A study is made of the extent to which correlations between items and between tests are affected by the difficulties of the items involved and by chance success through guessing. The Pearsonian product-moment coefficient does not necessarily give a correct indication of the relation between items or sets of items, since it tends to decrease as the items or tests become less similar in difficulty. It is suggested that the tetrachoric correlation coefficient can properly be used for estimating the correlation between the continua underlying items or sets of items even though they differ in difficulty, and a method for correcting a 2 × 2 table for the effect of chance is proposed.

It is shown that a “second-order” factor pattern is equivalent to the transformation employed in rotating an orthogonal factor pattern to an oblique form. The correlation among the second-order factors may then be interpreted as due to the original first-order factors.

The steady state of a simple reaction system has been shown to have some of the properties of a psychophysical discrimination system, including the possibility of deducing a generalized Weber-Fechner Law, both in integral form and in difference form. The Weber ratio so deduced is not constant, and its dependence on stimulus intensity is exhibited. The dependence of the difference limen on the internal threshold is discussed; it is found that in general there is a finite value of this threshold for which response is impossible. This critical threshold is lower for higher values of the reference stimulus intensity. Similarly, it is shown that the difference limen and the Weber ratio, for a fixed value of the threshold, become infinite (i.e., discrimination is impossible) for a value of the stimulus intensity which in general is finite.

Fifty-two subjects differing in sex, age, education and domicile (rural or urban) were given the problem of judging the height of an upright board in a natural setting. A preliminary analysis was made on the basis of the simple initial ratio method, both for the original data in feet and for original data converted to log units. Because the effects of interaction of the several variables made the results of this method inconclusive, the analysis of variance technique, as described by Yates (11) for data where the classes are not equally represented, was applied. This technique showed that, while together the four factors markedly affected judgment, sex had no significant individual effect, age had the biggest individual effect but possibly a spurious one, education and domicile had suspiciously large individual effects, and the effect of the four factors may be regarded as simply additive. The relation of the findings to those of previous investigators is discussed. The authors regard as an important result of the analysis the guidance it offers in the design of further experiments, since it demonstrates the value of equal representation for all classes into which data are to be segregated.

A method is given for determining the reliability of each of the components resulting from a factor analysis by the principal axis method.

Given I.B.M. cards punched with scores (or any numbers)—but not their squares—a method is presented of tabulating them (on the No. 405 alphameric I.B.M. tabulator) so as to obtain the sum of squares. The technique is also adaptable to summation of cross-products. The principle is an extension of the Mendenhall-Warren-Hollerith technique of vertical progressive digiting, without the necessity of manual addition or summary-punching, and is designed for machines not equipped with the “card cycle total transfer” device or “progressive total” device. Use is made of “counter rolling.” Efficient use of machine capacity is made only when intercorrelations between no more than two variables are required in addition to sums of squares. A resumé of some techniques now commonly employed is included.