A symptom validity test (SVT) is sometimes used to confirm diagnosis of psychiatric disorders. The paper “Developing a Symptom Validity Test for Posttraumatic Stress Disorder: Application of the Binomial Distribution” (Journal of Anxiety Disorders [2008]: 1297– 1302) investigated the use of SVTs in the diagnosis of post traumatic stress disorder. One SVT proposed is a 60 item test (called the MENT test), where each item has only a correct or incorrect response. The MENT test is designed so that responses to the individual questions can be considered independent of one another. For this reason, the authors of the paper believe that the score on the MENT test can be viewed as a binomial random variable with n = 60. The MENT test is designed to help in distinguishing fictitious claims of post traumatic stress disorder. The items on the test are written so that the correct response to an item should be relatively obvious, even to people suffering from stress disorders. Researchers have found that a patient with a fictitious claim of stress disorder will try to “fake” the test, and that the probability of a correct response to an item for these patients is 0.7 (compared to 0.96 for other patients). The authors used a normal approximation to the binomial distribution with n = 60 and p = 0.70 to compute various probabilities of interest, where x = number of correct responses on the MENT test for a patient who is trying to fake the test.
a. Verify that it is appropriate to use a normal approximation to the binomial distribution in this situation.
b. Approximate the following probabilities: i. P(x = 42) ii. P(x , 42) iii. P(x # 42)
c. Explain why the probabilities computed in Part (b) are not all equal.
d. The authors computed the exact binomial probability of a score of 42 or less for someone who is not faking the test. Using p = 0.96, they found P(x # 42) = .000000000013 Explain why the authors computed this probability using the binomial formula rather than using a normal approximation.
e. The authors propose that someone who scores 42 or less on the MENT exam is faking the test. Explain why this is reasonable, using some of the probabilities from Parts (b) and (d) as justification.