Inducing a Rule in Wason's 2-4-6 Task: A Test of the Information-Quantity and Goal-Complementarity Hypotheses

In the standard 2-4-6 induction task, subjects are instructed to discover the rule generating sequences of three numbers by inventing number triples for which they receive immediate feedback. The rule is “ascending numbers”. Performance is greatly aided with Dual Goal (DG) instructions that ask subjects to discover two rules, one that generates “Dax” triples (equivalent to “yes” instances with Single Goal [SG] instructions) and another that generates “Med” triples (equivalent to “no” instances). The present study eliminates two explanations for this effect suggested by Wharton, Cheng, and Wickens (1993). Experiment 1 tested their Information-Quantity hypothesis that the effect results simply from the DG subjects testing more triples prior to proposing a rule. Our DG subjects were more likely to solve the problem and produced more “negative” triples than SG subjects when both groups generated exactly 15 triples. Two further groups received feedback only after generating all 15 triples, and again DG subjects were more likely to solve the problem and to generate more “negative” triples. Experiment 2 tested Wharton et al.'s Goal-Complementarity hypothesis that success under DG instructions hinges on preserving the complementary representation of the two rules. We compared SG instructions with three types of DG instructions that suggested different types of triples (Dax, Med, both Dax and Med, neither Dax nor Med). DG instructions were more effective in promoting successful rule discovery regardless of differences in rule complementarity. Our analysis of the heterogeneity of the examplars generated with DG instructions in both experiments suggest that success on the 2-4-6 task is as much a consequence of the breadth of hypotheses that subjects entertain as it is a consequence of the testing strategy.     

Judgements of a 2 × 2 contingency table: Sequential processing and the learning curve

Shanks (1985) has used a video game to investigate how subjects estimate the effect of their behaviour in a task defined by a 2×2 contingency table. The subjects were able to distinguish positive and negative contingencies from zero contingencies. In addition, they showed a learning curve and a bias to rate zero contingencies with a high outcome density higher than low-density zero contingencies. He interpreted these data as being consistent with associative models derived from animal learning. In Experiment 1 we replicated these results using a task and instructions similar to his. In a second experiment we showed that the subjects' tendency to overestimate high-density zero contingencies did not arise because the “game” was so difficult that it interfered with processing the events. In this experiment subjects were given tables of the outcome frequencies that had been determined by the earlier subjects. These subjects were, if anything, less accurate in rating the zero contingencies. We point out several logical problems with Shanks's initial task. The task did not represent a true 2×2 contingency, and aspects of it were physically impossible. In Experiment 3 we modified the task to represent a true 2×2 contingency. Using this task, we found a similar pattern of results, except that there was no evidence of the learning curve predicted by the associative models. We conclude that there is little in our data to rule out a “rule-based” analysis of contingency judgements.     

Channel-capacity, intelligibility and immediate memory

When subjects try to remember lists of digits played to them through pulse-modulated white noise the number of errors they make is greater than would be expected if digitrecognition errors and immediate memory errors were independent (Exp. 1).

A second experiment compared recall of digits in early list positions, when digits in subsequent list positions were presented through noise, and in clear. Digits in early positions were less well remembered when digits in later list positions had to be discriminated through noise.

In a third experiment prose passages were played to subjects who subsequently answered questions about their factual content. Judged by this technique recall of the first half of a prose passage is less accurate if the second half must be heard through noise than if the entire passage is heard through a good fidelity system. These results together are interpreted as demonstrations that increased difficulty of recognition of speech through noise may interfere with other activities, (conveniently termed “rehearsal”) which may be necessary to efficiently retain data in memory.     

The effect of overlearning on transfer of training

The effect of overlearning on transfer of training on the A-B:A-B_r paradigm was studied in paired-associate learning with meaningful material (adjective pairs). One group of subjects was trained to criterion on list A-B, and two additional groups were given 100 per cent and 200 per cent overlearning on list A-B. Rate of learning list A-B_r was found to be directly related to amount of overlearning. Negative transfer on list A-B_r was found for errors with the criterion group, while positive transfer was found for the 100 per cent and 200 per cent overlearning groups. The results were consistent with previous paired-associate experiments, and with results of some maze, reversal learning experiments with infrahuman subjects.

The notation “A-B:A-B_r” will be used for the transfer paradigm in which the same stimuli and responses are used in both the original acquisition phase of paired associate learning and in the subsequent transfer of training phase. In the transfer phase, however, the responses (i.e. B) are rearranged so that they are paired with different stimuli (i.e. A). The notation “A-B:A-C” will be used for the transfer paradigm in which a new set of responses (i.e. C) are paired with the old set of stimuli in the transfer of training phase.     

Exhaustive memory-scanning and familiarity discrimination: Separate mechanisms in recognition memory tasks

Experiment I was a yes-no recognition task with lists of one, two or four items to remember. Each item in the experiment appeared in only one list, and each list was presented only once. One group of subjects performed the task with complex pictures. Their results were incompatible with the hypothesis of exhaustive memory scanning, since the function relating “yes” response latency to list length was not parallel to but steeper than the function for “no” responses. Another group performed the task with words. Their results were consistent with exhaustive memory-scanning. Experiment II was a similar task in which the familiarity was varied of the test items to which the subjects had to respond “no”. That variation affected response latency with pictures but not with words. From these results and from a consideration of relevant neurological data, the hypothesis is advanced that familiarity discrimination and exhaustive memory-scanning are separate mechanisms.     

Hypothesis-testing strategies: Why two goals are better than one

An intriguing finding in the hypothesis-testing literature concerns a large increase in the proportion of subjects who discover a rule when they are asked to determine two rules rather than that rule alone. This finding is based on Wason's (1960) “2 4 6” task, in which subjects try to discover a rule (ascending numbers) by generating and testing number triples. They are initially given an example (“2, 4, 6”) of the rule that leads to overly specific hypotheses. With single-goal (SG) instructions, subjects try to discover the correct rule and are told whether each triple proposed fits the rule. With dual-goal (DG) instructions, correct and incorrect categories are labelled, respectively, as DAX and MED. Subjects try to discover both rules and are told whether each proposed triple is DAX or MED. Two explanations of why DG subjects do better at rule discovery than SG subjects are tested: the quantity of information and the testing of complementary rules using the prevalent positive-test strategy. Results support the latter explanation: DG subjects outperform SG subjects only if they know the rules are complementary, and that SG subjects' performance does not improve when required to test more triples before announcing their first rule. A third explanation, the positivity of the linguistic label of the feedback, is ruled out. Understanding the superiority of DG instructions might suggest a general method for enhancing rule discovery.     

The perception of short phrases presented simultaneously for visual & auditory reception

Subjects were provided with outline maps that were incomplete in several details. Brief, simultaneous, visual and auditory instructions were given for completing some of the missing details. Certain items could be completed on the basis of direct information contained in one or other of the sensory modalities. Others, however, could be completed only because of their relation to details capable of location by direct instruction. Information important for the completion of map details was distributed randomly among short passages of unconnected words. All relevant visual and aural clues were presented simultaneously in every case. Opportunities for alternations of attention were curtailed.

Thirty-six subjects were randomly assigned to three experimental conditions, and to two groups that were given different instructions. One group was told that relevant information would always appear simultaneously, while the other group was not allowed this information.

The number of successfully located simultaneous pairs of items presented for direct location was found to be no greater than could be expected by chance. The total number of correctly located items was less than 50 per cent of the possible items. There was no difference in the number of correctly located simultaneous pairs of items between the “instructed” and the “uninstructed” groups. The “uninstructed” group did not learn in the course of the experiment that all relevant material was presented simultaneously. Significantly more correct completions were made with the visual material than with the auditory. It is concluded that successful division of attention did not occur.     

Specifying levels of processing

This study examines the nature of stimulus processing under semantic and nonsemantic orienting instructions. Two experiments are reported in which subjects were presented with a series of trials each beginning with the presentation of a “decision word” about which they made either a semantic or non-semantic orienting decision. This decision was followed by a word in coloured ink whose colour subjects were required to name as quickly as possible. On half the trails the coloured word was the primary associate of the decision word whilst on the other half the two words were normatively unrelated. On completion of the experiments the subjects were given an unexpected free recall test. The semantic orienting condition led to longer colour naming latencies on associate trials whilst no such difference was found in the non-semantic condition. The semantic condition also produced higher levels of incidental recall although paradoxically an analysis of associative clustering in recall failed to show any difference between the two orienting conditions. The results are interpreted as support for the “Levels of Processing” approach to memory since they provide an index of processing depth which is independent of retention performance.     

Instructions, self-instructions and performance

Four semantically equivalent instructions were used for a classification task, in which response was required to the larger of two classes of items. The variables in the instructions were (1) the explicitness of the negative used to define the smaller class, and (2) the order of reference to this class within the sentence. Superior performance was obtained with instructions containing “except” compared with those using “not,” regardless of order. Analysis of the self-instructions generated by the subjects, prior to performance, indicated that their form was largely determined by the given instruction. Speed of performance was related to form of self-instruction elicited prior to the task, but not to that elicited after completion of the task.     

Post-hypnotic amnesia as disrupted retrieval: A role-playing paradigm

Evans and Kihlstrom (1973) have proposed that the phenomenon of “disrupted retrieval” may be an unobtrusive measure of post-hypnotic amnesia not readily explicable in terms of role-playing or task motivational paradigms of hypnotic behaviour. An attempt was made to test the viability of a role-playing explanation of hypnotic disrupted retrieval by giving equivalent role-playing instructions to carry out hypnosis scale suggestions to unhypnotised subjects. When given the instruction to “pretend” to remember on a few items, unhypnotised subjects recalled items in a random and disorganised manner similar to Evans' and Kilstrom's “hypnotised” subjects; when not given this instruction the unhypnotised subjects showed the sequential organised recall of Evan's and Kihlstrom's hypnotically insusceptible subjects. It was concluded that the phenomenon of disrupted retrieval in post-hypnotic amnesia can readily be explained in terms of the role-playing behaviour implicitly demanded of hypnotically susceptible subjects.     

Effects of visual familiarity on “same” and “different” decision processes

An experiment was conducted in which subjects matched upper and lower case versions of well-known abbreviations, such as BBC and etc, and meaningless controls. “Same” RT showed a familiarity effect for upper case versions of abbreviations such as BBC and GPO, but not for the lower case versions bbc and gpo. The converse did not occur for abbreviations such as etc, which were thought to occur most frequently in lower case. The “different” RT was inhibited by familiarity, with pairs such as IBM GPO being classified less rapidly than their lower case versions or controls. These effects occurred for subjects instructed to report “No” for “same” displays and “Yes” for “different” displays as well as for subjects given a conventional decision-report assignment. Some implications of these results for an account of the manner in which familiarity affects graphemic comparison processes are considered.     

A comparison between “aware” and “naive” conditions in the suppression of GSR activity

“Aware” (A) and “naive” (N) groups received different instructional sets, the former being informed both of the nature of their task and the response-reinforcement contingency. Negative reinforcement was given to these groups whenever a spontaneous GSR was emitted during four 4-min trial periods. Two corresponding yoked-control groups, CA and CN, received non-contingent reinforcement over the same periods. The contingent reinforcement groups both showed learned suppression of spontaneous GSR activity, but comparison between the A and N groups revealed a significant interaction between Time and Instructional Set. It is suggested that the “aware” instructional set had an inhibitory effect upon learning.     

Visual search with meaningful and non-meaningful material

Two experiments are reported which attempt to assess the effects of variations in target word, context items and instructions on performance in a visual search task. In Experiment 1, subjects were required to search through context lists of three-letter nonsense syllables (of either high or low association value) for three-letter meaningful target words (of either high or low frequency). They were given either “positive” or “negative” instructions, i.e. were told either to pick out the meaningful word or to pick out the word which was not a nonsense syllable. The results showed that visual search times were significantly influenced by both frequency of target word and association value of context items. A significant interaction was observed between type of instructions and target word frequency. The design of Experiment 2 followed that of Experiment 1, with the exceptions that nonsense syllables now became target items, and meaningful words formed the contexts. Again, nonsense syllable association value and word frequency were found to be critical in determining visual search times.     

Saccadic Eye Movements in Parkinson's Disease: I. Delayed Saccades

The saccadic eye movements of nine patients with Parkinson's disease were compared to those of nine age-matched controls in two paradigms generating volitional saccades. In both paradigms, subjects had to make delayed saccades to peripheral LED targets: a peripheral target appeared 700 msec before a buzzer sounded, the buzzer being the signal to make a saccade to the target. In the first paradigm (“centre-off”), the fixation target was extinguished simultaneously with buzzer onset. In the second (“centre-remain”) it was not extinguished until 1000 msec later. The results showed that for outward saccades in both paradigms, there was no difference between Parkinsonian patients and controls, but saccadic latencies were significantly shorter in the “centre-remain” paradigm. The initial outward saccades were indistinguishable from the normal, reflex saccades of the same subjects. However, saccades returning to the centre (a type of remembered target saccade) were hypometric and showed multistepping. Both effects were more pronounced in patients with Parkinson's disease. The significance of these findings in terms of current hypotheses about the nature of the Parkinsonian saccadic deficit is discussed.     

The effect of instruction with relational and item-specific elaborative strategies on young children's organization and free recall

One hundred and sixty second-grade children were assigned on the basis of a free recall pretest to four instruction conditions and were given a series of lists of pictures for free recall. For three groups, the instructions were directed at encoding either (a) list organizational information, (b) item-specific semantic information, or (c) organizational and individual item information, while the fourth group constituted a “No-training” control with standard free recall instructions. The subjects received either related or unrelated lists during the training phase and related or unrelated lists during two post-tests, immediately following and 1 week after training. For both types of lists, instructions emphasizing list organization were more effective than those emphasizing item-specific elaboration. Subjects given individual item elaborative instructions showed levels of recall which were comparable to those of the control subjects. While the combined effect of organizational and individual item processing did not exceed the performance produced by organizational instructions alone, the degree of generalization was greater for subjects processing both kinds of information, especially when subjects received related lists during training.     

Divided attention, order of report and responses to immediately successive signals

Two effects, “divided-attention” and “order of report”, are operationally denned. Their relative contributions to the reduction in efficiency which accompanies the recognition of difficult nonverbal signals, presented simultaneously, is considered. Experiment I evaluated the two effects in the absence of a fixed order of report and emphasis instructions, confounding features of previous studies. The results showed: an overall impairment of performance with simultaneous signals; a contribution of both effects to the decrement, with a suggestion of the primacy of the “order of report” effect; and a significant interaction between the latter effect and modality, such that visual signals showed the greater effect. Experiment II using similar signals tested the assumption that simultaneity of presentation is a necessary condition for obtaining reduced efficiency with multiple signals. The assumption was only partially confirmed, a significant decrement in performance occurring only for the second of two successively presented signals. Similarities between the two sets of results are noted, as well as between these and modality differences obtained with verbal materials. Two possible accounts of the data are proposed, one based on “input”, the other on “storage” models of divided-attention. The hypothesis that subjects report the most clearly perceived signal first is rejected as an independent explanation.     

Attention in dichotic listening: Affective cues and the influence of instructions

In shadowing one of two simultaneous messages presented dichotically, subjects are unable to report any of the content of the rejected message. Even if the rejected message consists of a short list of simple words repeated many times, a recognition test fails to reveal any trace of the list. If numbers are interpolated in prose passages presented for dichotic shadowing, no more are recalled from the rejected messages if the instructions are specifically to remember numbers than if the instructions are general: a specific set for numbers will not break through the attentional barrier set up in this task. The only stimulus so far found that will break through this barrier is the subject's own name. It is probably only material “important” to the subject that will break through the barrier.     

A philosophical and empirical analysis of subjects' modes of inquiry in wason's 2-4-6 task

Investigations of hypothesis-testing behaviour typically conclude that subjects' methods are characterized by “confirmation bias.” However, these studies (a) relied exclusively upon Karl Popper's philosophy of science, (b) only described subjects' strategies via a falsificationist terminology, and (c) failed to determine subjects' precise intentions in the task situations. Alternative philosophies of science can be used to describe hitherto ignored aspects of rule discovery in Wason's (1960) 2-4-6 task as well as reinterpret findings from previous research. Using Wason's task, Experiment 1 adopted J. S. Mill's inductive methodology in order to assess better the extent of elimination in experimentation. While it was found that subjects did eliminate a large proportion of their hypotheses rather than merely confirm them, Mill's eliminative methods applied to this task failed to account for the entirety of subjects' behaviours. Experiment 2 examined subjects' methods in more depth by asking subjects during the task either to: (1) describe their procedures, (2) select from a list of methodology terms those that best characterized their methods, and (3) state on each learning trial their preferred hypotheses and their subjective assessments that those hypotheses were correct. Although subjects were generally unable to describe their methods of inquiry, they were able to typify them via the methodology terms as if their methods were tacitly held skills. Contrary to presumptions of previous research, analyses indicated that subjects were not testing particular hypotheses on every trial but were often examining possible instances of the rule “at random” or “different from ones examined” to that trial. It is also suggested that subjects' decisions to announce rules and their thematic lines of inquiry be given further consideration by researchers.     

Beoadbent's filter theory: Postulate H and the problem of switching time

Groups of digits were presented binaurally and dichotically to subjects who were asked to recall them. Different rates and patterns of presentation were used, the design being based on that of Broadbent (1954). Broadbent's findings in this field were confirmed. If subjects are presented with simultaneous pairs of digits at a rate of 2 pairs per second dichotically, they cannot recall them if they are asked to alternate between the ears. If however the presentation is staggered, so that although the rate is constant the signals do not overlap, subjects can recall alternately from the two ears. It is suggested that these findings are better interpreted as an interference effect, not a rate effect. Criticism is offered of similar designs to measure “switching rate”. Criticism is also offered of Broadbent's estimate of “perception time” in such experiments. An analysis of the quantity and type of errors made by subjects is given, which suggests that Broad-bent's theory of a short term store on the peripheral side of a selective filter is in need of revision.     

Preferred tempo in the learning of a gross cyclical action

Seventy-five subjects, randomly assigned to one of five training conditions, were required to learn to make large-amplitude, high-tempo, fluent movements on a so-called ski-simulator over a period of four days. Subjects trained under different tempo conditions. In four of the conditions the tempo was prescribed (“preferred”, high, low, or increasing), augmented feedback being provided to enable subjects to stay on “target”. “Preferred” tempo was based on the weight of the subject and was derived from a regression equation based on previous empirical research. In a fifth condition, subjects trained on “discovery learning” principles, i.e. without the tempo being prescribed. The results obtained on the three parameters (amplitude, frequency, and fluency) during the daily test sessions (in which the tempo was not prescribed) formed the data for the analyses.

A learning effect was apparent on all three parameters over the four-day training period. Subjects who trained under the high or the low prescribed tempos, however, were shown to produce significantly smaller amplitude movements than subjects who trained under the other three conditions. Training under the low-tempo condition was also shown to have disadvantageous effects on the parameters tempo and fluency. It was concluded that, for these kinds of action, training at a high or a low tempo—and particularly the latter—has undesirable effects. Such disadvantageous effects, however, were shown to be avoidable if training is begun with the “preferred” tempo of the subject and increased successively by 7% over days.