Test theory without an answer key

A general model is presented for homogeneous, dichotomous items when the answer key is not known a priori. The model is structurally related to the two-class latent structure model with the roles of respondents and items interchanged. For very small sets of respondents, iterative maximum likelihood estimates of the parameters can be obtained by existing methods. For other situations, new estimation methods are developed and assessed with Monte Carlo data. The answer key can be accurately reconstructed with relatively small sets of respondents. The model is useful when a researcher wants to study objectively the knowledge possessed by members of a culturally coherent group that the researcher is not a member of.This research was supported by NSF Grant No. SES-8320173 to the authors. We gratefully acknowledge comments and suggestions from John Boyd, Tarow Indow, and Kathy Maher as well as the editor and several anonymous referees.     

Above suspicion: Cognitive and intentional aspects of the ability to lie

This paper looks at the attribution of the ability to lie and not at lying or lies. It also departs from more familiar approaches by focussing on the appraisal of an ability and not on the ability in itself. We believe that this attribution perspective is required to bring out the cognitive and intentional basis of the ability to lie.     

A revision of the definition of lying as an untruth told with intent to deceive

The traditional and prevailing definition of lying is that lying is some variation or combination of: an untruth told with intent to deceive. I establish that this is the case, and that, as a result, contradictions and injustices arise. An alternative definition is proposed which is shown to avoid these difficulties. It is also shown that and how on the new definition the alleged Liar paradox is easily dissolved.     

Effects of relative reinforcer frequency on complex color detection

Pigeons were trained under a discrete-trials detection procedure in which one of a set of color stimuli was presented on the center key and a single response turned off the stimulus and illuminated two side keys. Single responses to one or the other side key produced occasional reinforcers depending on the value of the color stimulus. In Experiment 1, one color-stimulus set comprised 559, 564, 569, and 574 nm, and right-key pecks were occasionally reinforced following presentations of members of this set. The other stimulus set comprised 579, 584, 589, and 594 nm, and left-key pecks were occasionally reinforced following presentations of members of this set. Across seven experimental conditions, the left/(left + right) relative reinforcer frequency was varied from .1 to .9. In Experiment 2, one stimulus set contained only one member, 574 nm, and right-key responses were occasionally reinforced following its presentation. Over 12 experimental conditions, two manipulations were carried out. First, the number of stimuli comprising the other stimulus set was increased from one (579 nm) to two (579 and 584 nm) to three (579, 584, and 589 nm) and to four (579, 584, 589, and 594 nm), and left-key responses were reinforced occasionally following center-key presentations of members of this set. Second, for each stimulus combination, the left/(left + right) relative reinforcer frequency was varied from .1 to .5 to .9 across three experimental conditions. The principal finding of Experiments 1 and 2 was that reinforcers and stimuli interacted in their effects on behavior. In Experiment 3, pairs of adjacent stimuli (5 nm apart) in the range 559 to 594 nm were presented in each experimental condition, and the left/(left + right) relative reinforcer frequency was held constant at .5. The data from all three experiments were analyzed according to a detection model describing performance in multiple-stimulus two-response procedures. This model provided independent measures of stimulus discriminability, contingency discriminability, and bias. The analysis showed that (a) consistent with the color-naming function, pigeons were better able to discriminate between higher nanometer values than lower nanometer values; (b) their ability to discriminate between the stimuli was independent of the number of wavelengths comprising each stimulus set; (c) they allocated delivered reinforcers very accurately to the previously emitted response; and (d) no consistent biases emerged.     

The interaction of stimulus and reinforcer control in complex temporal discrimination.

Six pigeons were trained in a discrete-trials signal-detection procedure to discriminate between a fixed-duration stimulus (5 s or 20 s) and a set of variable durations ranging from 2.5 s to 57.5 s in steps of 5 s. For each fixed-duration stimulus, the ratio of reinforcer frequencies contingent upon reporting the fixed versus the variable stimulus was systematically manipulated. Detection performance was well controlled by both the stimulus value and the reinforcer ratio. Both the discriminability between the fixed duration and the set of variable durations, and the discriminability between the fixed duration and each of the variable durations, were independent of the reinforcer-frequency ratio when discriminability was measured as log d. The sensitivity of response bias to reinforcement-ratio changes was independent of the value of the fixed duration, but was not independent of the discriminability of the variable durations from the fixed durations. Under current models, discriminability measures in complex temporal discrimination may be independent of biasing manipulations, but bias measures are not independent of stimulus values.     

Effects of differences between stimuli, responses, and reinforcer rates on conditional discrimination performance

In a discrete-trial conditional discrimination procedure, 4 pigeons obtained food reinforcers by pecking a key with a short latency on trials signaled by one stimulus and by pecking the same key with a long latency on trials signaled by a second stimulus. The physical difference between the two stimuli and the temporal separation between the latency values required for reinforcement were varied factorially over four sets of conditions, and the ratio of reinforcer rates for short and long latencies was varied within each set of conditions. Stimulus discrimination varied directly with both stimulus and response differences and was unaffected by the reinforcer ratio. Sensitivity to reinforcement, estimated by generalized-matching-law fits to the data within each set of conditions, varied directly with the response difference but inversely with the stimulus difference arranged between sets of conditions. Because variations in stimulus differences, response differences, and reinforcer differences did not have equivalent effects, these findings question the functional equivalence of the three terms of the discriminated operant: antecedent stimuli, behavior, and consequences.     

Human Signal-detection Performance: Effects Of Signal Presentation Probabilities And Reinforcer Distributions

University students participated in one of four standard two-choice signal-detection experiments in which signal presentation probability was varied and the reinforcement distribution was held constant and equal. In Experiments 1, 3 and 4, subjects' performance showed a systematic response bias for reporting the stimulus presented least often. Experiments 1 and 4 showed that this effect was reliable with extended training and monetary, rather than point, reinforcement. In Experiment 2, all correct responses were signaled in some way, and this produced the opposite relationship between signal presentation probability and response bias. Experiments 1 and 3 found that explicitly deducting money (intended as punishment) for equal numbers of incorrect responses on each alternative, or varying the obtained overall rate of reinforcement, produced no clear change in response bias. The bias, shown by humans, for reporting the stimulus presented least often remains a challenge for theories of stimulus detection.     

Detecting a nonevent: Delayed presence-versus-absence discrimination in pigeons

Eight pigeons were trained on a delayed presence-versus-absence discrimination paradigm in which a sample stimulus was presented on some trials but not on others. If a sample was presented, then a response to one choice key produced food. If no sample was presented, a response to the other choice key produced food. The basic finding was that performance remained constant and well above 50% correct on no-sample trials as the retention interval increased, whereas performance dropped precipitously (to below 50% correct) on sample trials. In the second phase of the experiment, all of the trials were no-sample trials, and reinforcers were delivered probabilistically for one group of pigeons and according to time-based schedules for the other group. The exact reinforcement probabilities used in Phase 2 were those calculated to be in effect on no-sample trials in Phase 1 (according to a discrete-state model of performance). Subjects did not show exclusive preference for the richer alternative on no-sample trials in the first phase, but those in the probabilistic group developed near-exclusive preference for the richer alternative during the second phase. These data are inconsistent with the predictions of the discrete-state model, but are easily accommodated by an account based on signal detection theory, which also can be applied effectively to discrimination of event duration and the “subjective shortening” effect.     

On the discriminability of stimulus duration.

The performance of pigeons trained to detect differences in the duration of stimuli was analysed using a matching model of signal detection. Two white stimuli, S1 and S2, differing in duration, were arranged with equal probability on the center key of a three-key chamber. S1 was systematically varied from 5 seconds to 25 seconds while S2 remained constant at 30 seconds. On completion of the center-key stimulus, a peck on the center key turned on the two red side keys. A left-key response was "correct" when S1 had been in effect on the center key and a right-key response was "correct" on S2 trials. A correct response produced a 3-second magazine light accompanied intermittently by food. Incorrect responses produced 3-second blackouts. Detection performance was measured under two procedures. In the first, the obtained reinforcement ratio was uncontrolled by allowing the number of food reinforcements obtained for correct left- and right-key responses to vary as the stimuli were changed. In the second procedure, the presentation of food reinforcement was controlled by holding the obtained reinforcement ratio constant. Discriminability changed as a function of stimulus differences under both procedures. No such trend was found in response bias.     

The interaction between stimulus and reinforcer control on remembering.

In a symbolic matching-to-sample task, 6 pigeons obtained food by pecking a red side key when the brighter of two white lights had been presented on the center key and by pecking a green side key when the dimmer of two white lights had been presented on the center key. Across Part 1 and Parts 6 to 10, the delay between sample-stimulus presentation and the availability of the choice keys was varied between 0 s and 25 s. Across Parts 1 to 5, the delay between the emission of a correct choice and the delivery of a reinforcer was varied between 0 s and 30 s. Although increasing both types of delay decreased stimulus discriminability, lengthening the stimulus-choice delay produced a greater decrement in choice accuracy than did lengthening the choice-reinforcer delay. Additionally, the relative reinforcer rate for correct choice was varied across both types of delay. The sensitivity of behavior to the distribution of reinforcers decreased as discriminability decreased under both procedures. These data are consistent with the view, based on the generalized matching law, that sample stimuli and reinforcers interact in their control over remembering.