Reference no: EM132598364 , Length: 5 pages

Task One: ANCOVA

1. In this example, 3 tasks were employed to ascertain differences between good and poor undergraduate writers on recall and manipulation of information: an ordered letters task, an iconic memory task, and a letter reordering task. In the following table are means and standard deviations for the percentage of correct letters recalled on the three dependent variables. There were 15 participants in each group.

	Good writers		Poor writers
Task	M	SD	M	SD
Ordered letters	57.79	12.96	49.71	21.79
Iconic memory	49.78	14.59	45.63	13.09
Letter reordering	71.00	4.80	63.18	7.03

Consider this results section:

The data were analyzed via a multivariate analysis of covariance using the background variables (English usage ACT subtest, composite ACT, and grade point average) as covariates, writing ability as the independent variable, and task scores (correct recall in the ordered letters task, correct recall in the iconic memory task, and correct recall in the letter reordering task) as the dependent variables. The global test was significant, F(3, 23) = 5.43, p < .001. To control for experiment-wise type I error rate at .05, each of the three univariate analyses was conducted at a per comparison rate of .017. No significant difference was observed between groups on the ordered letters task, univariate F(1, 25) = 1.92, p > .10. Similarly, no significant difference was observed between groups on the iconic memory task, univariate F < 1. However, good writers obtained significantly higher scores on the letter reordering task than the poor writers, univariate F(1, 25) = 15.02, p < .001.
a. From what was said here, can we be confident that covariance is appropriate here?
b. The "global" multivariate test referred to is not identified as to whether it is Wilks' Λ, Roy's largest root, and so on. Would it make a difference as to which multivariate test was employed in this case?
c. The results mention controlling the experiment-wise error rate at .05 by conducting each test at the .017 level of significance. Which post hoc procedure is being used here?
d. Is there a sufficient number of participants for us to have confidence in the reliability of the adjusted means?

2. What is the main reason for using covariance analysis in a randomized study?

3. What statistical assumptions must be met to use Analysis of Covariance?

Task Two: MANOVA

1. An investigator has a 50-item scale and wishes to compare two groups of participants on the item scores. He has heard about MANOVA, and realizes that the items will be correlated. Therefore, he decides to do a two-group MANOVA with each item serving as a dependent variable. The scale is administered to 45 participants, and the investigator attempts to conduct the analysis. However, the computer software aborts the analysis. Why? What might the investigator consider doing before running the analysis?

2. Suppose you come across a journal article where the investigators have a three-way design and five correlated dependent variables. They report the results in five tables, having done a univariate analysis on each of the five variables. They find four significant results at the .05 level. Would you be impressed with these results? Why or why not? Would you have more confidence if the significant results had been hypothesized a priori? What else could they have done that would have given you more confidence in their significant results?

3. Consider the following data for a two-group, two-dependent-variable problem:

T1		T2
Y1	Y2	Y1	Y2
1	9	4	8
2	3	5	6
3	4	6	7
5	4
2	5

a. Compute W, the pooled within-SSCP matrix.
b. Find the pooled within-covariance matrix, and indicate what each of the elements in the matrix represents.
c. Find Hotelling's T2.
d. What is the multivariate null hypothesis in symbolic form?
e. Test the null hypothesis at the .05 level. What is your decision?

4. An investigator has an estimate of D 2 = .61 from a previous study that used the same four dependent variables on a similar group of participants. How many subjects per group are needed to have power = .70 at α = .10?

Task Three: Logistic Regression Analysis

1. Researchers are interested in identifying if completion of a summer individualized remedial program for 160 eighth graders (coded 1 for completion, 0 if not), which is the outcome, is related to several predictor variables. The predictor variables include student aptitude, an award for good behavior given by teachers during the school year (coded 1 if received, 0 if not), and age. Use these results to address the questions that appear at the end of the output.
For the model with the Intercept only: -2LL = 219.300
For the model with predictors: -2LL = 160.278

2. Complete the following:
a. Report and interpret the test result for the overall null hypothesis.
b. Compute and interpret the odds ratio for a 10-point increase in aptitude.
c. Interpret the odds ratio for the award variable.
d. Determine the number of outliers that appear to be present.
e. Describe how you would implement the Box-Tidwell procedure with these data.
f. Assuming that classification is a study goal, list the percent of cases correctly classified by the model, compute and interpret the proportional reduction in classification errors due to the model, and compute the binomial d test to determine if a reduction in classification errors is present in the population.

3. What statistical assumptions must be met to use logistic regression?

Attachment:- Logistic Regression Analysis.rar