I was sitting before my TV set, a while back, watching Captain Video and pondering the organizational problems of psychologists, psychometricians, psychodiagnosticians, psycho-somatists, psychosomnabulists, and psychoceramics (crack-pots to you). Wondering what I might do, in my small way, to help out, I decided to enlist Captain Video's help to bring me from the Black Planet that superogalactian hypermetrician, Dr. Idnozs Hcahscror-Tenib, cosmos-famous discoverer of Serutan.

Why delay? The Galaxy was on its way. and in half a light year Dr. Tenib was at my side prepared to devote his gargantuan talents to the task.

Seeing no point in confusing the good doctor by trying to describe to him the present administrative hodgepodge, I said, “Doctor, let's start from scratch. I want you to find out for me how these good people who are present at the annual meeting of the APA structure themselves? What families are represented? How many, or better, how few? And who belongs to each?”

A universe of infinitely many quantitative variables is considered, from which a sample of n variables is arbitrarily selected. Only linear least-squares regressions are considered, based on an infinitely large population of individuals or respondents. In the sample of variables, the predicted value of a variable x from the remaining n − 1 variables is called the partial image of x, and the error of prediction is called the partial anti-image of x. The predicted value of x from the entire universe, or the limit of its partial images as n → ∞, is called the total image of x, and the corresponding error is called the total anti-image. Images and anti-images can be used to explain “why” any two variables xj and xk are correlated with each other, or to reveal the structure of the intercorrelations of the sample and of the universe. It is demonstrated that image theory is related to common-factor theory but has greater generality than common-factor theory, being able to deal with structures other than those describable in a Spearman-Thurstone factor space. A universal computing procedure is suggested, based upon the inverse of the correlation matrix.

Thurstone's equation giving the probability of a correct response (p) as a function of practice time (t) when punishment and reward have equal effects has been generalized to the case where the effect of punishment is not necessarily equal to the effect of reward. Since the general equation is somewhat unwieldy, three special cases are considered, where reward has no effect, where punishment has no effect, and where these effects are equal. Equations are given together with tables for making a rectified plot for each of the three special cases.

Maximizing the discriminating power of a multiple-score test involves maximizing the homogeneity of each subtest and minimizing the correlations between subtests. A method is presented for constructing such tests from items whose intercorrelations are not too high. Under certain restrictions the saturation, defined as the proportion of inter-item covariance to total variance, is maximized for each subtest. The nucleus of each subtest is three items with high covariances inter se. All items which will lower the saturation are discarded; the one item is added which will maximize the saturation of the resultant test. This process is repeated until all the items are included or discarded for that subtest. If the correlation between any such subtests approaches the geometric mean of their saturations, their items form a new pool for one or more subtests. Formulas are presented for deciding which items to eliminate in order to reduce further the correlations between subtests.

The following development is a coordination of certain aspects of mental test methods and psychophysics. The biserial and triserial prediction equations of the Katzell-Cureton theory are utilized to reformulate the determination of absolute and differential limens from data produced by the constant method.

When a numerical transformation of raw data is used only to simplify the arithmetic of curve fitting, the transformation may lead to undesirable and even highly distorted results. This principle is illustrated with an approximation method of fitting parabolic equations to experimental data, as described recently in texts by Johnson and Lewis. Although the approximation method will never yield as good fits as the exact, least-squares method, satisfactory results are in general achieved whenever the transformed scores yield a linear plot as a function of X. The principal difficulty with the method is that some data which fall along a parabola may not yield a linear plot of the transformed scores versus X, and so cannot be fitted satisfactorily by the approximation method.