1. What does the alternate hypothesis ask for a one-way between-subjects analysis of variance?

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1 1. What does the alternate hypothesis ask for a one-way between-subjects analysis of variance? 2. What is the difference between between-group variability and within-group variability? 3. What does between-group variability reflect? Where does it come from? 4. What does within-group variability reflect? Where does it come from? 5. When will the F ratio approach 1.00? When will the F ratio be greater than 1.00? 6. What is the difference between the sums of squares total, the sums of squares between-groups, and the sums of squares within-groups? How are they related? 7. Consider the scores in an experiment involving four levels of an independent variable. Without computing anything, what value must the sums of squares within-groups equal? Why? A B C D 8. State the critical value of F-Value for a oneway ANOVA under each of the following conditions. Note the n values are the number of subjects in each group (they are not n T): a. k = 3, n = 7, α =.01 b. k = 5, n =10, α =.01 c. k = 4, n = 5, α =.05 d. k = 6, n = 4, α =.05 e. k = 3, n = 10, α =.01 f. k = 2, n = 12, α =.05 g. k = 5, n = 15, α =.01 h. k = 4, n = 5, α = State the null and alternate hypotheses for a oneway ANOVA with 5 levels of the independent variable: 10. Insert the missing entries in the summary table for a one-way analysis of variance having four levels of the independent variable. Between Within Total 23

2 11. Insert the missing entries in the summary table for a one-way analysis of variance having three levels of the independent variable and n = 20. Between 25 Within 140 Total Insert the missing entries in the summary table for a one-way analysis of variance having three levels of the independent variable and n = 15. Between 2 10 Within 4 Total Insert the missing entries in the summary table for a one-way analysis of variance having seven levels of the independent variable and n = 32. Between Within Total 14. Assume you have an independent variable, A, with three levels (A 1, A 2, A 3). If you set α =.05, what is the Familywise Type I error rate after running all possible t-tests? 15. Assume you have an independent variable, A, with four levels (A 1, A 2, A 3, A 4). If you set α =.01, what is the Familywise Type I error rate after running all possible t-tests? 16. Assume you have an independent variable, A, with four levels (A 1, A 2, A 3, A 4). If you set α =.03, what is the Familywise Type I error rate after running all possible t-tests? 17. Assume you have an independent variable, A, with four levels (A 1, A 2, A 3, A 4). If you want your Familywise Type I error rate to be.05 after running all possible t-tests, what must the alpha level be set to for each test? 18. Assume you have an independent variable, A, with three levels (A 1, A 2, A 3). If you want your Familywise Type I error rate to be.02 after running all possible t-tests, what must the alpha level be set to for each test?

3 19. Use the following information to answer the questions below. A researcher studied the relationship between task difficulty and performance. Twenty subjects worked on an identical task, but five subjects were told that the task was of easy, five were told the task moderately difficult five were told that the task highly difficult, and five were given no information. Scores range from 0 to 10, where higher values indicate better task performance. The data follow: Easy Moderate High No Info a. Calculate the mean for each condition. b. Determine the degrees of freedom total, the degrees of freedom between groups, the degrees of freedom within groups. c. Calculate the sum of squares total, the sum of squares within groups, and the sum of square between groups. d. Calculate the mean within groups, and the mean square between groups. e. Calculate the F-Ratio. f. Assuming α =.05, what is the critical F-ratio? g. Is the result of the analysis of variance statistically significant? What decisions do we make with the null and alternate hypotheses? h. Analyze the nature of the relationship between supposed task difficulty and task performance using the Tukey HSD test. That is, calculate Tukey s HSD value and then use that value to determine which means are significantly different. i. Compute the value of eta-squared and then Cohen s f. Does the observed Cohen s f value represent a small, medium or large effect? 20. Use the following information to answer the questions below. An investigator tested the relationship between drug intake and anxiety. Eighteen subjects who had been diagnosed with anxiety were given a different level of an antianxiety drug (100 mg/day, 200 mg/day, or 300 ms/day). Each subject had the same baseline level of anxiety, and each subject s level of anxiety was re-measured after three months taking the drug. Scores range from 0 to 10, with higher values indicating more anxiety. The data follow: 100 mg/day 200 mg/day 300 mg/day a. Calculate the mean for each condition. b. Determine the degrees of freedom total, the degrees of freedom between groups, the degrees of freedom within groups.

4 c. Calculate the sum of squares total, the sum of squares within groups, and the sum of square between groups. d. Calculate the mean within groups, and the mean square between groups. e. Calculate the F-Ratio. f. Assuming α =.01, what is the critical F-ratio? g. Is the result of the analysis of variance statistically significant? What decisions do we make with the null and alternate hypotheses? h. Analyze the nature of the relationship between supposed task difficulty and task performance using the Tukey HSD test. That is, calculate Tukey s HSD value and then use that value to determine which means are significantly different. i. Compute the value of eta-squared and then Cohen s f. Does the observed Cohen s f value represent a small, medium or large effect? 21. Use the following information to answer the questions below. The bystander effect is the phenomenon where an individual is less likely to help a person when others are around. I examine the bystander effect among Boy Scouts. I randomly select 24 Boy Scouts and assign each to one of four groups. In each group the scout is seated at a table with my assistant, but the scout believes my assistant is another subject. While the scout and my assistant complete paperwork, my assistant falls out of his chair and I record the time (in seconds) it takes the scout to get help. I vary the number of people seated at the table. In Group A only the one scout and my assistant are present (one bystander); in Group B the scout, my assistant, and one other person are present (two bystanders); in Group C the scout, my assistant, and three others are present (four bystanders); and in Group D the scout, my assistant, and seven others are present (eight bystanders). The time, in seconds, it took each scout to get help are below. Group A (1 Bystander) Group B (2 Bystanders) Group C (4 Bystanders) Group D (8 Bystanders) a. Calculate the mean for each condition. b. Determine the degrees of freedom total, the degrees of freedom between groups, the degrees of freedom within groups. c. Calculate the sum of squares total, the sum of squares within groups, and the sum of square between groups. d. Calculate the mean within groups, and the mean square between groups. e. Calculate the F-Ratio. f. Assuming α =.01, what is the critical F-ratio? g. Is the result of the analysis of variance statistically significant? What decisions do we make with the null and alternate hypotheses? h. Analyze the nature of the relationship between supposed task difficulty and task performance using the Tukey HSD test. That is, calculate Tukey s HSD value and then use that value to determine which means are significantly different. i. Compute the value of eta-squared and then Cohen s f. Does the observed Cohen s f value represent a small, medium or large effect?

5 ANSWER KEY 1. The alternative hypothesis states that the population means in question are not equal to one another. 2. Between groups variability comes from the differences between the means of the groups being studied. Within group variability comes from the variability among the individual scores within each of the groups 3. Between groups variability reflects the differences between group means, that is, by how much the means groups differ between the groups. Between group variability can come from (a) sampling error, or (b) the manipulation/effect of some independent variable on the dependent variable. 4. Within groups variability reflects the differences among the scores within the groups of interest, that is, by how much scores in all the groups differ. Within group variability comes only from sampling error. 5. The F ratio will approach 1.00 when the null hypothesis is true. The F ratio will be greater than 1.00 when the null hypothesis is not true. 6. Sum of squares total is the total variation in the dependent variable across all individuals in the study. Sum of squares between is total variability between the means of the groups under study and reflects the amount of between group variability. Sum of squares within is the total variability within each group and reflects the within group variability. They are related because SS-Total = SS-Between + SS-Within 7. The sum of squares within must be equal to 0, because there is no variability within any one of the groups; all of the scores in each group are equal. 8. a. F α (2, 18) = 6.01 b. F α (4, 45) = 3.78 c. F α (3, 16) = 3.24 d. F α (5, 18) = 2.77 e. F α (2, 27) = 5.49 f. F α (1, 22) = 4.30 g. F α (4, 70) = 3.60 h. F α (3, 16) = H 0: μ A = μ B = μ C = μ D = μ E H 1: μ A μ B μ C μ D μ E 10. Between Within Total Between Within Total

6 Between Within Total Between Within Total α FW = α FW = α FW = α i = α i = a. M Easy = 7; M Mod = 5; M High = 3; M No = 5 b. df T 19; df B = 3; df W = 16 c. SS T = 62; SS W = 22; SS B = 40 d. MS B = ; MS W = e f g. The ANOVA shows a statistically significant difference between means. Thus, we reject the H 0 and accept H 1. h. HSD = Low vs. Moderate 7-5 = 2 Not Significant Low vs. High 7-3 = 4 Significant Low vs. No 7-5 = 2 Not Significant Moderate vs. High 5-3 = 2 Not Significant Moderate vs. No 5-5 = 0 Not Significant High vs. No 3-5 = 2 Not Significant Based on the Tukey s HSD value: Individuals were significantly better in the Low Difficulty group (7) than in the High Difficulty group (3). i. η 2 = 0.645; f = 1.348; large effect 20. a. M 100 = 7.5; M 200 = 6; M 300 = 1.5 b. df T = 17; df B = 2; df W = 15 c. SS W = 21; SS T = 138; SS B = 117 d. MS B = 58.5; MS W = 1.4 e. F =

7 f g. The ANOVA shows a statistically significant difference between means. Thus, we reject the H 0 and accept H 1. h. HSD = mg/day vs. 200 mg/day = 1.5 Not Significant 100 mg/day vs. 300 mg/day = 6 Significant 200 mg/day vs. 300 mg/day = 4.5 Significant Based on the Tukey s HSD value: Individuals had lower anxiety in the 300 mg/day group (1.5) than in the 200 mg/day group and the 100 mg/day group. i. η 2 = 0.848; f = 2.236; large effect 21. a. M A = 7; M B = 9; M C = 9; M D = 15 b. df T = 23; df B = 3; df W = 21 c. SS W = 94; SS T = 310; SS B = 216 d. MS B = 72; MS W = e. F = f g. The ANOVA shows a statistically significant difference between means. Thus, we reject the H 0 and accept H 1. h. HSD = A vs. B 7-9 = 2 Not Significant A vs. C 7-9 = 2 Not Significant A vs. D 7-15 = 8 Significant B vs. C 9-9 = 0 Not Significant B vs. D 9-15 = 6 Significant C vs. D 9-15 = 6 Significant i. η 2 = 0.697; f = 1.516; large effect.