A Survey of Observed Test-Score Distributions With Respect to Skewness and Kurtosis1

THE purpose of the present survey of data was to check em-pirically on two hypotheses: i. Easy tests tend to yield negatively skewed score distribu-tions; hard tests, positively skewed distributions. This hypothe-sis is so prevalent that references need not be cited. 2. Symmetric score distributions are ordinarily platykurtic. This conclusion has been reached from theoretical considerations by Keats (5) (a symmetric beta function is always platykurtic) and Lord (6, 7). The same conclusion has been reached from practical experience by Mollenkopf (8), by Conrad and by Tucker (both cited in 8, p. 214). The practical advantages of a platykurtic score distribution are cited by Ferguson (2) and by Jackson and Ferguson (4). It may be noted that these two hypotheses derive from a con-sideration only of the peculiarities of psychological tests used as measuring instruments; these hypotheses are not related to any supposed peculiarities of the group tested. Data The distributions of raw scores for 48 different tests in about I I different testing programs of the Educational Testing Service over a twelve-month period starting February 1952 were selected for study. All the raw-score distributions conveniently at hand for regular testings within this twelve-month period were used in the study providing that the number of cases (N) was at least 500,