Using a case study, this exercise will investigate the predictive validity of two different tests for selecting applicants to a university.

ABC College Case Study

Until now, selection of students at ABC College has relied solely on high school grades and recommendations from teachers. The college wants to require that in applying for admission, students take its own College Aptitude Test (CAT) and World Affairs Test (WAT). The CAT is a test of verbal comprehension, quantitative reasoning, and abstract thinking. The WAT covers knowledge of current events, political affairs, cultural and sports activities, and general information in recent history.

To demonstrate the predictive validity of these tests, the college admissions director administered the two tests to 40 high school students (all of these students planned to enroll at ABC College). Admissions decisions were made based on high school grades and recommendations from teachers (all 40 students who took both the CAT and WAT were admitted and enrolled). At the end of the year, the college admissions director obtained the college GPA of the 40 students who had taken the CAT and WAT tests.

1. Create a scatterplot of the relationship between CAT and GPA. Create a scatterplot of the relationship between WAT and GPA. Submit your scatterplots (you can use MS Excel to create the scatterplots)

2. Compute the correlation between the CAT and college GPA. Compute the correlation between WAT and college GPA. Report both correlations. Which test is the better predictor of GPA?

3. The College proposed to create cutoff scores for each of the tests to use as a factor in deciding whether or not to admit. A GPA of 2.00 will be used as the criterion cutoff score. 
They also decide to admit only those students with a CAT score of 500 or above in the future. Using these two cutoff scores, compute and report the number of true positives, false positives, true negatives, and false negatives. Also, report the percentage of correct decisions using these cutoffs.

4. In general, what could be done to raise the rate of "true positives" and "true negatives"?

5. In general, what could be done to reduce the rate of "false positives"? What could be done to reduce the rate of "false negatives"? (Assume that our cutoff score for success - GPA of 2.00 - is fixed and cannot be changed)

6. a. Now compute the correlation between CAT and GPA, but only for those individuals who scored 600 and above on the CAT. What is the correlation?

b. Compute the correlation between CAT and GPA, but only for those individuals who received a GPA of 2.00 or better. What is the correlation?

7. Why is the correlation for CAT and GPA that you computed for 6a and 6b lower than the correlation you computed for CAT and GPA in Question 2?