1) Use the HCA-CCPROX (conditional covariance based cluster analysis) routine and the MDS-CCPROX (multidimensional scaling) to examine the dimensional structure of the test. Briefly describe how well the recovered pattern matches the exams paragraph structure. What is the probablility that the four paragraphs would be recovered perfrectly if the clusters were just formed randomly?

2) Use Mokken scaling with a minimum value of 0.3 to examine the dimensional structure of the test. Briefly describe how well the recovered clusters match the exams paragraph structure. Suggest a reason that some of the items may have been included/excluded in the recovered clusters. (Hint: At least one of the classic item statistics or one of the IRT item parameters would help.)

1) Use BILOG to estimate the 3PL item and ability parameters for read1.dat. Give the .BLM file, the first items estimated parameters, and the first examinee's estimated ability.
2) Use PARSCALE to estimate the generalized partial credit model item and ability parameters for read2.dat. Give the .PSL file, the first items estimated parameters, and the first examinee's estimated ability.
3) Plot the two sets of ability estimates against each other and report their correlation coefficient.

1) Estimate the lower bound on the reliability for this administration of the exam. What do the traditional reliability guidelines say about using this test for placing students into their first math course in college?

2) Briefly explain why your "lower bound" estimate for reliability of this administration might actually be too high if you want to use it for future years as well? (It has nothing to do with using estimates in the formulas.)

3) On average, how accurate are the scores on this exam? (Give an estimate.)

4) Give an estimate of how long the exam would need to be in order to achieve an estimated reliability of 0.9. (Hint: Don't get caught up in thinking one of the formulae needs an integer.)

5) Give an estimate of the SEM for this extended exam from question 4. You may make some simplifying assumptions (within reason) to help you estimate what var(x) would be as long as you say what extra assumptions you are making. (Hint: mean(cor(math)[upper.tri(cor(math))]) will give the average correlation between all of the item pairs. The apply, var, and sd functions may also be useful.)

6) Find the 95 % X+zSEM type interval estimate of the true score for an examinee with an observed score of 2. What flaw in this type of interval is demonstrated here?

7) Identify the easiest and hardest items on the exam.

8) Consider items 10, 11 and 21. Which one of these items do you think would work best at determining which students are placed into an honors section? Briefly justify your answer.

9) Briefly describe what you think are a reasonalbe set of steps for splitting this exam into two roughly parallel subtests of equal length. (You do not need to do it!)