An area theorem for the same-different experiment.

If observers in a same-different experiment base their decisions on the absolute difference between observations on a trial, the area under the receiver operating characteristic equals the maximum proportion of correct decisions that an unbiased independent-observations observer could attain. Even though the differencing strategy is suboptimal, the area measure yields an index of optimal performance.     

An assessment of response bias for thesame-different task: Implications for the single-interval task

Two auditory amplitude discrimination experiments were conducted using thesame-different experimental design. Observer bias was manipulated, in the first experiment, by varying payoff matrices and, in the second, by varying prior probabilities of signal presentation. Five levels of bias manipulation and four levels of difficulty were employed in each experiment. Each observer received all combinations of bias manipulation and difficulty, but with only one of these combinations within each block of trials. Nine indices of bias were assessed by simultaneously fitting isosensitivity and isobias functions to the data and by fitting isobias functions only. Although none of the indices tested provided an exceptionally good fit to the data, two indices stood out from the rest. These werec _sd ^* andc _i, indices with isobias contours similar in shape to those for thec index derived from theyes-no task.     

An impossibility theorem for verisimilitude

In this paper, we show that Arrow’s well-known impossibility theorem is instrumental in bringing the ongoing discussion about verisimilitude to a more general level of abstraction. After some preparatory technical steps, we show that Arrow’s requirements for voting procedures in social choice are also natural desiderata for a general verisimilitude definition that places content and likeness considerations on the same footing. Our main result states that no qualitative unifying procedure of a functional form can simultaneously satisfy the requirements of Unanimity, Independence of irrelevant alternatives and Non-dictatorship at the level of sentence variables. By giving a formal account of the incompatibility of the considerations of content and likeness, our impossibility result makes it possible to systematize the discussion about verisimilitude, and to understand it in more general terms.     

Likelihood-ratio decision strategy for independent observations in thesame-different task: An approximation to the detection-theoretic model

An optimal decision strategy for deciding whether two things are the same or different is to adopt a likelihood-ratio criterion. The parametric equations for the receiver operating characteristic (ROC) based on the likelihood-ratio strategy when observations are independent are complicated; they require the numerical evaluation of a double integral. An approximation to the parametric equations for the likelihood-ratio strategy was developed. This approximation takes the form of a pair of equations that describe ROCs virtually indistinguishable from those of the full model.     

A general area theorem for the same-different paradigm

According to a well-known theorem in psychophysics (Green & Swets, 1966), the area under the receiver operating characteristic (ROC) for the yes-no paradigm equals the proportion of correct responses of an unbiased observer in the two-interval, two-alternative, forced choice paradigm (2I2AFC). Here, we demonstrate a similar relationship between the ROC area in the two-interval same-different (AX or 2IAX) paradigm, and the proportion correct in the four-interval same-different (4IAX, also known as dual-pair comparison) paradigm. The theorem demonstrated here is general, in the sense that it does not require that the sensory observations have a specific distribution (e.g., Gaussian), or that they be statistically independent.     

The optimum decision rules in thesame-different paradigm

In this paper we derive the optimum (likelihood-ratio) decision statistic for asame-different paradigm. The likelihood ratio is dependent on the degree of correlation between the two observations on each trial. For the two extreme cases in which the observations are either independent or highly correlated, the optimum decision rule is identical to each of two previously suggested decision rules. For these two cases, the receiver-operating characteristic (ROC) curves are calculated. Finally, an experimental procedure is suggested for assessing the decision rule actually used by the observer in asame-different task.     

An impossibility theorem for amalgamating evidence

Amalgamating evidence of different kinds for the same hypothesis into an overall confirmation is analogous, I argue, to amalgamating individuals’ preferences into a group preference. The latter faces well-known impossibility theorems, most famously “Arrow’s Theorem”. Once the analogy between amalgamating evidence and amalgamating preferences is tight, it is obvious that amalgamating evidence might face a theorem similar to Arrow’s. I prove that this is so, and end by discussing the plausibility of the axioms required for the theorem.     

An almost general splitting theorem for modal logic

Given a normal (multi-)modal logic a characterization is given of the finitely presentable algebras A whose logics L A split the lattice of normal extensions of . This is a substantial generalization of Rautenberg [10] and [11] in which is assumed to be weakly transitive and A to be finite. We also obtain as a direct consequence a result by Blok [2] that for all cycle-free and finite A L A splits the lattice of normal extensions of K. Although we firmly believe it to be true, we have not been able to prove that if a logic splits the lattice of extensions of then is the logic of an algebra finitely presentable over ; in this respect our result remains partial.     

An experiment control system for the Amiga microcomputer

The Commodore Amiga microcomputer, with its powerful and versatile hardware features, is well-suited to many areas of behavioral research. The complexity of the hardware and software, however, creates considerable difficulties for the researcher who wishes to construct real-time experiment-control programs. The present article describes a coordinated package of routines that have been designed to support experiment-control programs written in FORTRAN 77. The package was constructed specifically for cognitive research on verbal processes, but is sufficiently flexible to be useful in a variety of other applications. The functions performed by the program include the construction of stimulus displays, response detection, and timing operations.     

Positive effect of heterogeneity of difference on thesame-different disparity in letter matching

Subjects judged whether two adjacent letters were identical or different.Different pairs were similar, for example HM, DO, VY, or dissimilar, for example DY, HV,MO. According to the noisy-operator theory, increasing the heterogeneity of difference (external noise) by intermixing similar and dissimilardifferent pairs ought to produce faster but less accurate responses ondifferent trials. As predicted, the tendency to make more false-different responses (i.e., errors on same pairs) decreased when the similar and dissimilardifferent pairs were intermixed rather than presented in separate blocks. The fast-same effect did not change, however, seemingly due to criterion misadjustment. Proctor and Rao apparently found no effect of heterogeneity of difference on RT and errors because they used a less sensitive procedure (between-subjects design; different set of letters for more and less heterogeneous conditions). Consistent with the internal-noise principle, but not with the response-competition model of Eriksen, O’Hara, and Eriksen, the enhanced fast-same effect on blocks containing only similar (vs. dissimilar)different pairs was accompanied by an increased preponderance of false-different errors.     

An experiment in psoblem solying

Trial-and-error problems are described in terms of “stimulus” difficulty, which is a measure of the number of possible modes of response left to the individual when all the information given is taken into account; and “phenomenal” difficulty, which is a measure derived from the individual's performance. An experiment is described in which three types of problem were presented to human subjects. In all three problems the stimulus difficulty was calculable, stage by stage, in the solution. The problems differed in this stimulus difficulty and also in the qualitative nature of the information provided—from unequivocal to conditional. It is shown that the qualitative difference of the nature of the information bears most relationship to phenomenal difficulty. Some observations are made on the modes of solution adopted, and further experimental work is suggested.     

An experiment on obsessional checking

An experiment was carried out on 12 patients complaining of obsessional checking rituals in order to determine whether: (a) the execution of potentially ‘harmful’ acts produces discomfort and (b) whether the act of checking produces relief. With some exceptions and reservations, it was concluded that execution of the act does produce discomfort and completing a check does bring relief. The results are seen as providing some support for theories which depend on the concept of anxiety reduction/avoidance.     

Evidence that thesame-different disparity in letter matching is not attributable to response bias

When pairs of letters or letter strings are judged assame ordifferent, correctsame responses are usually faster than correctdifferent responses. Recently, Ratcliff and Hacker (1981, 1982) have argued that thissame-different disparity is likely attributable solely to a bias to respondsame. The present article reports an experiment in which the relative bias to respondsame ordifferent was varied for matches of single-letter pairs. Bias was manipulated by having 80, 60, 40, or 20 pairs in a block of 100 besame, with the remainder beingdifferent. For both sequential and simultaneous presentation of the letters,same reaction times had an overall advantage overdifferent reaction times that could not be attributed to response bias. Moreover, consistent with Proctor’s (1981) facilitation principle, this reaction time disparity was greater with sequential presentation than with simultaneous presentation. The larger reaction time advantage forsame pairs with sequential presentation was obtained without an increase in the relative number of false-same responses, supporting the view that the facilitation is attributable to changes in sensitivity and not to changes in encoding criteria.     

An effective fixed-point theorem in intuitionistic diagonalizable algebras

Summary Within the technical frame supplied by the algebraic variety of diagonalizable algebras, defined by R. Magari in [2], we prove the following:LetT be any first-order theory with a predicate Pr satisfying the canonical derivability conditions, including Löb's property. Then any formula inT built up from the propositional variables q, p₁, ..., p_n, using logical connectives and the predicate Pr, has the same fixed-points relative to q (that is, formulas (p₁ ..., p_n) for which for all p₁, ..., p_n T((p₁, ..., p_n), p₁, ..., p_n) (p₁, ..., p_n)) of a formula ^* of the same kind, obtained from in an effective way.Moreover, such ^* is provably equivalent to the formula obtained from substituting with ^* itself all the occurrences of q which are under Pr. In the particular case where q is always under Pr in , ^* is the unique (up to provable equivalence) fixedpoint of .Since this result is proved only assumingPr to be canonical, it can be deduced that Löb's property is, in a sense, equivalent to Gödel's diagonalization lemma.All the results are proved more generally in the intuitionistic case.The algebraization of the theories which express Theor, IXAllatum est die 19 Decembris 1975     

An experiment with occasional false information

An experiment is described in which subjects were presented, under one condition, with advance information of doubtful value. The evidence suggests that advance information was accepted, although the uncertainty created had a detrimental effect on the subjects' performance.