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On the Statistical Treatment of Test Scores

Lord, Frederic M.
Publication Year:
Report Number:
ETS Research Memorandum
Document Type:
Page Count:
Subject/Key Words:
Humor, Psychometrics, Statistical Analysis, Test Analysis, Test Theory


Appearances to contrary notwithstanding, this memorandum represents an earnest attempt to dispel a popular "libel" on test scores and on most of the statistical work done with them. This "libel" within the past few years stood unchallenged when affirmed at length by members of a symposium on measurement at a meeting of the Eastern Psychological Association. According to this "libel," although we may actually calculate means, standard deviations, and product-moment correlations of test scores as a practical method of dealing with certain problems, it is, rigorously speaking, incorrect to draw conclusions from such parametric statistics, in view of the fact that test scores are at best ordinal and not cardinal numbers. Only nonparametric statistics such as the median, interquartile range, and rank order correlation may, according to this view, be used with rigorous justification in dealing with test scores. Presenting a fictional story of a fictional Professor selling football numbers and presuming the "libel" to be true, the author concludes that "when he has added together a sample of 1600 'football numbers' he finds that the resulting sum obeys the same laws of sampling as they would if they were real honest-to-God cardinal numbers."

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