Score Inflation due to Examinee Control of a Stopping Rule

Examinees like methods that improve their results without improving their performance. I tried one method myself on a recent administration of the Graduate Record Examination (GRE).

The GRE was computer-administered with the instruction that a minimum number of items must be answered. After that, the examinee could stop answering items at any point and let the time allotted for the examination run out. I tried a strategy identified by Slater and Schaeffer (1996):
After the minimum number of items have been answered, continue to answer items until you are fairly certain you will get the item on your computer screen wrong. Do not answer that item and let time expire.

This strategy is intended to increase the number of correct answers while holding the number of incorrect answers constant. Since an examinee's estimated measure is Reported measure = loge(Right/Wrong) + Average Item Difficulty, increasing the number of right answers increases the measure. Avoiding wrong answers prevents the measure from decreasing. This is called the Numerator Inflation Strategy (NIS). Does it work?

I took real response strings from a fixed-length 90 item CAT administration and implemented NIS perfectly with different minimum item response requirements. I truncated each response string just before the first wrong answer after the minimum number of responses. This produced two measures, one for the truncated string and one for the whole string. The Figure summarizes the results.

In the Figure, three representative performance levels are shown. Measures for those levels are at 0, 1 and 2 logits. The slightly sloped lines are average NIS measures for each of the three levels. In this example, when the minimum number of items required is very low (right side of Figure), and you know what you are doing, then you can, on average, raise your reported measure by about .1 logits above your overall measure. But when the minimum number of items is high (left side of Figure), then, on average, you will lower your reported measure by about .1 logits. The reason for these results is that avoiding a wrong answer on a short test raises your measure by minimizing the denominator of wrong answers. But on a long test, stopping just before the first wrong answer penalizes you because you no longer have the opportunity to improve your measure with a subsequent run of right answers.

In my case, employing the NIS strategy probably did me no good and may even have lowered my reported measure. But, for the marginally low performer willing to gamble, about 1% of the time the NIS strategy can raise your reported measure .2 logits or more - perhaps just enough to lift you above some crucial criterion value. I understand that, in light of this, GRE procedures have been modified.

Thomas O'Neill American Society of Clinical Pathologists 2100 W. Harrison St. Chicago IL 60612-3798

Slater SC, Schaeffer GA (1996) Computing scores for incomplete GRE general computer adaptive tests. Paper presented at NCME, New York.

Score inflation due to examinee control of a stopping rule. O'Neill T. … Rasch Measurement Transactions, 1996, 10:3 p. 522.

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