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Study of Linearity and Homoscedasticity of Test Scores in the Chance Range SAT

Boldt, Robert F.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Chance Level Scores, College Entrance Examinations, Guessing (Tests), Negative Scores, SAT, Scoring Formulas


A study was designed to test whether negative scores, i.e., scores in the "chance" range, have predictive value. To circumvent difficulties encountered in previous studies: 1) two tests measuring the same ability were used; 2) both tests measured the ability well over the upper range, but one test was sufficiently difficult to obtain a relatively large proportion of negative formula scores; 3) the examinees of lesser ability, who produced the negative formula scores on the difficult test, were well measured by the broad range (easy) test; and 4) both tests were administered to the same group of examinees. Both broad range and difficult test items were compiled from SAT-V and SAT-M items from the May 2, 1964 administration. Plots of the scores on both tests show a linear regression for the broad-range test but not for the difficult test. The array means in the chance range do differ, increasingly as the score on the difficult test increases. Hence the study establishes clearly that chance level scores should not be assumed to arise from purely random processes and therefore have predictive value. Expected criterion performances are not the same for people who score at different levels of the chance range. That equal increments in score on the difficult test do not imply equal increments in the broad range test means, in general, that the variance of the error of prediction is not the same in the chance as in the nonchance levels, with a regular decrease as the difficult test score increases. (JGL)

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