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Subjects made comparative ratings of two vertical lines. If the two lines were side by side, judgments were more accurate than if one line was higher in the field than the other. If one line was moderately higher in the field than the other, the higher line appeared shorter. This effect diminished when the higher line was raised, and disappeared when the higher line no longer overlapped with the lower. The direction of the illusion is opposite to the usual “anisotropy of visual space” or to expectations based on foreshortening or misplaced constancy. An explanation based on the configuration of the two lines, using the mathematical structure of adaptation level theory, was offered.

In tests with naive subjects, it was found that: the apparent length of a test shaft (1) increases with angle of wing to shaft to a maximum of about 160° (wings out), and (2) is an inverted-U function of wing length, with maximum when wing length equals shaft length; (3) all effects are approximately proportional to shaft length; and (4) the angle exerts its effect within a small region near the tip of the shaft, the region extending about one-seventh the shaft length. The effects apparently do not result from simple distortion of the retinal image, but some may result from assimilation or confusion in coding image into lengths, and some effects apparently arise as lengths are combined into judgments. The new data are shown to agree in quantitative detail with results collected from 1896 to the present.

Four experiments on serial anticipation learning of lights by college students show that (a) the operations of transposing and taking the mirror image are used, (b) temporal inversion is not used, (c) a sequence made of two contrasting halves may be as easy to learn as a sequence having a single homogeneous hierarchical structure. Data revealed intrasequence confusion errors made by importing an operation from one part of the sequence to another. In homogeneous sequences, subjects appear to lose track of where they are in a sequence, and therefore repeat an operation already performed. The evidence supports the idea of an hierarchical cognitive structure, but shows that learning is not a simple function of that structure. Errors and difficulties arise from structural ambiguities, substrings of events that can be reconciled with more than one possible cognitive structure.

No matter whether an experiment is a success, a failure, or a mixture of the two, the E needs to see his results immediately to be able to plan his next study. For this purpose, he needs a rapid, simple, relevant analysis of the data. We define a version of this data-summarizing problem and describe a monitor program to solve it. One major decision is what search method and data file organization to use; We use the n-dimensional array method. We specify dependent variables in two parts: first, a measure code like proportion correct, reaction time, etc., and second, a series of coefficients to specify what items will make up the desired dependent measure. Our program is interactive and makes extensive use of default options. Some suggestions are made for the implementation of monitor programs on other hardware.

Morinaga's paradox of displacement is constructed by setting several copies of the two Mueller­ Lyer figures one above the other. The Mueller-Lyer illusion is that the wings pointing out seem farther apart than wings pointing in, and Morinaga's paradox is that when one looks down a column of wings pointing alternately one way and the other, they appear misaligned but in the opposite direction from the Mueller-Lyer illusion. The hypothesis of this paper is that the subject, under instructions to align the vertical array of wings, sets up a vertical figure-ground organization different from that used in judging the horizontal distance between wings, and that the two illusions are contingent upon the two organizations. The experiment showed that Morinaga's paradox occurs when only one column of wings is shown, in agreement with the figure-ground hypothesis, and also shows that Morinaga's paradox disappears when short line segments are introduced which disrupt the vertical figure-ground organization.

Seven psychological laboratories, capable of testing 22 human and 4 animal Ss in seven different experiments using a variety of peripheral equipment, are in various stages of operation using an IBM 1800 process-control computer in the Psychology Department at Indiana University. Each experiment utilizes four appropriate software programs: SETUP, PROCEDURE, UI1LITY, and OUTPUT. The programming is usually simple enough to be done by nonprofessional programmers. This simplification was made possible by (1) a set of subroutines written to handle many of the process-control programming complexities, and (2) the IBM-provided Time-Sharing Executive (TSX) program.

Analysis of an empirical theory into a formal system with specified primitive notions and axioms has the advantage of making it clear what deductions from the theory are permissible, and clarifying the internal structure of the theory. An example of such analysis is presented in this paper.

College students pushed buttons to predict which of two lights would appear, as in probability learning, except that the lights formed a periodic and therefore predictable sequence. The process of predicting was thought of as a system of grammatical rules. Locations in the sequence generated by mandatory first-order rules were learned quickly and all-or-none; locations generated by optional first-order rules were learned with more errors and in at least two stages. The systems of rules enable Ss to recode the sequence into run lengths (integers). Some typical higher-order rules were suggested.

Beginning with sets of arbitrary elements, concepts of distance and betweenness of sets are defined. Since betweenness as defined is not transitive, an investigation is made of the conditions which ensure desirable regularity. It is found that a straight line or linear array of sets is a generalization of nested sets (Guttman scales). Close relationships among the notions of distance, betweenness, and linear arrays are demonstrated. Parallel and perpendicular arrays, dimensions, and multidimensional spaces are characterized.

A theory of cue learning, which gives rise to a system of recurrent events in Feller's sense, is analyzed mathematically. The distribution of total errors and sampling distribution of mean errors are derived, and the learning curve is investigated. Maximum likelihood estimates of parameters and sampling variances of those estimates are derived. Likelihood ratio tests of the usual null hypotheses and approximate tests of goodness of fit of substantive hypotheses are developed. The distinguishing characteristic of these tests is that they are concerned with meaningful parameters of the learning process.

A description of deficiencies in the method of constant stimuli, published by Levison and Restle (1968), was criticized as logically invalid by Sekuler and Erlebacher (1971), who then interpreted the findings as the result of a tendency to use available responses equally often. Sekuler and Erlebacher erroneously thought that the comparison adaptation-level (CAL) theory described the frame of reference for judgments. Correctly interpreted, the theory presents no logical difficulties. An experiment was performed to compare this frame-of-reference interpretation of CAL with the Sekuler-Erlebacher response-bias theory. The results agreed in detail with CAL theory and were in direct opposition to the response-bias interpretation. Thus, although the Sekuler-Erlebacher hypothesis is logically possible, it does not seem to be empirically true.