A clinical psychologist conducted a study comparing cognitive-behavioral therapy (CBT) and client-centered therapy (CCT). Participants were randomly assigned to a therapy condition. The psychologist is also interested in gender differences, so gender is included as a second factor in the design. However, the resultant cell sizes are somewhat unequal (reflecting sampling error and/or attrition, presumed to be random here). The following cell sizes and cell means are obtained: Notice that the mean score for CBT is 4 points higher than the mean for CCT for both females and males. Thus, our single best estimate is that CBT is, 4 points better than CCT. However, it may be important to know the margin of error in this estimate. The precision of the estimate is revealed by forming a confidence interval. We suppose throughout the remainder of this problem that mean square within (M5W) = 19. a. From we can see that the Type III sum of squares for the therapy main effect here is based on a contrast of the form Form a 95% confidence interval for •ft. Explain in one sentence what this interval means, b. From we can see that the Type II sum of squares for the therapy main effect is based on a contrast of the form Form a 95% confidence interval for the corresponding contrast that preserves the original metric of the dependent variable. c. Which contrast can be estimated more precisely, the one corresponding to Type III sum of squares or the one corresponding to Type II sum of squares? What does this result suggest about which type of sum of square is preferable when there is no true interaction. (Notice in these data that there is literally no interaction, even in the sample.) d. Some investigators would take an entirely different approach here. Instead of dealing with the nonorthogonal design, observations might be randomly deleted to produce 4 participants in each cell. Although the subsequent analysis is undoubtedly simpler, is there a cost associated with this approach? To answer this question, we again consider the precision of our estimated treatment effect. Suppose that after participants are randomly deleted, the data are as follows: Notice that the cell means and MS ware unchanged from their previous values, which is what we would expect in the long run when observations are randomly deleted. The therapy main effect is represented by the following contrast: Find a 95% confidence interval for this contrast. e. How does the confidence interval you found in part d compare to the intervals you found in Parts a and b? What does this result imply about the wisdom of randomly deleting observations to obtain an equal-n design?
We Write Essays for Students
Tell us about your assignment and we will find the best writer for your paper
Get Help Now!
PLACE THIS ORDER OR A SIMILAR ORDER WITH AMAZON PAPERS TODAY AND GET AN AMAZING DISCOUNT
The post What does this result imply about the wisdom of randomly deleting observations to obtain an equal-n design? appeared first on Wise Papers.
Welcome to originalessaywriters.com, our friendly and experienced essay writers are available 24/7 to complete all your assignments. We offer high-quality academic essays written from scratch to guarantee top grades to all students. All our papers are 100% plagiarism-free and come with a plagiarism report, upon request
Tell Us “Write My Essay for Me” and Relax! You will get an original essay well before your submission deadline.
