In many a psychometric problem, particularly in practical problems, the only data conveniently obtainable are the first choices given to certain stimuli among a list of stimuli that are available for selection. By assuming that such choices represent real comparative judgments, we may apply Thurstone's law of comparative judgments, extract experimental proportions from the numbers of first choices, and compute psychological scale values for the stimuli. Two procedures are proposed for estimating such proportions and examples of their applications are given. A procedure for allocating a meaningful zero point on the scale by the use of absolute judgments is explained and demonstrated. Suggestions are added for overcoming certain weaknesses and limitations of the method of choices.

The theoretically best estimate of the reliability coefficient is stated in terms of a precise definition of the equivalence of two forms of a test. Various approximations to this theoretical formula are derived, with reference to several degrees of completeness of information about the test and to special assumptions. The familiar Spearman-Brown Formula is shown to be a special case of the general formulation of the problem of reliability. Reliability coefficients computed in various ways are presented for comparative purposes.

An interpretation of the semi-major axis of the Thurstone-type learning curve fitted by the authors to animal maze data is given. This interpretation affords a quantitative description of “insight”.

The formula for the Pearson correlation coefficient of a dichotomous variable with a multiple-categoried variable is simplified for computational purposes by effecting in the multiple-categoried variable two types of arbitrary distributions: (1) rectangular and (2) proportional to binomial expansion coefficients. The formulas which result are convenient for the selection of test items and are applicable to the objective estimation of the comparative merits of the alternatives in multiple-choice test items. It is shown that the authoritative answer should have a high positive criterion coefficient, while the omissions and several wrong-answer alternatives should each have low (algebraic) negative criterion coefficients.

A technique is indicated by which approximations to the factor loadings of a new test may be obtained if factor loadings of a given group of tests and the correlations of the new test with the other tests are known. The technique is applicable to any orthogonal system and is especially adapted to cases in which Σajiajk = 0 when i ≠ k. Application is also made to the simultaneous determination of the factor weights of a group of tests in which no additional common factor is present. The technique is useful in adding tests to a completed factorial solution and in using factorial solutions involving errors to give results which are approximately correct.

A comparison is made between the scales constructed by the Method of Paired Comparison, Rank Order, and the Method of Successive Intervals. Application of the three psychophysical methods to handwriting specimens and to nationality preferences results in mutually linear scales. Choice of scaling methods becomes, then, a matter of practical convenience rather than of relative validity.

It is shown that from a somewhat more precise form of the fundamental postulates, used in a previous paper as a starting point for a system of mathematical biophysics of psychological phenomena, a mechanism can be derived, which represents the important features of conditioning.