A Comparison of Three Methods of Computing Composite Scores
Edward F. Potthoff · The Journal of Educational Research · 1931
It is a well known fact that a variety of methods are now available for representing a pupil's attainment on a group of tests by means of a single composite score. The relationships which exist among various types of scores, however, are not always clearly understood. It is the purpose of this article to consider the nature of three types of scores, all of which are based upon the same test and involve the same group of students. The individuals concerned in this study consist of six hundred stu dents to whom was administered the 1924 edition of the Psychological Examination which is edited by the National Research Council. This Examination consists of nine separate tests, each of which yields its own score. The examination provides that a composite score be determined in the following manner. Percentile ranks are computed for each test so that each of the nine raw scores earned by a student may be con verted into its corresponding percentile rank. The median of the nine percentile ranks is then found, this median being used as a single index of attainment in the entire examination. A second method of computing a composite score is to find the total of the raw scores earned by an individual on the nine tests. Under this procedure the various tests have equal weights in determining the com posite score only when the variabilities of the tests are equal or approxi mately equal. The tests under consideration do not have equal varia bilities, however, since their standard deviations for the group studied range all the way from 3.34 to 18.65, this large range being due chiefly to the fact that perfect scores on these tests range from 15 to 150. A totaling of the raw scores on these tests does not, therefore, result in giving them all equal weights. A composite score which does give equal weights to all of the tests may be obtained by converting the raw or original score on each test into the corresponding standard score, and then finding the sum of the standard scores earned by an individual on the nine tests, the resulting total being used as a single index of attainment in the entire examination. 224