A continuing practical problem in rating performances is eliminating ambiguity introduced by deficient judging plans. A recent conference aired data in this form:
Judge A Judge B Items: P Q R P Q R Person: Task X 101 2 2 1 3 1 2 102 3 2 2 103 2 3 2 2 3 2 104 4 3 3 3 3 3 Task Y 201 3 2 3 202 3 3 3 2 2 2 203 4 3 3 204 4 4 3 3 3 4
At first glance, all seems well. The three items, P, Q, R, can be in one frame of reference, because they share the same judge-person-task combinations. The two judges, A, B, can be in the same frame of reference, because they rate every second person together. Now comes the problem. The persons seem to share the same frame of reference because so many of them are rated on the same tasks. But there are two tasks. Why are the four 100-group people rated lower on Task X than the four 200-group people on Task Y? Are the 100-group people less able than the 200-group? Is Task X is harder than Task Y? These data cannot say which!
Resolving this ambiguity requires perception and decision. The first step is to notice the problem. If you detect it during data collection, a slight change to the judging plan can remedy the situation. For instance, some people could be asked to perform both tasks. Nevertheless, continue to be on the look out for this ambiguity during analysis. Many statistical procedures fail to report it, and so may produce misleading results.
There are only two choices for resolving this issue: either the tasks are said to be alike or the people are said to be alike. If Task X and Task Y were intended to have the same difficulty, and that still seems a reasonable assertion, then anchor them together at the same calibration. This resolves the ambiguity, and interprets the overall score difference between the 100-group and the 200-group of persons as a difference in ability levels.
On the other hand, you may have intended that the tasks be different by an amount unknown as yet. Then the only solution is to treat the two groups of persons as though they estimate the same mean ability. Specify the analysis to set the mean ability level of the 100-group at the same value as the mean ability level of the 200-group. Now the overall score difference between the 100-group and the 200-group will express a difference in difficulty between Task X and Task Y.
This type of ambiguity is common. It is seen in data where supervisors rate their own trainees. Do good ratings signify good trainees or a lenient rater? It is wise to try both options. First analyze the data as though the supervisors rated equally strictly, then analyze the data as though the groups of trainees were of the same average ability. A comparison of the two analyses frequently implies that the trainees are rather similar (particularly if they are at the end of regular training), but that the supervisors' rating styles are rather different. Who your supervisor is may turn out to be more important than what you accomplish.
Juggling Judging Ambiguity, J Linacre Rasch Measurement Transactions, 1991, 5:3 p. 167
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