The Gold Medal in Olympic figure skating is awarded to the skater with the lowest median rank. Gold Medals in diving and gymnastics are awarded to contestants with the highest trimmed means. Both statistical techniques are attempts to reduce the influence that any one judge has on who wins the competition. The challenge is to increase fairness by counteracting judge bias.
Rasch measurement is a promising solution to this bias problem. It models skater ability to be independent of the judges' idiosyncrasies and the programs skated(technical and free skate). In other words, the skaters' ability measures are adjusted for unique characteristics of the program skated and the severity of the judges. Maverick (biased) ratings are flagged. Their influence on the measurement system can be determined by estimating skater ability measures with and without them. Substantive differences (e.g., in the awarding of medals) are immediately evident to decision makers.
In the 1994 Ladies event, 9 judges rated 27 skaters on each of two tasks (technical program and free skate). These ratings were rank ordered (as the current regulations require), and then the ranking structure was reanalyzed as a partial-credit rating scale. Rasch analysis (with the Facets computer program) produced measures, standard errors, and fit statistics for each skater, task and judge.
Rankings on the technical program (skated first) were considerably less predictable(Outfit mean-square: 1.3) than for the free skate (Outfit: 0.5). This is because the technical program is more difficult to judge. Nevertheless, of all 459 rankings, only 5 were noticeably unexpected, i.e., misfits. These occurred on the technical program when a poorer skater was ranked unexpectedly high by one judge.
Most judges exhibited a high degree of internal consistency (Outfit: 0.5 - 0.8), but the British and Canadian judges were more variable in their rankings than the others (Outfit: 1.2). In fact, there was a tendency toward too little variation in the rankings (Infits: 0.5). This was not surprising given the familiarity of the judges with the competitors, the experience level of the judges, and the psychological pressure on the judges not to disagree with each other.
The judges exhibited a marked lack of consensus for two only skaters, Zhao (Outfit:1.6) and Zemanova (Outfit: 1.7). The judges from Great Britain and the United States ranked Zhao (China) unexpectedly high on the technical program, and the Ukrainian judge ranked Zemanova (Czech Republic) unexpectedly high on both tasks. Consequently, the measures for Zhao and Zemanova may be inaccurately high. But this had no practical consequence because these skaters were not medal contenders.
Since most skaters' rankings fit the model, the skaters' ability measures constitute useful indicators of skating ability along the linear scale. According to these measures, the top three skaters in descending order were Kerrigan, Baiul and Chen. In fact, the Gold Medal was awarded to Baiul, the Silver to Kerrigan and the Bronze to Chen. This suggests that detecting and, only if necessary, correcting for bias (the Rasch approach) is fairer than assuming the existence of bias and using a statistical technique to attenuate its effects (the current approach).
Marilyn A. Looney
Dept of Physical Education
Northern Illinois University, Dekalb IL 60115-2854
Figure skating fairness. Looney M.A. Rasch Measurement Transactions, 1996, 10:2 p. 500
|Rasch Measurement Transactions (free, online)||Rasch Measurement research papers (free, online)||Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch||Applying the Rasch Model 3rd. Ed., Bond & Fox||Best Test Design, Wright & Stone|
|Rating Scale Analysis, Wright & Masters||Introduction to Rasch Measurement, E. Smith & R. Smith||Introduction to Many-Facet Rasch Measurement, Thomas Eckes||Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr.||Statistical Analyses for Language Testers, Rita Green|
|Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar||Journal of Applied Measurement||Rasch models for measurement, David Andrich||Constructing Measures, Mark Wilson||Rasch Analysis in the Human Sciences, Boone, Stave, Yale|
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