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

Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. George Engelhard, Jr. & Jue Wang	Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene	Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver	Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone	Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	Statistical Analyses for Language Testers (Facets), Rita Green	Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind	Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind	Rasch Measurement: Applications, Khine	Winsteps Tutorials - free Facets Tutorials - free	Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre	Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan
Other Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free	An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse	Rasch Measurement Theory Analysis in R, Wind, Hua	Applying the Rasch Model in Social Sciences Using R, Lamprianou	El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar	Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch	Rasch Models for Measurement, David Andrich	Constructing Measures, Mark Wilson	Best Test Design - free, Wright & Stone Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias	Diseño de Mejores Pruebas - free, Spanish Best Test Design	A Course in Rasch Measurement Theory, Andrich, Marais	Rasch Models in Health, Christensen, Kreiner, Mesba	Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen

Forum

Rasch Measurement Forum to discuss any Rasch-related topic

Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement

Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website, www.rasch.org.

The URL of this page is www.rasch.org/rmt/rmt253f.htm

Website: www.rasch.org/rmt/contents.htm