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FIGURE 2.1. Lack of generalizability of individual differences in grades across the teacher and type of exam facet.

FIGURE 2.1. Lack of generalizability of individual differences in grades across the teacher and type of exam facet.

Lack of relative consistency always results from interactions among two or more facets of the data box. However, in the research world interactions are rarely as clear cut as our example. Usually, interactions are less systematic and smaller in size. Therefore, it is often difficult to measure the importance of an interaction. Ignoring an interaction increases parsimony but decreases precision. Taking interactions into account increases precision and decreases parsimony. This conflict between parsimony and precision remains a general dilemma in lay epis-temics, the sciences, and technology (Gigerenzer & Selten, 2001). Shannon and Weaver (1949) called it the bandwidth-fidelity-dilemma. Cronbach (1960) and Wiggins (1973) discussed its implications for psychological assessment and prediction. Several rules have suggested how to deal with this dilemma. One of these rules states that as long as differences between objects on one dimension vary only in size but not in sign across another dimension (ordinal interaction), aggregation is appropriate. According to this rule, aggregation is inappropriate whenever the sign of differences on one facet changes across another facet—as was the case in our example (disordinal interaction). However, this is only a rule of thumb. Whether or not aggregation is appropriate must be carefully considered and depends on research goals and practical purposes. In basic research, precision often presides over parsimony, whereas the opposite is true in applied contexts (Schmitt & Borkenau, 1992). Intelligence and achievement serve as typical examples. In applied contexts, a general IQ score or a grade point average may be sufficient for discriminating individuals (e.g., job applicants). In basic research, it is more useful to break down intelligence and achievement into specific components.

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