Dr. Zak Case Study Instructions Read the following case study. ✓ Solved

Dr. Zak Case Study Instructions Read the following case study.

Read the following case study. 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 for 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: 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 .5.

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. Justify your reason for each suggestion 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 you about the relationship between these two instruments?

Paper For Above Instructions

In the given case study, Dr. Zak's intention to measure depression through a test designed for university students introduces several critical considerations regarding the psychometric properties, sample size representation, and testing methodology. To answer the follow-up questions thoroughly, let's break them into discernible parts.

1. Calculating Standard Deviations for Sally

Sally scores 1.5 on Dr. Zak's test. To find out how many standard deviations she is from the mean, we use the formula:

Standard deviation = (Sally's score - Mean) / Standard Deviation

Standard Deviation = (1.5 - 3.5) / 0.5 = -4.0

This means that Sally is 4 standard deviations below the mean, indicating significantly lower depressive symptoms compared to the average tested.

2. Standard Score for Billy

Billy scores 5 on the same test. To calculate his standard score (Z-score):

Standard Score = (Billy's Score - Mean) / Standard Deviation

Standard Score = (5 - 3.5) / 0.5 = 3.0

Billy's standard score signifies that he is 3 standard deviations above the mean, reflecting significantly higher levels of happiness in this context.

3. Scale of Measurement

Dr. Zak employs a nominal scale of measurement since the responses to his questions are binary (Yes/No), indicating the presence or absence of depressive symptoms. Although this binary choice is simple, it may not capture the nuance of depressive experiences. A Likert scale could potentially enhance measurement fidelity by providing more gradation in responses (e.g., Strongly Agree to Strongly Disagree).

4. Sample Norming

The sample size of 100 students, comprising more women than men, raises questions about diversity and representativity. It might be inadequate for norming purposes due to its limited ethnic representation—only 11% being minorities. A broader and more diversified sample would allow for a more reliable generalization of the test across different demographics.

5. Domain Sampling Adjustments

To enhance the validity of Dr. Zak's test, additional items might focus on various aspects of depression not currently explored. For example, items assessing the influence of social interactions, physical health, and familial relationships could capture a more comprehensive picture of an individual's mental health status. A wider pool of items will allow for better content validity.

6. Suggested Test Improvements

To make the test robust, I suggest several changes:

  • Use of a Likert scale: Instead of simple Yes/No responses, using a 5-point scale can provide a nuanced understanding.

  • Increase item number: Adding questions targeting different symptoms, such as anxiety, fatigue, and mood fluctuations can improve measurement precision.

  • Incorporate validity checks: Including reverse-scored items can help in assessing response consistency and help mitigate response bias.

The justification lies in ensuring comprehensive assessment and the psychometric principles of reliability and validity, emphasizing that a more detailed inquiry will likely lead to a more accurate reflection of an individual’s mental health.

7. Correlation Evaluation

Dr. Zak’s test shows a correlation of r = 0.14 with the Beck Depression Inventory, which is considered weak. This suggests that these two instruments may be measuring different constructs, or that Dr. Zak's test has limited predictive validity regarding established measures of depression. Such a low correlation could be indicative of the limited range of symptoms assessed and calls for a critical re-evaluation of the test’s construct validity.

Overall, Dr. Zak’s test presents a foundational approach toward measuring depression among university students but would benefit from methodological rigor, enhanced representativity of the sample, and comprehensive psychometric assessment measures to ensure that it accurately reflects the target construct it aims to evaluate.

References

  • Beck, A. T., Steer, R. A., & Brown, G. K. (1996). The Beck Depression Inventory-II. Psychological Corporation.

  • Furr, R. M., & Bacharach, V. R. (2014). Psychometrics: An Introduction. Sage Publications.

  • American Psychiatric Association. (2013). Diagnostic and Statistical Manual of Mental Disorders (5th ed.). Arlington, VA: American Psychiatric Publishing.

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