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Abstract:
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Statisticians may be tempted to ignore ambiguity in problem definition for the sake of convenience or to avoid conflict with those whom we are engaged in collaborative efforts. But problem definition can have dramatic effects on the results of analysis. For example, consider academic undermatching, which refers to the situation in which a student enrolls in a college that is less selective than the college for which he or she is academically prepared. Higher education researchers wish to identify characteristics of students that might predict undermatching, and to relate demographic variables to the occurrence of undermatching. But, undermatching is not a concept free from ambiguity. We show that seemingly minor changes in how undermatching is defined can have large impacts on both which students are considered to be undermatched, and determining associations of demographic variables to undermatching. In this area of educational research, problem definition ought to be recognized as being of equal if not greater importance to the statistical methods used in an analysis.
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