A behavioral psychologist is interested in whether goal-setting activities can be applied successfully in public school classrooms. The psychologist randomly selects 30 middle-schools students and...

Analysis of Covariance

1 question
6 parts

A behavioral psychologist is interested in whether goal-setting activities can be applied successfully in public school classrooms. The psychologist randomly selects 30 middle-schools students and randomly assigns them to three different groups that are assigned different levels of goal difficulty. The dependent variable is performance on a verbal-fluency task. Before the study each student is give a general-ability test, whose scores are used as the covariate. The data for this research scenario are given below. Conduct an analysis of covariance using these data and answer the following questions. Use an alpha = .05 for all statistical tests. The average verbal fluency score is 48.267. The average general ability score is 20.7. Group Verbal Fluency General Ability Group Verbal Fluency General Ability 1 42 16 2 50 20 1 40 16 2 62 23 1 48 19 2 60 24 1 55 24 2 48 21 1 45 20 2 47 20 1 51 22 3 46 20 1 47 20 3 47 21 1 38 23 3 43 19 1 46 20 3 54 26 1 45 18 3 49 21 2 51 25 3 44 25 2 50 18 3 53 24 2 45 17 3 52 23 2 52 19 3 42 18 2 47 17 3 49 22 1. Is the assumption of homogeneity of regression met for these data? What specific information did you use to come to this conclusion? (2 points) 2. Does the covariate, general ability, have a significant relationship to the dependent variable? What specific information did you use to come to this conclusion? (2 points) 3. Assuming that homogeneity of regression was met, are there differences in the mean verbal fluency of the three groups? What specific information did you use to come to this conclusion? (2 points) 4. Assuming you conclude that all three groups are not the same in verbal fluency, use a Bonferroni procedure to determine which of the groups differ. Conduct Cohen’s d standardized mean difference effect sizes for each of these pairwise differences. (4 points) 5. What proportion of variance in verbal fluency can be explained by the general ability and differences among the goal setting groups? What is the strength of association for the goal setting groups for participants that have the same general abilities? (4 points) 6. Write-up the results of your analysis in APA-format including a discussion of assumption testing, results of all statistical analyses, and effect size reporting (6 points).