC 7 3 5 4 6 ASIAN 8 3 5 1 7 Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05. 77. A grassroots group opposed to a proposed increase in the gas tax claimed that the increase would hurt working-class people the most, since they commute the farthest to work. Suppose that the group randomly surveyed 24 individuals and asked them their daily one-way commuting mileage. The results are as follows. WORKING CLASS 17.8 26.7 49.4 9.4 65.4 PROFESSIONAL (MIDDLE INCOME) 16.5 17.4 22.0 7.4 9.4 PROFESSIONAL (WEALTHY) 8.5 6.3 4.6 12.6 11.0 47.1 19.5 51.2 2.1 6.4 13.9 28.6 15.4 9.3 Determine whether or not the variance in mileage driven is statistically the same among the working class and professional (middle income) groups. Use a 5% significance level. 81. Is the variance for the amount of money, in dollars, that shoppers spend on Saturdays at the mall the same as the variance for the amount of money that shoppers spend on Sundays at the mall? Suppose that the Table 13.34 shows the results of a study. SATURDAY 75 18 150 94 62 73 SUNDAY 44 58 61 19 99 60 89 SATURDAY 62 0 124 50 31 118 SUNDAY 137 82 39 127 141 73 Week 8 Homework 10. If an experiment is conducted with 5 conditions and 6 subjects in each condition, what are dfn and dfe? 17. The following data are from a hypothetical study on the effects of age and time on scores on a test of reading comprehension. Compute the analysis of variance summary table. 30 min 60 min 12 years old 66 68 59 72 46 69 61 69 73 61 16 years old 74 71 67 82 76 95 92 95 98 94 Treatment Effects of a Drug on Cognitive Functioning in Children with Mental Retardation and ADHD for questions 28 and 29 OVERVIEW This study investigated the cognitive effects of stimulant medication in children with mental retardation and Attention-Deficit/Hyperactivity Disorder. This case study shows the data for the Delay of Gratification (DOG) task. Children were given various dosages of a drug, methylphenidate (MPH) and then completed this task as part of a larger battery of tests. The order of doses was counterbalancedso that each dose appeared equally often in each position. For example, six children received the lowest dose first, six received it second, etc. The children were on each dose one week before testing. This task, adapted from the preschool delay task of the Gordon Diagnostic System (Gordon, 1983), measures the ability to suppress or delay impulsive behavioral responses. Children were told that a star would appear on the computer screen if they waited \"long enough\" to press a response key. If a child responded sooner in less than four seconds after their previous response, they did not earn a star, and the 4-second counter restarted. The DOG differentiates children with and without ADHD of normal intelligence (e.g., Mayes et al., 2001), and is sensitive to MPH treatment in these children (Hall & Kataria, 1992). QUESTIONS TO ANSWER Does higher dosage lead to higher cognitive performance (measured by the number of correct responses to the DOG task)? DESIGN ISSUES This is a repeated-measures design because each participant performed the task after each dosage. DESCRIPTIONS OF VARIABLES VARIABLE d0 d15 d30 d60 DESCRIPTION Number of correct responses after taking a placebo Number of correct responses after taking .15 mg/kg of the drug Number of correct responses after taking .30 mg/kg of the drug Number of correct responses after taking .60 mg/kg of the drug 28. (AT) The dataset ADHD Treatment has four scores per subject. a. Is the design between-subjects or within-subjects? b. Create an ANOVA summary table. 29. (AT) Using the Anger Expression Index from the Angry Moods study as the dependent variable, perform a 2x2 ANOVA with gender and sports participation as the two factors. Do athletes and non-athletes differ significantly in how much anger they express? Do the genders differ significantly in Anger Expression Index? Is the effect of sports participation significantly different for the two genders? Use the following information to answer the next three exercises. Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses. Northeast 16.3 16.1 South 16.9 16.5 West 16.4 16.5 Central 16.2 16.6 East 17.1 17.2 16.4 16.5 ________ ________ = S2 = 16.4 16.2 ________ ________ 16.6 16.1 ________ ________ 16.5 16.4 ________ ________ 16.6 16.8 ________ ________ H0: 1 = 2 = 3 = 4 = 5 H: At least any two of the group means 1, 2, ..., 5 are not equal. 61. degrees of freedom - numerator: df(num) = _________ 63. F statistic = ________ 69. A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same. CNN 45 12 18 38 23 35 FOX 15 43 68 50 31 22 LOCAL 72 37 56 60 51 Suppose that Table 13.24 shows the results of a study. Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05. 71. Are the mean number of times a month a person eats out the same for whites, blacks, Hispanics and Asians? Suppose that Table 13.26 shows the results of a study. WHITE 6 8 2 4 6 BLACK 4 1 5 2 HISPANIC 7 3 5 4 6 ASIAN 8 3 5 1 7 Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05. 77. A grassroots group opposed to a proposed increase in the gas tax claimed that the increase would hurt working-class people the most, since they commute the farthest to work. Suppose that the group randomly surveyed 24 individuals and asked them their daily one-way commuting mileage. The results are as follows. WORKING CLASS 17.8 26.7 49.4 9.4 65.4 47.1 19.5 51.2 PROFESSIONAL (MIDDLE INCOME) 16.5 17.4 22.0 7.4 9.4 2.1 6.4 13.9 PROFESSIONAL (WEALTHY) 8.5 6.3 4.6 12.6 11.0 28.6 15.4 9.3 Determine whether or not the variance in mileage driven is statistically the same among the working class and professional (middle income) groups. Use a 5% significance level. 81. Is the variance for the amount of money, in dollars, that shoppers spend on Saturdays at the mall the same as the variance for the amount of money that shoppers spend on Sundays at the mall? Suppose that the Table 13.34 shows the results of a study. SATURDAY 75 18 150 94 62 73 SUNDAY 44 58 61 19 99 60 89 SATURDAY 62 0 124 50 31 118 SUNDAY 137 82 39 127 141 73