Explaining Discrepancies between the Sum of Subtest Scale-Scores and Total Scale-Scores

When high-stakes examinations are administered, examinees are keenly interested in the accuracy of their test scores, especially when their scores are close to, but below, the pass/fail cutpoint. When exam blueprints are available that outline various content percentages, test-takers will often attempt to reverse engineer their score reports in such a way that they can evaluate the extent to which the sum of their subtest scores is congruent with the overall test score. In some instances, the weighted sum of the subtest scores will be higher than the total score. This discrepancy may give test-takers a seemingly legitimate reason to question the accuracy of the overall score, thus prompting a phone call to the Examiners.

Fortunately, much of the problem can be easily explained as simply due to the range of the reported scale. For instance, if scores are reported on a scale that ranges from 200 to 800, extreme scores (<200 or >800) will be reported as either 200 or 800. Typically, this is the reason for the discrepancy. Examinees, however, will likely be unaware that the actual scale extends beyond the reported range. Therefore, when asked for assistance in interpreting scores, it is helpful to immediately ask if the examinee had any extreme scores on any of the subtests. If the answer is "yes" (and usually it is), the aforementioned explanations should suffice for the inquiring test-taker. For instance, if the pass-fail score is 500, and three equally weighted sub-scores are 700, 600, 200, then is looks like the total score should be 500 (a pass), but, in fact, it may be reported as 490 (a fail), because the reported 200 corresponds to an actual 170..

Issues of reported-score granularity, such as reporting by rounded increments of 5 or 10 may also contribute to a discrepancy. So that reported sub-scale scores of 600, 500, 400 (apparently averaging 500) may actually be 597, 497, 397 producing a rounded total score of 495.

On the other hand, if extreme scores and rounding are not the culprits, then it is helpful to have Wright (1994) and sometimes Bowles (1999) readily available to assist with explaining the technical aspects of the phenomenon in excruciating detail. Usually, the caller does not really care about the mechanics of subtest scoring, but merely wishes to argue his/her case for passing. Having the detailed and technical answer ready for discussion will usually dissuade callers from continuing down that path and hopefully will allow them to refocus on questions that are more salient to their future success on the examination.

Kenneth D. Royal & Thomas R. O'Neill
American Board of Family Medicine

Bowles, R. (1999). Combining and dropping subtest measures. Rasch Measurement Transactions, 13(1), p. 686. www.rasch.org/rmt/rmt131f.htm

Wright, B. (1994). Combining part-test vs whole-test measures. Rasch Measurement Transactions, 8(3), p. 376. www.rasch.org/rmt/rmt83f.htm

Explaining Discrepancies between the Sum of Subtest Scale-Scores and Total Scale-Scores, Kenneth D. Royal & Thomas R. O'Neill ... Rasch Measurement Transactions, 2011, 25:3, 1338

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