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Use of the Logistic Model as an Alternative to Linear Interpolation for Computing Percentile Rank

Marco, Gary Lee.
Publication Year:
Report Number:
ETS Research Memorandum
Document Type:
Page Count:
Subject/Key Words:
Law School Admission Test (LSAT), Mathematical Models, Percentage, Scores, Scoring Formulas


A method of interpolation has been derived that should be superior to linear interpolation in computing the percentile ranks of test scores for unimodal score distributions. The superiority of the logistic interpolation over the linear interpolation is most noticeable for distributions consisting of only a small number of score intervals (say fewer than 10) particularly distributions that are relatively unskewed. Logistic interpolation thus should be useful in practical situations in which percentile ranks of number right scores must be estimated from very coarse groupings. The logistic method may also be applied to distributions of formula scores. However, the method should probably not be used for unsmoothed distributions of formula scores unless it is desired to smooth out the peaks and valleys that result from rounding scores to integer values. The usefulness of logistic interpolation in computing percentile ranks for test score distributions is illustrated using three score distributions for item analysis samples from 1974 Law School Admission Test (LSAT).

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