William G. Mollenkopf

Variation of the standard error of measurement

As usually interpreted, the standard error of measurement is assumed to be constant throughout the test-score range. In this investigation the standard error of measurement was assumed to be not higher than a second-degree function of the test score. By conceiving a test score to be made up of the scores on two parallel tests, an equation was derived for predicting the standard error of measurement from the test score. In the derivation the corresponding first four moments of the score distributions for the parallel tests were assumed to be identical, and certain errors of estimate involved in predicting the second test score from the first were assumed to be uncorrelated with powers of the score on the first test. An empirical verification was carried out, using nine synthetic tests and a 1000-case sample, and showed good agreement between predicted and observed results. The findings indicated that the standard error of measurement was constant only for a symmetrical, mesokurtic distribution of scores.

An experimental study of the effects on item-analysis data of changing item placement and test time limit

Item-analysis data are usually obtained from a single test administration, with a given item sequence and time limit. Questions can be raised as to the effects upon item data resulting from changes in item-position and test-timing. In this study, two forms of a verbal test and two forms of a mathematics test were used. In each case, both forms of each test contained the same items, but items coming early in one form were placed late in the other. Each of these forms was administered once with a short time limit and once with generous timing to comparable groups of high school students. The relationships of various speed and power scores were determined, and the changes which occurred during the added time were studied. Values of the item indicesp (proportion right), Δ† (another difficulty index), and the item-test biserial correlation coefficient were obtained for both the speed and the power conditions and were systematically compared. The proportion right of those attempting the item, the Δ index, and the biserialr were all found to have undesirable characteristics for items appearing late in a speeded test.

VALIDITIES OF TESTS GIVEN IN 1950 FOR PREDICTING AVERAGE GRADES FOR THE FIRST TWO TERMS AT THE U. S. NAVAL POSTGRADUATE SCHOOL

In August 1950 nine aptitude and achievement tests constructed by the Educational Testing Service under an Office of Naval Research contract were given to the members of the incoming class at the U. S. Naval Postgraduate School. Two tests provided by the Research Division of the Bureau of Naval Personnel were also administered. Scores on these eleven tests have now been studied in relation to the quality-point ratios earned by officers in this class for their first two terms at the Postgraduate School. Bar charts are presented showing for each of four score intervals on each test what per cent of students achieved quality-point ratios of 2.0 or higher. In addition, product-moment coefficients of correlation between scores on each test and the criterion of quality-point ratios have been obtained. The most effective of the tests for predicting this criterion were the Mathematics Aptitude Test, the Advanced Mathematics Test, the Physical Science and Engineering Test, the Interpretation of Data Test, and the two BuPers tests: General Mathematics NAVPERS and General Physics NAVPERS. Results of the 1950 experimental tests were found to be highly consistent with those obtained from the 1948 and 1949 tests.

VALIDITIES OF TESTS GIVEN IN JULY 1948 FOR PREDICTING FIRST YEAR AVERAGE GRADES AT THE U. S. NAVAL POSTGRADUATE SCHOOL

Scores on the twenty aptitude and achievement tests administered in July 1948 to the incoming class at the U. S. Naval Postgraduate School have been related to the quality-point ratios of the officers in this class for their entire first year. Charts have been prepared showing for each of four score intervals on each test the percentage of students having such test scores who earned quality point ratios above 2.00. Also, product-moment coefficients of correlation between scores on each test and the criterion of quality-point ratios have been computed. Examination of the charts and consideration of the correlations presented in this report reveal that the tests which showed high relationships with the academic grades were those in mathematical aptitude end mathematical achievement, engineering, reading comprehension, and physics. It was concluded that a very premising start has been made on the task of developing a battery of tests suitable for use as part of the means of selecting students for the Naval Postgraduate School.

A COMPARISON OF ADMITTED AND NON‐ADMITTED GROUPS AT THE U. S. NAVAL POSTGRADUATE SCHOOL

In the fall of 1948 the five-part Naval Postgraduate School Aptitude Test Form WNPF was administered at shore installations and on ships to applicants for admission to the Postgraduate School. Test data for those later admitted to the School have now been compared with similar data for those who were not selected, to allow comparisons of the applicant and admitted groups and to estimate the effects of the present selection process on the magnitudes of the test validities being obtained in the experimental test-development program being carried on at the Postgraduate School. It was found that the greatest reduction in range of talent had occurred for the Mathematics Aptitude part of the test, and, as a consequence, that the validity of this part was most markedly affected by the selection process. Lesser effects were noted for the Beading Comprehension, Spatial Intersections, and Physics parts of the test. No reduction in range of talent was observed for the Verbal Antonyms part, and since it seems probable that the validity of this test is not seriously affected by the selection process, its observed low validity may be concluded not to be a result of rigorous selection on verbal ability. It was concluded that in the future interpretation of test validities, the fact must be taken into account that the present method of selection restricts the range of ability in mathematics aptitude somewhat more than in other areas. Observed validities for mathematics tests are therefore likely to have been lowered more by the selection process than those of other tests involved in the study.

PRELIMINARY REPORT ON THE SELECTION TEST DEVELOPMENT PROGRAM OF THE U. S. NAVAL POSTGRADUATE SCHOOL (JULY 1948 TESTING)

Statistical work not requiring the class grades of students has now been completed for the tests given in July 1948. Appreciable relationships were found between hours or lessons of refresher work and mathematics achievement test scores. Comparisons of the Postgraduate School results with those for College Entrance Examination Board candidates for five tests taken by both groups revealed the distinct superiority of the Postgraduate group. One verbal test had been given also to a Naval Academy entering class, and here again the average score for the Postgraduate group was markedly the higher of the two. Comparison of the Postgraduate School group with the 1947 freshman class at the Coast Guard Academy revealed that for three tests the groups were quite similar, while each group excelled the other on one of two other tests. The Postgraduate group was found to be markedly superior on the same tests, and on one other test, to a group of freshman liberal arts students at a large Eastern university. Comparisons of the test performances of six instructional groups at the Postgraduate School revealed only small differences among groups except for the Applied Communications group, which did not do nearly as well on certain of the tests as did the other groups, especially on tests in the quantitative area. The findings indicating the superiority of the Postgraduate School group over most of the other comparison groups point to the need for the study of the test performances of the total group of applicants. The group tested in July was a select one, and hence the present data cannot be used by themselves to decide upon the appropriate level of difficulty for future tests.