The demonstration of capacity limitation

The study of divided attention has produced many apparent demonstrations of “capacity limitation.” Possible ambiguities in such demonstrations are considered for three major types of experimental situation: simultaneous inputs with separate responses; choice; and classification. Two issues emerge. First, demonstrations always rest on assumptions about process set, i.e., the set of internal processes by which the task actually is performed. Alternative process sets are considered for situations of each type. Second, a demonstration of capacity limitation is made either by increasing the number of simultaneous processes, or by changing the bias between them. In either case effects unrelated to capacity limitation may influence the results. If several processes contribute to a single response, some performance decrement must accompany an increase in their number, simply through the increased overall chance for error. If the subject is biased toward one alternative in a choice or classification situation, the benefits enjoyed by this alternative may reflect not a preferential allocation of attentional capacity, but simply a willingness to decide in favor of this alternative with relatively little evidence.     

Two classes of models for magnitude estimation

One class of models assumes that presentation of a signal results in an internal representation as a random variable. Depending on whether the signal is close to or far from the preceding signal, the variance of the representation is smaller or larger. Responses are determined largely by this random variable; however, when the signal is close to the preceding one, the response is generated by modifying the representation multiplicatively by some function of the ratio of the previous response to its representation. Power and linear functions are explored. The form of the random variable is assumed to be that arising from either the timing or the counting model operating on a Poisson process. Detailed analyses are carried out successfully only for the timing model with neural sample sizes independent of intensity; however, the data require the sample to increase with intensity. The linear response function coupled with the constant sample size counting model appears somewhat viable, but detailed calculations are very difficult to carry out. The second class of models postulates a power function relation between magnitude estimates and signals intensity for which the exponent is a Gaussian distributed random variable and the unit is the product of two log normal random variables. Again we assume an attention band such that succesive stimuli that are widely separated in intensity lead to independent samples of the random variables while a variety of assumptions is explored for successive stimuli that are near each other in intensity. Although they each give rise to the qualitative features of the data, estimates of parameters are sufficiently inconsistent that we are led to reject all of the submodels studied.     

Variability of magnitude estimates: A timing theory analysis

Three procedures for magnitude estimation were investigated, and a sufficient number of responses were obtained to make reasonable estimates of both the mean and variance of the responses. The conventional magnitude estimate procedure, without a standard signal, appeared to produce the most sensible data. The best method of establishing the central tendency of the data appears to be the plot of the mean ratio of successive responses against the intensity ratio of the corresponding signal intensities. When this is done, the average response ratio increases roughly as a power function of the signal ratios. The coefficient of variation, σ/m, varies from about 0.1 for small signal ratios and increases to 0.3 at about 20 dB and greater signal separations. The distribution of response ratios appears to be reasonably well approximated by a beta distribution. The change in σ/m with signal ratio is suggestive of an attention mechanism in which the sample size depends on the location of the attention band. The ratio estimation procedure suffers badly from discrete number tendencies.     

Detection of auditory signals presented at random times: III

Reaction times to a pure tone in noise were measured. Throughout, the time from the warning signal to the reaction signal was exponentially distributed, and the signal was response terminated. Response criterion, signal intensity, and mean foreperiod wait were varied. A model that assumes a Poisson sensory transduction, a pulse-activated decision process, and an additive bounded residual process was tested. It was concluded that the assumed decision process was in error. Among the empirical results, the dependence of mean reaction time on signal waits was shown to depend largely on the average wait, not the actual one, and that this relationship between mean reaction time and average stimulus wait increased for strong signals and decreased for weak ones.     

Induction of a principle

Two experiments are reported in which student subjects attempted to discover a principle obtaining among pairs of numbers and letters. In the first experiment, subjects were more successful when they were free to select whatever number-letter pairs they wished than if they were restricted in whole or in part to pairs specified by the experimenter. In the second experiment, subjects who did discover the principle were compared to those who did not. Successful subjects were shown to be slightly more systematic in their approach to the task, to work at a faster pace, to write down more positive instances, and to have a much stronger tendency to vary only one variable of the task at a time.

Wason (1960) reported a study in which subjects tried to discover a principle applying to instances each of which consisted of three numbers. He discovered that subjects mostly showed enumerative rather than eliminative induction, i.e. they made little use of instances that would have enabled them to eliminate wrong hypotheses. Wetherick (1962) found that by modifying Wason's procedure in certain ways, enumerative behaviour was reduced and the subject's chance of discovering the principle was increased. Elimination of hypotheses remained infrequent.

In the Wason study, the subject was free to write down, for each instance, any three numbers he wished, i.e. his choice of instances was not restricted in any way. This may account in part for the behaviour Wason observed. In the first experiment to be reported here, the subject is restricted, in various degrees, in his choice of instances, to determine whether the principle is discovered more (or less) readily under such restriction.     

Affect and memory in young children

The state-dependent theory of the relationship between affective states and memory holds that recall will be best when the affective state at recall matches that during learning. Sequential happy, neutral, and sad affective states that were either consistent (e.g., Happy-Happy) or inconsistent (e.g., Sad-Neutral) were experimentally induced in preschool children prior to encoding and then again prior to retrieval (free and cued recall, recognition memory). Facial ratings indicated that the inductions were effective in inducing affect. Nevertheless, emotional states did not influence children's ability to recall items under free or cued conditions, and recognition memory was essentially perfect for all subjects. Thus, there was no evidence for state-dependent learning or for a positive loop between subjects' positive affect at retrieval and memory for positively rated information. Results are discussed in terms of the generally inconsistent findings in the literature on the role of affect in children's memory and factors that may limit affective state-dependent learning in children.This research was supported by Research Grant No. 11776 from the National Institute of Child Health and Human Development to Marion Perlmutter, by Grant BNS 78-01108 from the National Science Foundation to John C. Masters, and by Program Project Grant No. 0527 to the Institute of Child Development. Wayne Duncan is now at the University of Denver, and Christine Todd is now at the University of Illinois, Urbana. Marion Perlmutter is now at the University of Michigan. We would like to thank Keith Elliott and LuAnne Tczap for their work as experimenters; Jule Kogan, Carol Revermann, and Sonya Hernandez for their help in coding data; and Jayne Grady-Reitan for her administrative assistance throughout the study.