Harold Gulliksen

Regression tests for several samples

In many situations it is desirable or necessary to administer a set of tests to several different groups, and to ask if the results obtained in the different groups may be regarded as being essentially the same in some sense. In the case of two variables (one dependent and one independent) one may, for instance, ask if the errors of estimate and the regression lines may be regarded as being the same for the populations from which the different groups are drawn. For this case, the present article considers tests for three hypotheses regarding the populations from which the different groups are drawn: (a)HA, the hypothesis that all standard errors of estimate are equal; (b)HB, the hypothesis that all regression lines are parallel, (assumingHA); and (c)HC, the hypothesis that the regression lines are identical, (assumingHB). Test criteria for these three hypotheses and their sampling theory for large samples are presented. The results are extended to the case of several independent variables. An illustrative problem is presented for two groups, two independent and one dependent variable.

A theory of learning and transfer: II

The theory of discrimination learning developed in Part I of this paper is extended to more complex learning situations such as those used for differentiating relative from absolute habits. The greater difficulty of learning an absolute discrimination than of learning a relative discrimination is predicted. The theory is also extended to cover cases of transfer. It predicts that under the ordinary training conditions transfer to new stimulus situations will be on a relative basis, and it predicts the type of transfer to be expected under other training conditions. A number of additional established facts of learning and transfer can be deduced from the theory. Methods of testing the adequacy of the theory by new and more crucial experiments are suggested.

The relation of item difficulty and inter-item correlation to test variance and reliability

Under assumptions that will hold for the usual test situation, it is proved that test reliability and variance increase (a) as the average inter-item correlation increases, and (b) as the variance of the item difficulty distribution decreases. As the average item variance increases, the test variance will increase, but the test reliability will not be affected. (It is noted that as the average item variance increases, the average item difficulty approaches .50). In this development, no account is taken of the effect of chance success, or the possible effect on student attitude of different item difficulty distributions. In order to maximize the reliability and variance of a test, the items should have high intercorrelations, all items should be of the same difficulty level, and the level should be as near to 50% as possible.

An analysis of learning data which distinguishes between initial preference and learning ability

Several sets of learning data furnished by I. Krechevsky have been analyzed in terms of meaningful parameters of the learning curve, and the changes in the frequency distributions of these parameters with changes in the experimental conditions have been studied. One of the parameters represents the animals initial preference for the light or dark, the other represents learning ability. The analysis shows that destruction of about ten or fifteen per cent. of the cortex, increases the animals preference for the light and decreases the learning ability slightly. By ordinary methods of analysis, it is not possible to discover thatboth initial preference and learning ability have been changed by any given factor.

The relationship between degree of original learning and degree of transfer

SummaryAn experiment was performed to determine the relationship between the accuracy of the original learning and the accuracy of transposition. The usual method of comparison of the average number of errors in the transposition test made by a group of rats trained to a criterion of 10 consecutive errorless trials with the average number of errors made by a group of rats trained to a criterion of 30 consecutive errorless trials reveals no clear difference between the groups.However, the degree of learning at the point when training ceased, plotted against errors made in transposition, brings out a clear relationship between degree of original learning and accuracy of transposition. Within the range of learning tested, the more accurate the original learning was, the more accurate was the transposition.

The content reliability of a test

The content unreliability of an essay test is the error due to the items used or the content of the test. The reader unreliability is due to variation in judgment of the persons who read and score the essay test. The content reliability of an essay test is accordingly defined as being independent of the reader reliability. Formulae are derived for the reader reliability and for the content reliability. The content reliability is found to be equal to the geometric mean of the test reliabilities computed from the scores assigned by the two readers, divided by the reader reliability.

Comments on Guttman's review ofTheory of Mental Tests

Dr. Guttman’s review of Theory of Mental Tests is essentially an attempt to indicate the main avenues along which he would like to see contributions made to test theory. My aim in writing Theory of Menlal Tests was to summarize the major areas of the literature in the field, to indicate some of the major areas for needed work, and to make some progress toward a unified theory. Guttman’s review indicates both that these objectives were fulfilled and that much still remains to be done. For purposes of this discussion the principal adverse comments ou the book will be grouped under three major criticisms. 1. Reliability is treated primarily from the standpoint of parallel tests which cannot yield a unique coefficient and only secondarily from the retest viewpoint that has been developed by Guttman. 2. Test theory has not been developed in terms of modern statistical theory. 3. Item analysis and item selection are presented in terms of a bivariate theory rather than in terms of a multivariate structural theory such as Guttman’s theory of scales and quasi-scales.

Effect of group heterogeneity on item parameters

Most indexes of item validity and difficulty vary systematically with changes in the mean and variance of the group. Formulas are presented showing how certain item parameters will vary with these alterations in group mean and variance. Item parameters are also suggested which should remain invariant under such changes. These parameters are developed under two different assumptions: first, the assumption that thetotal distribution of the item ability variable is normal, and, second, that the distribution of the item ability variablefor each array of the explicit selection variable is normal.

A course in the theory of mental tests

An outline for a course in test theory is presented, together with a list of assignments, problems, and a bibliography. The course has been given in the Psychology Department of the University of Chicago. The material is presented in outline form at the present time because of the increased need for training in test theory due to the increase in the use of psychological tests for classification of military personnel, and because much of the material in such a course must be selected from a wide array of articles in the literature. This material is presented in order that an organized body of material for instructional purposes may be readily available to those interested.