16. Studies show that groups of three people consistently outperformed the best of the individuals working alone on a letters to numbers substitution problem. The following data describe the number of trials needed to solve each problem for a sample of n = 15 groups and a sample of n = 15 individuals.
n = 15 n = 15
M = 3.8 M = 4.7
SS = 15.4 SS = 18.2
a. Make a point estimate of how much better groups perform than individuals for the general population. (Estimate the mean difference in the number of trials needed for a solution)
b. Make an interval estimate of the mean difference so that you are 95% confident that the true mean difference is in your interval.
c. Based on your answer to part b, what would be the decision from a hypothesis test evaluating the significance of the mean difference using a two tailed test with a alpha level = .05. Explain your answer.
16. Recent research indicates that the effectiveness of antidepressant medication is directly related to the severity of the depression. Based on the pre-treatment depression scores, patients were divided into four groups based on their level of depression. After receiving the antidepressant medication, depression scores were measured again and the amount of improvement was recorded for each patient. The following data are similar to the results of the study.
A. Do the data indicate significant differences among the four levels of severity? Test with a alpha level = .05.
B. Compute eta squared, the percentage of variance explained by the group differences.
Low moderate 0, 2, 2, 0
high moderate 1, 3, 2, 2
Moderately severe 4, 6, 2, 4
Severe 5, 6, 6, 3
G = 48
Ex(squared) = 204
M = 1 M = 2 M = 4 M = 5
T = 4 T = 8 T = 16 T = 20
SS = 4 SS = 2 SS = 8 SS = 6
The solution provides step by step method for the calculation of confidence interval for mean difference & ANOVA. Formula for the calculation and Interpretations of the results are also included.