Suppose a clinical psychologist working at a veteran’s hospital has been treatin

Question

Suppose a clinical psychologist working at a veteran’s hospital has been treating patients for depression for over 30 years. During this time, he has consistently measured their levels of depression at the end of their treatment on a well-established, widely-used, valid, and reliable scale. He knows based on various research already published using this depression scale that most depressed patients score an average of 150 on the scale . He also knows that the scale is scored to indicate levels of the severity of a patient’s depression. Specifically, patients who score less than 125 tend to experience few depression symptoms, if any. Patients who score 126-141 tend to experience slight depression symptoms; those who score 142-157 experience moderate symptoms of depression, and those who score 158 or more tend to experience severe, prolonged depressive symptoms.

Assuming his patients are a representative sample of the population, he compared his former clients’ scores (M = 147, SD = 35, N = 1180) at the end of their treatment to the scores of depressed patients in the general population. He wanted to use this information to support the effectiveness of his treatment and charge more for his services.

Please help me answer the following essay questions:

1. Describe the problem this psychologist is addressing from all relevant perspectives to demonstrate thorough understanding of the issue

2. Given the information in the problem, compute the appropriate statistical test to evaluate the psychologist’s hypothesis that patients who have been in his care are less depressed than those in the population. Then, calculate the effect size index for this test.

3. Interpret the results of the hypothesis test and the effect size computation, both in terms of their statistical significance and in terms of the effect size index. Explain the distinction between these statistics and the need for both a hypothesis test to examine potential treatment effects and the need for an effect size calculation.

4. Consider and explain the implications of each type of data considered (e.g., the implications of the treatment on patients’ lives in the context of population scores)

Explanation / Answer

Most depressed patients score an average of 150 on the scale scored to indicate levels of the severity of a patient’s depression.
score less than 125 tend to experience few depression symptoms
score 126-141 tend to experience slight depression symptoms
score 142-157 experience moderate symptoms of depression
score 158 or more tend to experience severe, prolonged depressive symptoms


clients’ scores (M = 147, SD = 35, N = 1180)

Average=150 so population mean of 150 is considered as indicative level of severity of a pateint's depression.

The null hypothesis for this test is that the mean depression score for the patients is the same as before, which is 150. The alternate hypothesis would be that the mean depression score had decreased, which would show that his treatment is effective.

Calculating, the z score for the sample.
z = (sample mean - population mean)/(SD / sqrt(n)).
The sample mean is 147, SD is 35, and N is 1180. The population mean is the 150.

z = (147-150)/(35 / sqrt(1180)) = -2.94

Corresponding to (z=-2.94) we get a p value of .0016.
Since we are doing a one tailed test, there is no need to multiply this by 2.
The p value is small, less than .05, so we can reject the null hypothesis at the .05 level. This gives us evidence to support our null hypothesis, so we can say that the treatment is effective.
The effect size, d is just |sample mean - population mean|/SD, so |147-150|/35 = 3/35 = .0857.

A one sample z test was done to test if the mean depression score for patients on a new treatment has decreased from 150. The sample yielded M=147,SD=35,N=1180, with z = -2.94, effect size d = .0857, and p = .0016. We reject the null hypothesis, and support the alternate hypothesis. The results are statistically significant; we can conclude that the treatment is effective in decreasing depression.

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