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# A test to measure depression

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CASE STUDY
Dr. Zak developed a test to measure depression. He sampled 100 university students to take his five item test. The group of students was comprised of 30 men and 70 women. In this group, four persons were African American, six persons were Hispanic, and one person was Asian. Zak's Miraculous Test of Depression is printed below:

1. I feel depressed: Yes No

2. I have been sad for the last two weeks: Yes No

3. I have seen changes in my eating and sleeping: Yes No

4. I don't feel that life is going to get better: Yes No

5. I feel happy most of the day: Yes No

Yes = 1; No = 0

The mean on this test is 3.5 with a standard deviation of 0.5.

The test developed by the hypothetical 'Dr. Zak' and administered to 100 students has some flaws in design. Discovering those flaws, confirming them mathematically, and commenting on possible improvements appear to be a part of the lesson plan. For example, each 'yes' equates to a '1' score, but only the first four out of the five questions might imply depression with a 'yes' answer. Further, number three provides an opportunity for ambiguity. Because of the design weaknesses of this test, it probably will not correlate favorably with the results of the well-designed BDI. Question 7 provides an r=.14 value for this correlation is requesting an evaluation of what this correlation value implies.

FOLLOW-UP QUESTIONS

1. Sally scores 1.5 on this test. How many standard deviations is Sally from the mean? (Show your calculations)

2. Billy scores 5. What is his standard score?

3. What scale of measurement is Dr. Zak using? Do you think Dr. Zak's choice of scaling is appropriate? Why or why not? What are your suggestions?

4. Do you think Dr. Zak has a good sample on which to norm his test? Why or why not? What are your suggestions?

5. What other items do you think need to be included in Dr. Zak's domain sampling?

6. Suggest changes to this test to make it better. For each suggestion justify your reason supporting each reason with psychometric principles from the text book or other materials used in your course.

7. Dr. Zak also gave his students the Beck Depression Inventory (BDI). The correlation between his test and the BDI was r =.14. Evaluate this correlation. What does this correlation tell us about the relationship between these two instruments?

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#### Solution Preview

1. Sally scores 1.5 on this test. How many standard deviations is Sally from the mean? (Show your calculations)

Ignoring the impossibility of getting a 1.5 on a whole number based scale, Sally is 2 points below the mean. With an SD of .5, this puts her 4 standard deviations below the mean. Assuming a normal distribution, she's quite the outlier.

Z = (1.5-3.5)/.5 = -2/.5 = - 4

2. Billy scores 5. What is his standard score?

When we standardize scores, we put them on a scale such that the mean is 100, with an SD of 15. Thus, a 3.5 would score as 100, and Billy's score of 5 (3 SD's above the mean) would score as 145.

Z = (5-3.5)/.5 = 1.5/.5 = 15/5 = 3
So the standardized score is 3.

3. What scale of measurement is Dr. Zak using? Do you think Dr. Zak's choice of scaling is appropriate? Why or why not? ...

#### Solution Summary

This solution is comprised of a detailed explanation on descriptive statistics, statistical tests, reported results and relationship between variables based on the cases study. All questions were answered based on the case study which are given in the description of the problem.

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## Development of a Test to Measure Depression

Dr. Zak Case Study
INSTRUCTIONS
Read the following case study. Then, use the information in the case study to answer the accompanying follow-up questions. Although questions 1-2 have short answers, you should prepare a 150 to 200-word response to each of the remaining questions.
CASE STUDY
Dr. Zak developed a test to measure depression. He sampled 100 university students to take his five item test. The group of students was comprised of 30 men and 70 women. In this group, four persons were African American, six persons were Hispanic, and one person was Asian. Zak's Miraculous Test of Depression is printed below:

The mean on this test is 3.5 with a standard deviation of .5.

1. Sally scores 1.5 on this test. How many standard deviations is Sally from the mean? (Show your calculations)

z= x-m / SD
z= 1.5-3.5/.5
z= .-2/.5
z= -0.4

2. Billy scores 5. What is his standard score?
z= x - m/ SD
.5= x-3.5/.5
.5*.5= x-3.5/.5*.5
.25=x-3,5
3.5+.25= x-3.5+3.5
3.75=x
3.75=t-score

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