The contradictory findings in the classical literature on the rate of reversal of perspective illusions stem, at least partly, from a failure to isolate three major sources of variance: set, subjects, and sequence. This paper provides a model for the statistical isolation of these variables. It consists of the square-root transformation of reversible data which appear to constitute a Poisson distribution. Such a transformation permits the full utilization of the analysis of variance.

Samples are often obtained under circumstances which make it less likely to draw individuals from some parts of a population than from others. In this paper a method is presented which makes it possible, under certain assumptions, to correct for the resulting bias and thus reconstruct the means, standard deviations, and correlation coefficients of the original population.

For any fixed total time of testing it is possible, through proper item-and-time allotment, to combine tests into a battery so that the multiple correlation with a pre-assigned criterion will be maximized. By holding constant the ratio of the length in number of items to the time length for each test, a set of general equations has been derived which will yield this maximum value of the multiple R and will enable one to determine, in any given case, the optimal fraction of total testing time that should be devoted to each type of test under consideration. The set of general equations is applied to a two-test-battery problem to obtain the optimal length of each type of test for one hour total testing time. If two other tests had been selected for the two-test sample problem, different subdivisions of the total time would generally occur. The manner in which the results would change when using other tests with different initial reliability, validity, and intercorrelation values is briefly presented. Some general implications of this method of battery development are also discussed.

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 indices p (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 biserial r were all found to have undesirable characteristics for items appearing late in a speeded test.

Elsewhere in this issue is an article by Dr. Calvin Taylor entitled “Maximizing Predictive Efficiency for a Fixed Total Testing Time.” The purpose of this note is to point out that the formulation developed by Dr. Taylor is mathematically equivalent to one presented by me in a previous issue of this journal.

We start from Taylor’s equation (36) .

A method of ratio scaling is described for treating comparative judgments of paired stimuli. A method of comparative judgment developed by Metfessel is employed. Formulas for scale values and the solution of a sample problem are provided. The method is designed to provide internal-consistency checks on the scale values. Experimental interpretations of equal-unit and ratio properties of measurement scales are inherent in the procedure.

When K tests are given to N individuals, and for each individual there are two criterion measures, then (1) the multiple regression weight to be applied to the standard score for each test to predict the criterion-difference score equals the difference of the weights for predicting each criterion separately; (2) the difference between the predicted scores equals the predicted difference (each test being assigned the appropriate multiple regression weight); (3) the square of the multiple correlation between predicted and actual criterion-difference scores equals the sum of squares of the multiple correlations of the battery with each criterion less the product of these correlations and the correlation between predicted scores all divided by twice the quantity one minus the criterion intercorrelation; and (4) the variance of errors of estimating the criterion-difference score equals the sum of the variances of errors of estimating each criterion score minus twice the criterion intercorrelation, plus twice the correlation between predicted scores multiplied by the product of the square root of one minus the variance of errors of estimating one criterion and the corresponding square root for the second criterion.

It should be possible to make a test a more accurate measuring instrument by discarding some of the items which have been found, by item analysis, to be inefficient. If this is so, fresh and more reliable scores from the already marked scripts would be obtained by neglecting the discarded items, and, in the future, the abbreviated test would be used. The present article offers two solutions, based on slightly different premises, to the problem of which items to discard when the test has been designed to measure a single ability. In a practical example these yield almost the same result, which is also the result obtained by a less rigorous grouping method described, which is by no means laborious to use.

Alternative procedures for calculating discriminant function coefficients have been illustrated in reported research. One method proceeds from data which has been expressed in deviation score units, whereas the other method implies that the data has been expressed in standard units. It is shown algebraically that both procedures yield identical discriminant function coefficients, and therefore, the method involving less mathematical manipulation and computation is preferable.