Statistics - ANOVA Projects

A clinical psychologist has noted that autistic children seem to respond to treatment better if they are

Problem: A clinical psychologist has noted that autistic children seem to respond to treatment better if they are in a familiar environment. To evaluate the influence of environment, the psychologist selects a group of 115 autistic children who are currently in treatment and randomly divides them into three groups. One group continues to receive treatment in the clinic as usual. For the second group, treatment sessions are conducted entirely in the child's home. The third group gets half of

the treatment in the clinic and half at home. After 6 weeks, the psychologist evaluates the progress for each child. The data are as follows:

Clinic Home Both

1 4 4

1 7 1

5 4 2

2 6 2

2 5 3

State the hypotheses both symbolically and narratively. Discuss each assumption and test those you can.

Present your results in two tables: a table of means and standard deviations by group and an analysis of variance summary table.

Discuss statistical significance and practical significance. Use the appropriate post hoc test. State your conclusions.

Problem: Two types of outdoor paint, enamel and latex, were tested to see how long (in months) each lasted before it began to crack, flake, and peel. They were tested in four geographic locations in the United States to study the effects of climate on the paint. At a = .05, analyze the data shown, using a two-way ANOVA. Each group contained five test panels. Discuss hypotheses, assumptions, significance (statistical and practical), necessary tables, and conclusions.

A school principal traces reading comprehension scores on a standardized test for a random sample of dyslexic students across three years. The data are given below. Complete the ANOVA, using a = .05.

Student Grade

Third Fourth Fifth

1 2.8 3.2 4.5

2 2.6 4.0 5.1

3 3.1 4.1 5.0

4 3.6 4.9 5.6

5 2.4 3.1 4.4

6 2.4 3.1 3.9

7 3.2 3.8 4.3

8 3.0 3.6 4.4

Analyze the data as discussed in the course. Include hypotheses in narrative form, assumptions, ANOVA table, and practical significance. Provide a concluding statement for your results.

Exam Problem 4 Nonparametric

A researcher in a counseling center is interested in whether different counseling methods may influence the number of times a patient makes negative comments about him/herself in therapy sessions. The desire is to reduce the number of such negative comments. Thirty-six patients are randomly assigned to one of the four counseling methods. Following are the results.

Method 3 Method 4

8 10 3 4

10 2 17 2

4 8 4 2

3 6 13 4

6 3 20 3

5 12 25 2

6 7 12 5

6 4 14 1

5 6 27 2

Conduct tests of the hypotheses of interest using SPSS® and provide a write-up which includes all of the following:

State appropriate omnibus F test and follow-up hypotheses narratively