Symposia on Child Psychology: v.1

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY, VOLUME 1

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MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY Volume 1

JOHN P. HILL, EDITOR

THE UNIVERSITY OF MINNESOTA PRESS • MINNEAPOLIS

© Copyright 1967 by the University of Minnesota. All rights reserved Printed in the United States of America at the Lund Press, Inc., Minneapolis

Library of Congress Catalog Card Number: 67-30520

PUBLISHED IN GREAT BRITAIN, INDIA, AND PAKISTAN BY THE OXFORD UNIVERSITY PRESS, LONDON, BOMBAY, AND KARACHI, AND IN CANADA BY THE COPP CLARK PUBLISHING CO. LIMITED, TORONTO

"Linear Structural Models for Response and Latency Performance in Arithmetic on Computer-Controlled Terminals" © copyright, 1967, by Patrick Suppes, from his book, Computer Assisted Education, published by Random House, Inc., is printed here by permission of the copyright holder.

Preface

THIS volume inaugurates a series of annual reports of the Minnesota Symposia on Child Psychology. In May of each year, beginning in 1966, six investigators are invited to the University of Minnesota to present papers on their programs of research in child psychology. Each investigator is given the opportunity to discuss a series of related studies from the perspective of the theory or set of issues that guides his program of research. This format has some unique advantages for the investigator and for the reader: Journal reports are necessarily fragmentary with respect to the research program, and conclusions based on studies published early in the course of a research project stand without benefit of reinterpretation suggested by later results. The programmatic perspective — clearest to the investigator himself — is lost in a second-person review of an area, whereas the investigator's own overview can integrate findings from previously published and as yet unpublished studies and provide the reader with an appreciation of the objectives, strategy, and outcomes of the program as a whole. In so doing, the investigator also provides an economical way for the general reader to learn about an area of research from a particularly well-informed observer. Considerations such as these led to the organization of the Minnesota Symposia on Child Psychology and to the belief that there was value in their publication. The symposia are sponsored by the Institute of Child Development of the University of Minnesota. A committee composed of Institute faculty select the participants. There is no theme for each symposium: our wish for an annual presentation of outstanding research contributions by child psychologists and others whose work is relevant to V

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY child psychology precluded a thematic format because, at any one time, not enough investigators within a suitably circumscribed area are ready to write integrative statements about their own programs of research. Thus we opted for excellence and diversity in selecting contributors each year. The papers in the present volume show that there are many ways of doing good work in child psychology; that the field, more responsive to general psychology than ever before, retains a commitment to developmental issues; that heterodoxy of theory and method prevail. One of the characteristics of the child psychology of the late 1950's and early 1960's was the replication of animal learning studies using children as subjects. It was hoped that these studies would forward and further legitimate the application of general behavior theory to human beings. In Gewirtz's research, however, we have an instance where the direction of influence is likely to be reversed. Gewirtz points out that the intensity of the deprivation and satiation operations employed in animal research limit their application to the less extreme human condition. Understanding the impact of the environment on the behaviors of the young organism requires the study of the operation of stimuli at levels of low and moderate intensity. The basic datum across Gewirtz's studies is an inverse relation between the reinforcing efficacy of a stimulus and the number of prior presentations of it to the subject. He argues that the phenomenon is best understood by regarding the effectiveness of a stimulus as qualified by the context in which it occurs. The setting conditions for a stimulus as reinforcer include the child's recent history of exposures to the stimulus. Repeated exposure satiates the child for the stimulus; its efficacy as reinforcer is reduced. Recovery of stimulus efficacy occurs in the absence of exposure. Gewirtz's explanation for his findings on satiation and recovery of stimulus efficacy after satiation does not rest on such traditional concepts as general drive, anxiety, or arousal. Short-term satiation and deprivation of a stimulus class are independent setting conditions that govern the reinforcing efficacy of a stimulus. At a more molar level of analysis, social class may be regarded as a setting condition. However, studies consisting only in the demonstration of social class differences in children's behavior leave the impression that this setting exerts its influence in some superorganic and perhaps even miasmic fashion. Hess and Shipman have not been content with the documentation of social class differences in children's cognitive development. They study those aspects of social class that are operative in determining the preschool vi

PREFACE child's behavior. The functional meaning of social class for them lies in the mother's behavior — the mother's behavior toward the child is social class. The relatively inferior achievement of the lower-class child is shown to be related to the mother's typical strategies of controlling the child's behavior and the ways in which she behaves in teaching him, wittingly and unwittingly, a construction of his universe. Hetherington's paper also deals with socialization within the family. The outcome studied here is not cognitive development but the child's assumption of appropriate sex role behavior. No other area of personality development research (with the possible exception of aggression), has received so much attention in the past decade as have identification and sex typing of behavior. Hetherington's contribution has been to demonstrate that"identification-with-the-same-sex-parent-leads-to-appropriately-sextyped-behavior" is too simple a hypothesis. The most distinctive feature of her work has been an empirical rather than only a theoretical consideration of the role in sex typing of the distribution of power within the family. The study of power, in terms of executive decisions about child rearing within the family, turns out to provide important empirical and theoretical leverage. The importance of the father for sex typing in children of both sexes also is demonstrated, a feat possible because Hetherington's studies, unlike most made in this area, encompass both parents and children of both sexes. Sex role learning is shown to be a family matter in more than a trivial sense. The subjects of Gewirtz's, Hess and Shipman's, and Hetherington's researches are responsive to social stimuli. The nature and degree of their responsiveness under varying natural and laboratory conditions is the matter of interest. Lovaas's application of reinforcement theory principles to modifying the behavior of schizophrenic children, on the other hand, may be seen as an effort to induce and sustain the very responsiveness that makes these other studies possible. Selecting as subjects children who have a history of failure in response to traditional means of intervention, Lovaas programs their environment in such a way as to bring their behavior under social control. Impressive changes in the size and complexity of the children's behavioral repertoires are documented. The flexibility with which reinforcement principles are applied and the behavioral freedom that can result will be surprising to readers for whom the process and outcome of "conditioning" evokes images of automatons. Friendly and flexible automatons play a major role in the research revii

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY ported by Suppes, Hyman, and Jerman, who have used computers to present carefully programed sets of arithmetic problems to children in school. The object is not to test the merits of computer-based instruction relative to traditional instruction but rather to gain increased understanding of the determinants of arithmetical problem solving. The child's answers are flashed to a central computer via teletype, thus initiating the presentation of new problems and providing a record of the child's responses and their latencies. Accuracy and latency of response are shown to be predictable functions of the structure of the problems presented the child. Predictions are made on the basis of a priori analysis of the number of transformational, operational, and memory steps required to solve the problem. This research demonstrates not only the use of computers for basic research but also the fruitfulness of a careful specification of stimulus parameters in the study of cognition. The study of cognitive development is united with that of infancy in White's work. The course of development of visual accommodation and visual-motor coordination were first carefully traced by repeated observation over time. Then certain responses were shown to be plastic to environmental modification. Extra handling of the infant, making increased motility possible for him, and providing a visually compelling environment can have decelerative as well as accelerative effects on the age at which onset of certain accommodative and visually directed reaching responses occurs. The power of combining longitudinal and experimental approaches in the study of development is no better illustrated anywhere. The papers appearing in this volume were presented at the University of Minnesota on two successive weekends in May 1966. The symposia and their publication are made possible by grants from the Public Health Service (National Institute of Child Health and Human Development, Grant No. HD-01765-01) and from the research funds of the Graduate School, University of Minnesota. The faculty of the Institute of Child Development and the staff of the University of Minnesota Press have played important roles in making the series, and this volume in particular, a reality. The faculty of the Institute not only chose participants but provided editorial consultation as well. The staff of the Press encouraged the project at the start and have been creative collaborators in seeing its first set of papers into print. Anne Harbour Jirasek of the Editorial Department did the copyediting and, with patience and tact, educated a novice at editing about style and the techniques of publishing books. viii

PREFACE An editor cannot close with the usual author's disclaimer of others' responsibility for a book's content. Instead he has the responsibility of thanking each of the participants for their contributions and for their toleration of his harassments. I do so with pleasure.

JOHN P. HILL

South Acton, Massachusetts August 1967

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Table of Contents

Deprivation and Satiation of Social Stimuli as Determinants of Their Reinforcing Efficacy BY JACOB L. GEWIRTZ Cognitive Elements in Maternal Behavior BY ROBERT D. HESS AND

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VIRGINIA C. SHIPMAN

57

The Effects of Familial Variables on Sex Typing, on Parent-Child Similarity, and on Imitation in Children BY E. MAVIS HETHERINGTON

82

A Behavior Therapy Approach to the Treatment of Childhood Schizophrenia BY o. IVAR LOVAAS

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Linear Structural Models for Response and Latency Performance in Arithmetic on Computer-Controlled Terminals BY PATRICK SUPPES, LESTER HYMAN, AND MAX JERMAN

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An Experimental Approach to the Effects of Experience on Early Human Behavior BY BURTON L. WHITE

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List of Contributors

227

Index

231

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MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY, VOLUME 1

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JACOB L. GEWIRTZ

Deprivation and Satiation of Social Stimuli as

Determinants of Their Reinforcing Efficacy

THERE are a great variety of contextual conditions that can determine stimulus efficacy or salience for behavior at any particular moment. These conditions can qualify the functional effectiveness of stimuli in any of their roles in controlling behavior — in evoking it, in signaling occasions for its occurrence, and in strengthening or weakening behavior when made contingent upon it. They have often been termed "drive," "set," or "setting" conditions (the last is Kantor's term [19591). In analysis of behavior systems, concepts like these have evolved to order the conditions that account for the considerable variation often found in responses to apparently homogeneous stimuli. Apart from these conditions, the contextual aspects of stimuli that determine whether an event will evoke a response have traditionally been the domain of those studying problems like attention, vigilance, or perception. It appears that conditions which heighten or lower the salience of stimuNOTE: The writer appreciates the discrimination and perseverance of the three experimenters in this series of studies: Rivka Landau in Experiments 1 and 4; Penny Peterson in Experiments 2, 3, and 6; and James Turnure in Experiment 5. Miss Peterson also assisted in initial confrontations with the data. E. J. Haupt was most helpful in the statistical analyses of the results. Linda Brandt, E. J. Haupt, Deborah Singer, and Karen Stingle provided discriminating editorial assistance as well as numerous useful suggestions in the preparation of this report. This research program could not have been carried out without the generous cooperation of the directors, teachers, and students of the following schools in the Washington, D.C., area: Alexander, Brownie, Burgundy Farm Country Day, Georgetown Day, Green Acres, Kenwood, Landon, Potomac, Primary Day, Sidwell Friends, and Louise Whitney. In addition, the officials and members of several Boys' Clubs in the Washington area cooperated in the studies. 3

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY li for behaviors may operate: (a) at one time point concurrent with the functioning focal stimulus (e.g., as the ground for the stimulus figure); (b) immediately before the point of stimulus functioning (e.g., as a cue to the region in which the focal stimulus will appear); and (c) across time points before focal stimulus functioning (e.g., as deprivation or satiation contexts for a stimulus). The bases of stimulus effectiveness in several roles acquired via the paradigms of associative learning are well understood relative to the contextual determinants of momentary stimulus salience considered here. Such setting conditions are also important in the experimental analysis of behavior, for they can account for considerable variation in both performance and learning. The efficiency of conditioning procedures depends on the effectiveness of each available stimulus in its role (Gewirtz, in press, b), including its reinforcing role, a primary concern of this paper. Setting conditions are particularly important for an understanding of child behavior systems in natural settings, given that (a) the child's capacities are continually and rapidly developing but limited, (b) background events can mask the stimuli presented, (c) competing responses to stimuli are often involved, and (d) both organismic conditions (like food deprivation) and the stimuli provided are typically of low intensities. The present conceptual analysis will survey a variety of short-term setting conditions that can account for variations in the functioning of a stimulus. Emphasis will be placed on one somewhat neglected set of conditions, namely that involving the reciprocal concepts of deprivation and satiation of a stimulus class, and on one stimulus role, that of reinjorcer. These operations may be similar to those underlying concepts like curiosity or exploration, stimulus novelty, and response habituation or adaptation, whose effects are typically assessed for stimuli in evocative or discriminative roles (Gewirtz, 1961b, 1965b). This analysis will be followed by a summary of a series of preliminary experiments conducted to illustrate the operation of short-term stimulus satiation (and its reciprocal, deprivation, or recovery from satiation) as a determinant of the efficacy of a social stimulus class in reinforcing behavior. Levels of satiation were effected by varying the frequency of receipt of a stimulus class by subjects (5s) in a period immediately preceding a test for its effectiveness in reinforcing their behavior. Recovery was implemented by varying the time between the satiation treatment and the test. To elucidate further the processes involved, some initial steps were 4

JACOB L. GEWIRTZ

taken to implement different maintenance patterns of stimulus availability. In each experimental paradigm, there is little interference with the availability of stimulus classes not directly involved in the experiment.

The Conceptual Milieu CONTEXTUAL SETTING CONDITIONS

Setting conditions may qualify the effectiveness of stimuli both for performance and for the learning inferred from such performance. Some of the most familiar of such conditions are those involving deprivation and satiation operations for food and water (appetitive) stimuli. A more general and often neglected context has to do with the circumstance (ground) present when stimuli (figures) are provided. In perceptual research the ground has often been varied systematically to increase or decrease the salience of the stimulus figure. However, in learning experiments, where the attempt is usually made to match performance to some set of focal stimuli, background stimuli are typically held constant or overlooked. Premack (1959, 1962; Weisman & Premack, 1966) has demonstrated that a response emitted by the rat at a higher rate will positively reinforce a response emitted at a lower rate (and that the latter will negatively reinforce the former) when made contingent upon its prior occurrence. Since a setting condition often operates on behavior by determining its rate in the situation (Premack, 1965), knowledge of setting conditions could thus specify the quantitative reinforcement value of particular responses and predict which one of a pair of responses will reinforce the other in a given situation. The role of setting conditions may be illustrated by research examples from several areas. Change of background color in paired-associate learning decreased syllable recall (Dulsky, 1935); the presence of an incorrect majority (confederates of the experimenter [E1]) affected adult 5s' judgments of line lengths (Asch, 1952); a low reinforcement rate (33 per cent) on a prior task led to more correct responding in a subsequent discrimination problem with 66 per cent reinforcement than did continuous (100 per cent) reinforcement (Stevenson & Zigler, 1958); and more children with originally low levels of aspiration raised them following positive verbal reinforcement than did 5s with high levels (V. C. Crandall, Good, &V.J. Crandall, 1964). Earlier experience with the contextual stimuli can also qualify the effica5

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY cy of social stimuli in controlling behavior. Prior interaction between E and S involving the withdrawal of E's nurturance constituted a setting condition that enhanced stimulus functioning in children's performance and learning (Hartup, 1958). Reinforcing stimuli were more effective for child Ss after sessions of familiar-positive than after sessions of neutral interaction with E, and more effective after the latter condition than after no previous interaction with E (McCoy & Zigler, 1965); but the effect of £'s reinforcers on child performance was greater after a negative than after a positive interaction experience with E (Berkowitz, Butterfield, & Zigler, 1965).* Similarly, the effectiveness of a verbal reinforcer in maintaining child behavior was an inverse function of the degree of liking for the peer reinforcing agent (Hartup, 1964) and of that agent's sociometric popularity (Tiktin & Hartup, 1965). Further, the absence of any reaction from the adult E functioned not as a neutral condition but as a positive reinforcer for Ss given negative verbal reinforcement during an earlier treatment and as a negative reinforcer for those given positive reinforcement earlier (Crandall et al., 1964). DEPRIVATION AND SATIATION AS SETTING CONDITIONS

Until recently, short-term deprivation-satiation relations were thought by many to hold uniquely for appetitive stimuli, with effects typically identified in the reinforcing efficacy of these stimuli. But functional relations like these have been found to hold for a variety of non-appetitive and even social stimuli that do not seem immediately relevant to organismic "needs." For example, deprivation relations have been identified for observing (Butler, 1957) and for gaining visual information (Jones, Wilkinson, & Braden, 1961; Jones, 1964); and satiation relations have been proposed for the loss of differentiation between word meanings effected through repeated presentations or prolonged inspection of them (e.g., Lambert & Jakobovits, 1960; Jakobovits & Lambert, 1962), for a per* Berkowitz et al. propose that, as a result of the positive or negative quality of S"s prior interaction experience with E, E acquires a "valence" which qualifies the reinforcing efficacy of the stimuli E dispenses for S's behavior. In the terms of the present analysis, it is thought the valence would only modify the focal deprivationsatiation laws dealt with in this paper (within the limits in which they are studied) in a way parallel to that in which a food preference can modify the general deprivation-satiation functions governing the efficacy of appetitive stimuli. Thus, both the prior experience of S with E and food preferences may be taken as modifiers of setting or ground condition (or as second-order setting conditions) that qualify the functioning of the stimulus as a figure in eliciting, discriminative, or reinforcing roles.

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JACOB L. GEWIRTZ son's passive presence (Bacon & Stanley, 1963),* and for auditory and visual stimuli tested for reinforcing efficacy on instrumental behavior (Odom, 1964). Similar functions have been identified for curiosity-exploration and stimulus novelty, as is seen in the next section. Stimulus Satiation and Familiarity — Recovery and Novelty. Systematic decrements in response attributes often occur as a function of continuous or repeated exposure to a stimulus event or to different stimuli presented successively (independent of their "novel" or "familiar" qualities). These effects, found in work with different species according to various experimental paradigms, are manifest, in operational terms, as changes in evoking or discriminative value of stimuli rather than in their reinforcing value. Glanzer (1953, 1958) demonstrated a decline in the relative response rate of rats in a T-maze with repeated exposure to the stimulus. Denny replicated these results (1957). Likewise, Berlyne (1955) reported that a stimulus object evoked less exploration when rats were exposed to it for a time before testing, as well as a decline in exploration across exposure minutes, though there was occasionally some recovery when novel stimuli (not presented earlier in the situation) were included in the series. (In these reports, and in Hinde's studies of response habituation [e.g., 1960], there was some recovery after periods in which the response could not be emitted to the stimulus, but this recovery was never complete.) When a novel stimulus (not involved in an earlier habituation treatment) was presented simultaneously with one familiar from earlier treatment, human adult 5s were then found to notice the novel stimulus more frequently (Berlyne, 1957). Preschool 5s also devoted more observation time to novel stimuli (not presented earlier) than to familiar stimuli, with no difference in this pattern found between a 5-minute delay and a 48-hour delay (J. H. Cantor & G. N. Cantor, 1964). Similarly, response latencies of preschool 5s were shorter to a stimulus to which they had not responded earlier than to one to which they had responded earlier (G. N. Cantor & J. H. Cantor, 1965). In the same vein, Mendel (1965) and Harris (1965) reported children's preference for toys to which they were not exposed earlier. * Although these writers conceive their functional relation to be one of "deprivation," the convention in this paper is to label such functions "satiation." Bacon and Stanley provided puppies with a short ("high deprivation") and a long ("low deprivation") exposure to a passive person just before a test series in which two minutes of exposure to that passive person was made contingent upon an instrumental running response. 7

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY Before continuing, we must take note of two qualifying points. First, "novelty" has been used in at least three ways in the literature: (a) The term has been applied to a stimulus never before experienced by the organism. This "complete" novelty does not concern us here.* (b) The term has been applied to a stimulus that has been experienced but is now presented in combination with unfamiliar elements or in an unfamiliar context or is incongruent with expectation from past experience. In this usage, the concept of novelty may converge with the author's use of a contextual setting condition that can heighten the salience of a stimulus figure.f (c) The term novelty has been applied also to a stimulus which is known to the organism but has not recently been presented to him and so may have recovered some or all of its stimulus value for his behavior. In this last sense, the concept of novelty converges in meaning with the concept of recovery from satiation (deprivation) as used in the present analysis. Less basic for this analysis, the second qualification is that novel stimuli can evoke either approach or avoidance behaviors, depending on contextual factors. One notion has been that elements sufficiently incongruent with stimuli presented in the past might evoke fear and avoidance, whereas more congruent but still novel elements might evoke curiosity and investigatory behaviors (see Hebb, 1946, 1949). Habituation and Adaptation. Phenomena similar to those of stimulus satiation and recovery have sometimes been classified under the overlapping descriptive concepts of short-term response habituation or adaptation (Martin, 1964; Thompson & Spencer, 1966) and the recovery from conditions implied by those concepts in a period of stimulus absence during which the response was not evoked. This usage of the term habituation * Complete novelty should characterize stimuli only very early in life, for, as the organism grows, all newly experienced stimuli are likely to resemble stimuli experienced earlier, whether or not the combination of which such a novel stimulus is an element has some resemblance to stimulus complexes experienced earlier (Berlyne, 1960). f Sheffield and Campbell (1954) have used a novelty interpretation in this second sense to account for increases in activity when the presence of novel stimuli is tested with food-deprived animals. In a contrasting interpretation, Premack and Collier (1962) have suggested that a categorization of stimuli by activity rate of responses to them is more appropriate than a distinction between responses to novel and responses to not-novel stimuli. They proposed that a typically high rate of activity in the presence of the stimulus, rather than its novelty, is a sufficient condition for an increase in activity under food deprivation. The effect of Premack and Collier's interpretation is to suggest that two variables — time since last presentation and typical rate of response in the presence of a stimulus — must be considered as setting factors for the performance of a response. 8

JACOB L. GEWIRTZ

has been especially common in cases of systematic decreases in the rate of apparently unconditioned responses to a stimulus after its continuous or repeated presentation. The nature and magnitude of habituation effects vary with the lengths of initial stimulus presentation and inter-trial rest interval, initial response strength, and various other factors. The processes involved can be classified as well by the extent to which they are specific to a given stimulus (and response), the form of the decay function, and the like. The response decrements have generally appeared to include a temporary recoverable component as well as a more permanent component (Berlyne, 1955; Hinde, 1960). These decrements may be due in part to changes in the value (salience, efficacy) of the stimulus per se effected by a process like habituation of passive registration responses, and in part to the accumulation of response factors incompatible with molar responding (e.g., fatigue). Thus, it is difficult to isolate the underlying bases of inverse, negatively accelerated habituation curves, which, when they involve absolute rather than relative response rates, are uncorrected for response inhibitors like fatigue. Even so, they seem to reflect factors similar to those apparently involved in deprivation-satiation functions for stimuli. As indicated earlier, a variety of responses to repeated presentations of stimuli may be characterized by habituation functions. Typically, these behaviors have been classified under the headings of curiosity, exploratory behavior, and animal play, as well as under that of stimulus satiation (Berlyne, 1960; Glanzer, 1953; Montgomery, 1953; Sokolov, 1963; and Welker, 1956). For children's responses maintained by short stimulus exposures, an inverse, negatively accelerated curve across successive exposures was found (Clapp & Eichorn, 1965), like the habituation curve characterizing avian responses to continuous or successive stimuli (Hinde, 1954, 1960) or infant smiles to discrete and continuous presentations of an unresponsive human face (Ambrose, 1961; Gewirtz, 1965a, and in preparation, a). Gewirtz found that individual, negatively accelerating smile frequency curves often fit reasonably to a negative exponential curve, and that recovery from habituation apparently can occur when a more responsive face stimulus is presented either immediately after habituation or 24 hours later. Hinde also demonstrated some recovery over time from habituation of avian responses, not unlike the recovery pattern sometimes effected by stimuli never before introduced into the experimental setting. Thus, repeated or continuous exposure to a stimulus leads to a systematic decrement in the rate of response to it, and recovery can result either from 9

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY interspersing in the series stimuli that are discriminably different from the preceding stimulus, or from scheduling a passage of time during which the stimulus is absent. A PARALLEL THEORETICAL CONTEXT: THE GEWIRTZ AND BAER STUDIES

At this point, it is useful to examine a parallel setting condition for which the studies reported here are also pertinent. Gewirtz and Baer (1958a, 1958b; Gewirtz, Baer, & Roth, 1958) reported that the reinforcing effectiveness of a class of approval words such as good and fine in a discrimination-learning task with young boys was enhanced when immediately preceded by 20 minutes of social isolation (which they have conceptualized as a level of relative deprivation of the stimulus class used) and lowered when preceded by a 20-minute period in which the stimulus class was provided in relative abundance (conceptualized as a level of relative satiation for the stimulus class). Thus, they identified a functional relation between different numbers of times the social stimuli were provided (as setting conditions) and subsequent differences in response levels maintained by those stimuli. Gewirtz and Baer emphasized the parallel between the functional relation they identified and those involving deprivation and satiation for appetitive stimuli. Because the label "drive" has traditionally been applied to the latter deprivation relations, for heuristic reasons the writers equated the term "social drive" with the functional relation they identified, although they recognized that this label was gratuitous and added surplus meaning. The basic Gewirtz and Baer findings have been replicated or extended in similar experimental contexts with human 5s of various ages (Walters & Ray, 1960; Erickson, 1962; Stevenson & Odom, 1961, 1962; Hill & Stevenson, 1964; Lewis, 1965; Rosenhan, 1967). However, the mechanism (s) underlying this array of experimental results have not yet been made explicit, and have been viewed as differential dependency "frustration" and/or "anxiety" (e.g., Walters & Ray, 1960) and as "arousal" brought on by the isolation condition (Walters & Parke, 1964), the two concepts apparently differing in name only, or as "frustration," which could, under some conditions, manifest itself in aggressive behaviors (Hartup & Himeno, 1959). Gewirtz and Baer's original aim was to implement a stimulus-availability operation that would selectively affect behaviors controlled by a single stimulus class. Nevertheless, the condition found expedient for limiting 10

JACOB L. GEWIRTZ

the availability of the class of social-approval stimuli was a brief period of isolation, although it was noted that isolation might produce wide-range effects — "fear" ("anxiety"), "frustration-annoyance," the appearance of "disapproval-reproof," or a heightened "vigilance" and attentiveness to stimuli generally — in addition to those effects directly relevant to the independent and residual conception of deprivation-satiation. But, given the limited scope of pilot experiments such as Gewirtz and Baer's, which are necessarily oriented to isolating a relation and replicating it in order to confirm its reliability, the attempt to define the conceptual mechanism that would best account for the heightened reinforcer efficacy had to be deferred. Their procedure could have been tailored only in a limited way to preclude the operation of such artifacts as conditions implying frustration or anxiety, and although their discussion of the experimental outcome took account of such mechanisms, this temporary expedient has left a void which is only now being filled. Thus, in the program of research being reported here conditions of relative stimulus satiation (and, to a limited degree, also of deprivation) are implemented without isolation (in accord with Gewirtz and Baer's original aim), by controlling the availability of a specific class of social stimuli to 5s before a test for its reinforcing effectiveness, but neither removing these stimuli entirely nor specifically restricting the availability of other stimulus classes. STIMULUS MAINTENANCE LEVEL AND DEPRIVATION-SATIATION FUNCTIONS

Although the mechanisms in deprivation and satiation functions are not yet understood, learning is thought to modify these functions by establishing a maintenance level based on a long-term pattern of stimulus receipt. The maintenance level is thought to function as a reference standard * to determine the impact of any current level of deprivation or satiation on the control value of a stimulus. This maintenance level may acquire stimulus value itself, even for the young organism. The organism would act to raise the rate of a particular stimulus to the maintenance rate when it drops discriminably from it (deprivation) and to lower the rate of the * The maintenance level could possibly be estimated as a central tendency or as a comparable summary representation of previously experienced stimuli, in the manner of Kelson's concept of "adaptation level" (1964). This level changes as stimuli are experienced. Since stimulus rates received in the recent past ("background") may possibly be weighted differently from stimulus rates received relatively long before ("residual"), a simple average may not suffice.

11

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY stimulus when it rises above it (satiation). Discrimination of a change from the maintenance level may be in terms of such stimulus qualities as amplitude, degree of regularity of its presentation pattern, and other distribution characteristics besides simple rate of receipt. Thus, maintenancelevel learning would determine for each organism the degree of deprivation or satiation corresponding to a particular rate of stimulus provision. Different lengths of time during which there is limited access to the stimulus could correspond to equivalent degrees of deprivation in different individuals, and, conversely, individual differences in levels of deprivation could correspond to the same length of time of stimulus unavailability. It remains to be determined empirically whether such operations hold only in given ranges and for particular stimuli. Models for the Operation of Reference Levels and Background Standards. Those who follow a behavior theory approach to development have so far attended little to the earliest perceptual and dimensional learning by the individual. However, some models for the operation of these setting factors have been provided —for example, that of Helson (1964) and others like the learning conception detailed above. Glanzer (1958) has speculated that exploratory and curiosity behaviors may be a function of the discrepancy between the organism's required information level which summarizes his past experience with a particular stimulus and the current input level of that stimulus or related stimuli. In the same vein, Baron (1966) has proposed that S acquires a preference level for social reinforcers on the basis of past schedules against which he judges the adequacy of the current rate of reinforcement. Substantial disparities above or below the preference level for (i.e., the baselevel of) reinforcer receipt lead S to correct the disparity. The model advanced by Bevan and Adamson (1960, 1963) specifies an adaptation level for reinforcing stimuli, where the reinforcing value of a stimulus is presumed to be a function of the discrepancy between a current level of receipt of the stimulus and the adaptation level for it. As each reinforcer is presented, it is added to the set of "primary" (focal) stimuli, which are then averaged over time and weighted according to the relative importance of primary stimuli for the adaptation level. Although this approach does not specify the way in which setting conditions influence reinforcement value, these conditions would probably be termed "background" stimuli in Kelson's system. A discrepancy hypothesis advanced by McClelland et al. (1953) proposes that a "hedonic response" to stimu12

JACOB L.GEWIRTZ li is determined by the discrepancy between the present level of provision of a stimulus and the organism's adaptation level for it. Hedonic responses corresponding to smaller stimulus discrepancies from the adaptation level (in either direction) reflect "positive affect" with larger discrepancies increasingly evoking responses which reflect "negative affect." (Thus, as a function of discrepancy from the adaptation level, the intensity and direction of affect responses are represented by a symmetrical "butterfly" curve.) If, within the limits in which the function is thought to operate, the hedonic response to the stimulus can be assumed to correlate with the efficacy of the stimulus for other behaviors (a point about which McClelland et al. are inexplicit), this model may reduce to one rather similar to that of Bevan and Adamson. Various other incongruity hypotheses that involve the behavioral consequences of a discrepancy between a current level of stimulation and some baselevel for stimulation have been advanced in diverse areas of psychology. They have been surveyed and some problems in their use have been identified by Harvey (1963). In a different vein, Premack and Collier (1962) have postulated that behaviors can be divided into two classes: "nonrecurrent" behaviors whose rates are asymptotic to zero under conditions of ad libitum availability of stimuli, and "recurrent" behaviors whose asymptotic response levels are greater than zero under those conditions. An example of a nonrecurrent behavior of the rat is the light-contingent bar press, whereas eating, drinking, and activity-wheel running are recurrent for the rat. Premack and Collier suggest that only recurrent behaviors are subject to deprivationsatiation laws. Lockard (1964) has suggested a model which assumes a constant response rate by the organism for each repetitive response system. Following a deprivation operation (which precludes the occurrence of the response), when the response may again occur freely a particular response system can be described by (a) the stable response rate representing recovery from deprivation and (b) the percentage of replacement — that is, the percentage of the loss in normal response rate owing to deprivation that is compensated for after the return to ad libitum responding. The effects of deprivation and subsequent recovery from deprivation can be characterized by these parameters. Thus, under this model, the effectiveness of a stimulus can be determined by the values of these two parameters for the relevant response. This analysis allows the parameters to take a range of values, in contrast to the Premack and Collier analysis in which 13

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY stimulus efficacy depends on the dichotomous classification of the response as either recurrent or nonrecurrent. Operational Limits for the Functioning of Appetitive Stimuli. Appetitive stimuli often have been thought uniquely involved in deprivation-satiation laws. Extreme deprivation of food and water can lead through successive states of debilitation and ultimately to death; such consequences have not been demonstrated convincingly for other stimuli. Further, for the reinforcing qualities of food stimuli, a compelling physical model exists, based on the size of the stomach and the time it takes to empty after being filled. However, as the assumption here is that many non-appetitive stimuli are similarly subject to deprivation and satiation, an examination of some of the functional limits for appetitive stimuli can be instructive. The reinforcing properties of food and water have often been taken for granted, but there are limits on their effectiveness that are not often recognized explicitly. For example, such a stimulus has almost no value when the organism is satiated for it; in forced overfeeding, food can become a noxious stimulus; and the reinforcing value of the drinking response can be modified to such a degree that drinking becomes reinf orceable by a response like running, rather than running by drinking (Premack, 1965). Further, the behavioral effects of the deprivations of food and water are not always parallel, and some interaction can exist between the efficacies of the two stimuli (Verplanck & Hayes, 1953). Although appetitive stimuli appear exceptional in some ways and individual non-appetitive stimuli may seem exceptional also, these factors may qualify the deprivation-satiation functions only for certain portions of the range of values of the individual stimulus. In conclusion, therefore, it is conceivable that nearly all stimuli are subject to the same general class of deprivation-satiation functions. Some Relevant Research. There is scant relevant research about maintenance conditions as determinants of deprivation-satiation functions, even for food and water — which, because the organism has periodic requirements for them, would seem to be obvious stimuli on which to conduct such research. However, the little research available shows quite clearly that maintenance conditions can qualify the deprivation-satiation functions underlying the efficacy of appetitive stimuli in controlling behavior. For example, the inter-feeding interval (3-4 hours) can become a discriminative stimulus for behaviors associated with hunger in the first ten days of human life (Marquis, 1941). Also a group of rats with their 14

JACOB L.GEWIRTZ access to water limited to 1 hour at the same time every day uniformly drank more during tests after various water-deprivation intervals than did a control group maintained with free access to water (Kessen, Kimble, & Hillmann, 1960). Further, in conditioning, reversal, and consummatory tests, a group of rats on an irregular maintenance schedule for food was more similar to a group in a high-deprivation state than were animals deprived regularly every 12 hours or animals on an ad libitum schedule, when equated for amount of food consumed and average deprivation length (Mandler, 1957, 1958). A maintenance condition can be even more important than a customary drive operation, as in the case where the maintenance inter-feeding interval rather than the interval between last feeding and an acquisition test determined the rate at which rats learned a discrimination (Eisman, 1956; Eisman et al., 1956). Lastly, compared to rats fed ad libitum, those fed on a regular 23-hour food-deprivation schedule for fourteen maintenance days showed an increased runway speed for sucrose-solution reinforcement when both groups were tested after 23 hours of deprivation (Brush et al., 1961, 1963). As an example of maintenance conditions with non-appetitive stimuli, the ambiguous results of the light-contingent bar-press literature suggest that light-maintenance conditions may be important in determining (reinforcing) stimulus efficacy, since strong light can be aversive, and dim light, though it may be a reinforcer, is a weak one. Roberts et al. (1958) showed that rats reared in darkness responded at a higher rate when a bar press led to darkness, and rats reared in light responded at a higher rate when a bar press turned the light on. Lockard (1962, 1964) has reported that rats kept under a higher level of illumination for twelve treatment days, after being reared in strong light, exposed themselves to more total time in light during the test period immediately following than did control rats placed in complete darkness during treatment, though this relation held only for higher levels of test illumination. Berlyne (1966) reports that for rats maintained under noisy conditions, a buzzer or an increase in illumination presented every minute during a treatment period was a more effective reinforcer for bar pressing in the later test period than was a stimulus not presented in the treatment; but for rats maintained in a quiet room, the novel stimuli were more effective reinforcers than were the familiar stimuli. Also relevant here are Bevan and Adamson's (1960) suggestive findings that groups of human 5s receiving different distributions of shock intensities assigned systematically different psychophysical15

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY scale values to a standard shock stimulus, depending on the average level of previously experienced distributions. In addition, the reinforcing efficacy of a standard shock stimulus in human maze learning was an inverse function of the intensity of a single shock level presented repeatedly before the task. Results anomalous for a deprivation-satiation law were found by Premack and Collier (1962). Experimenting with the light-contingent bar press, they found that the response rate was decreased after long adaptation to a dark environment. As noted earlier, Premack and Collier have proposed that the light-contingent bar press belongs to a class of nonrecurrent behaviors that are not subject to normal deprivation-satiation laws, as are the more usually studied eating, drinking, and running responses. Aims of this Study Results from six experiments on satiation of a social stimulus will be presented. Experiments 1 and 2 implement levels of stimulus satiation by differential stimulus provision in a treatment period preceding a test for stimulus efficacy. In Experiment 3, two levels of recovery interval are interposed between treatment and test, crossed with two levels of satiation. Table 1. Details of the Experimental Series Experiment MainteNo." nance

Satiation Treatment Levels b

Sex ofE

1 . .. 2a d . 2b a . 3a e . 3b e . 3c e . 3d" . 4 ... . 17c 5 ... . 16c 6 ... . 16c

4c, 12c, 30c, or 60c 2n, 16n, or 32n On or 6n 2norl6n 2norl6n 2n or 1 6n 2n or 16n 4c, 17c,or30c 2c, 16c, or64c 2n, 16n, or 64n

F F F F F F F F M F

a

StimuTreatment5s' Age in lus Ss per Test Years Groups Cell Interval 5-6 6-81/2

6-8 71/2-91/2 71/2-91/2

6-71/2 6-71/2 51/2-6 6-8 8-10

4 3 2 2 2 2 2 3 3 3

10 16 16 7 7 7 7 7 7 11

immediate e immediate immediate 1 min. 8min. 1 min. 8 min. immediate immediate immediate

Study numbers correspond to those in Figure 9 and Table 2. "Number of stimulus presentations in 10 minutes. Stimulus presentations were contingent (c) or non-contingent (n) upon behavior. c Within 30 seconds. d The three groups in Experiment 2a were tested a month before the two groups in Experiment 2b and in different schools. 8 Each of several schools provided a portion of the subjects for each of the experimental groups 3a-d; all groups were studied simultaneously.

16

JACOB L.GEWIRTZ A preliminary attempt was made to establish a maintenance level for stimulus receipt in Experiments 4, 5, and 6, and to implement satiation and deprivation conditions in terms of that level. The details of the designs of these experiments are outlined in Table 1. In each experiment, one E worked with all Ss. Care was taken to ensure that E behaved uniformly with all 5s, for E knew the expected pattern of results. Even so, only systematic replication of the experiments with various Es, S samples, and designs can guarantee elimination of E bias. It is assumed that in their role in controlling behavior, the stimulus words used operate like other physical and social stimuli, even though those stimuli differ in their physical properties and may have acquired their value on different bases. Further, though a test of reinforcing stimulus efficacy is used in these studies, the literature suggests that satiation and recovery functions similar to those in these experiments will hold for the efficacy of stimuli tested also in discriminative and evoking roles. This expectation remains whether the satiation operation provides the stimulus non-contingent or contingent upon behavior. The equivalence of the particular reinforcing stimulus used in each study to other physical and social stimuli and to stimuli with different functions remains to be tested. A single reinforcing stimulus has been used in each experiment, in order to eliminate stimulus type or function as a source of variation. One of the stimulus words used here, good, has also been used in many experiments that were intended as replications of the original Gewirtz and Baer studies (e.g., Walters & Ray, 1960) as well as in experiments conducted to extend the original results. Stimulus Satiation The design, experimental manipulations, and response indices of these experiments are formally similar to those typically used in designs for satiation effects of pre-feeding in studies of appetitive drives. In such studies, several levels of relative satiation for a stimulus are implemented by varying the number of stimulus presentations in a period of constant length. A test for the effects of the satiation operations on the reinforcing efficacy of the stimulus follows after a time interval of fixed length. In these experiments the test is a discrimination-learning task which follows immediately after the operation of stimulus provision. A maintenance level for the stimulus is assumed to operate in any such design. However, it was thought that it would not be difficult to find levels

17

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY of stimulus provision that would function as satiation operations (by lowering the subsequent potency of the stimulus in controlling 5's behavior), regardless of 5's maintenance level for the stimulus, the length of the last major recovery interval from satiation, or the degree of recovery since S last received such stimuli. FIRST EXPERIMENT

The 40 male 5s in the first of these experiments (Landau & Gewirtz, 1967) were five-and-one-half-year-old boys enrolled in seven municipal kindergartens in Jerusalem. The relative satiation design used a fixedlength treatment phase in which E, a woman in her mid-twenties, provided the stimulus contingently different numbers of times, according to one of four fixed-interval (FI) schedules, immediately before a discriminationlearning test under 100 per cent reinforcement with the same stimulus. This test for the reinforcing efficacy of the pre-fed stimulus was standard for all 5s. Treatment. For the treatment task, S was asked to describe each of a standard set of forty-one successive pictures of artisans, furniture, tools, and so forth which had been cut out of children's books. The stimulus, presented contingent upon the emission of the first descriptive word after the end of the fixed interval, was the Hebrew word yafeh, meaning "nice" or "well done." The four FI schedules, which facilitated presenting the stimulus the required number of times during the 10-minute treatment period, were 180, 50, 20, or 10 seconds for 4,12, 30, or 60 stimulus presentations respectively. The numbers of times the treatment stimulus was provided defined the experimental conditions. Sixty-nine potential 5s completed the treatment phase. Test. A two-choice simultaneous discrimination-learning procedure was used in the test phase to determine whether the differential satiation for the stimulus lowered proportionately its reinforcing effectiveness for 5's behavior. This test was selected both to be sufficiently interesting for 5s of the ages studied so that they would not habituate to the task before completing all the trials, and at the same time to permit a reasonably rapid learning of the discrimination. The correct response was reinforced with yafeh every time it occurred. The test was preceded by a block of 15 unreinforced baselevel trials to establish which stimulus choice would be reinforced in testing as correct — that is, the stimulus preferred less often in the 15 trials. Subjects who chose one stimulus fewer than 4 times out of 18

JACOB L.GEWIRTZ

15 in this initial block were eliminated because the base rate of that choice response was assumed to be too low to permit ready conditioning. Since twenty-nine Ss who had gone through the treatment phase were eliminated on this basis, the test used in this and the following studies is seen to be less than optimally efficient. The 15 baselevel trials were followed by the 75-trial discrimination test. The cards for the conditioning test were set up by E within thirty seconds after the completion of the treatment. She instructed each S to choose the picture he preferred from the pair on each test card presented. The stimuli in the discrimination task, which had not been involved in the treatment phase, were plants and animals. The experimenter's manner throughout was intended to prevent S's acquiring the notion that aesthetic considerations were at issue. (If S seemed to ask for E's approval of his stimulus choice on any of the baselevel or discrimination trials, E said yes matterof-factly.) The test cards in this and all subsequent studies were presented in a standard order to all 5s. The stimuli of each class were randomized and their positions counterbalanced within the successive sets of 10 pairs. Results and Discussion. The main between-groups effect was partitioned by an orthogonal-polynomial analysis of the mean total test scores, employing equal rather than proportional distances between the four or-

Figure 1. Mean number of words (minus baselevel) emitted by Ss in treatment (at left) and mean correct (reinforced) choices in the 75 test trials (at right) of Experiment 1 for four groups with different numbers of contingent presentations of the stimulus word yafeh in treatment. 19

Figure 2. Treatment (at left) and test (at right) response scores in Experiment 1 for the four groups given different numbers of contingent stimulus presentations during treatment. Baselevel scores are subtracted from 5s' word emission scores in treatment, and these adjusted scores are plotted in 2-minute treatment blocks. Mean number of correct (reinforced) choices are plotted by 15-trial test blocks.

Figure 3. Treatment (at left) and test (at right) response scores in Experiment 1 with the four groups combined into two in terms of their treatments: a low satiation group with few presentations of the stimulus (4 or 12) and a high satiation group with many presentations (30 or 60). Mean scores are plotted as in Figure 2. 20

JACOB L. GEWIRTZ dered satiation levels implemented. A linear component of trend was found (p UL O LL & ADC (p UL G? LL& ADC O UL, LL, & ADC (p LL (p LL (p L L (pUL&ADC (p UL, LL, & ADC (p UL, LL, & ADC (p where Xi 2 — (fi~PiN) 2 /[pi(l — pi)N] and ft = observed frequency of correct responses, pi = predicted probability of a correct response, N = number of students. Addition — Grades Four and Five. The three independent variables used in the regression analyses for addition were the variable NSTEPS, which was described in detail earlier, and the two magnitude variables, magnitude of sum (MAGSUM) and magnitude of the smallest addend (MAGSMALL). It is obvious that the value of MAGSUM and MAGSMALL is independent of whether the problem for the student was to find the missing sum or a missing addend. For example, in the three related problems 180

PATRICK SUPPES 7 + 9 = , 7 + =16, and + 9 = 16, MAGSUM = 16 and MAGSMALL = 7. The coefficients obtained for the regression equations are shown in Table 2. This table indicates the level of problems analyzed, the number of children who worked on the problems in that level (Subjects),* the number of different problems analyzed, t the regression constant, and the Table 2. Linear Regression Coefficients for Addition in the Fourth and Fifth Grades

Level

No. of No. of Sub- Probjects lems

2 3 4 5

6 21 24 9

2 3 4 5

6 21 24 9

2 3 4

7 41 34

2 3 4

7 41 34

3 & 4 combined 12 3 & 4 combined 12

Constant

MAG-

R

Ra

-0.03 0.05 -0.09

0.61 0.56 0.86 0.40

0.37 0.32 0.74 0.16

-0.07 -0.09 0.07 0.00

0.64 0.69 0.86 0.44

0.40 0.48 0.74 0.19

-0.02 -0.01 0.01

0.54 0.64 0.80

0.29 0.41 0.64

-0.09 -0.06 0.02

0.64 0.82 0.75

0.42 0.68 0.56

0.03

0.81

0.66

0.07

0.73

0.54

NSTEPS MAGSUM SMALL

Grade 4, Set 1, Proportion of Errors 19 -2.73 0.16 0.09 38 -2.65 0.16 0.05 38 -1.44 0.24 -0.01 19 -1.74 0.08 0.03 Grade 4, Set 1, Success Latency 19 0.24 0.18 0.14 38 -0.76 0.47 0.13 38 2.32 0.57 -0.02 19 2.19 0.17 0.00 Grade 4, Set 2, Proportion of Errors 57 -1.69 0.17 0.02 95 -0.73 0.21 -0.01 76 -1.60 0.20 0.00 Grade 4, Set 2, Success Latency 57 0.95 0.56 0.06 95 1.77 0.73 0.01 76 1.55 0.47 0.01 Grade 5, Proportion of Errors 57 -2.41 0.10 0.03 Grade 5, Success Latency 57 -2.22 0.47 0.09

-0.03

regression coefficients for the three independent variables. The absence of a value of a given coefficient indicates that the variable it applies to made no significant contribution to the regression equation, and the computer program therefore did not use that variable in obtaining a regression line. In reading the regression table it should be remembered that the transformation described previously was applied to the observed proportion of * The number of subjects or students shown in the various tables is always an approximation, with the exact number varying slightly from day to day. t For reasons mentioned below, the first problem was deleted from each drill, leaving 19 problems per drill. The number of different daily drills in an analysis can be calculated by dividing the number of problems by 19. 181

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY errors, and therefore when obtaining a prediction from the coefficients for proportion of errors, the numbers zt calculated from the coefficients must be transformed to obtain the predicted proportion of errors. It is clear from scanning the coefficients in Table 2 that NSTEPS is the most important of the three variables in predicting both errors and sucTable 3. Predicted and Observed Proportions of Errors and Success Latency in Fourth-Grade Addition, Concept Block 1, Level 4 Rank

Equations

n -4- 79 = o 41 ,1+18= +o 2 1 4- 77 = 0 43 7 + 16 = 044 04-14 = 0 + 5 1 4- 7,6 = 0 46 1+75= +0 7 4 4- 7.7 = 7 48 . . 11 4- 3 = 4-29 9 . .174- 10= +0 10 104- 16 = 6411 7.7 4- 7 = 1 0 412 74- 18 = 0413 Q 4- 78 = 7 414 104-79 = 8415 11 4- 17= +1 16 744-1 = 5417 18 , 17+5= +11 94-14 = +7 19 94- 18= 4-5 20 144-5=11 421 774-7= 4-14 22 7 + 77 = 6 + 23 11 4-78 = 8424 77 4- 7 = 4-70 25 .174-77=5426 ..154-1= 4-17 27 104-7= 4-5 28 71 + 7 = +8 29 . . 75 4- 4 = 1 1 430 194-8= 4-6 31 . . 17 4- 5 = 4-9 32 .794-7= 4-15 33 774- 17=16 + 34 ..174-77= +6 35 36. . . 114-1 =7 + 144-10 = 9437 ..794-1= 4-17 38

Observed Predicted Observed Predicted d-P.) (1-pi) Latency Latency

0.01 0.05 0.06 0.09 0.09 0.14 0.17 0.27 0.27 0.28 0.39 0.39 0.39 0.46 0.46 0.53 0.58 0.58 0.58 0.61 0.64 0.72 0.72 0.73 0.73 0.73 0.73 0.73 0.75 0.75 0.75 0.91 0.91 0.91 0.91 091 0.92 0.96

0.03 0.13 0.16 0.13 0.03 0.16 0.16 0.68 0.79 0.18 0.41 0.64 0.38 0.77 0.53 0.56 0.46 0.40 0.72 0.76 0.59 069 0.53 0.67 0.66 0.59 0.54 0.54 083 0.61 078 0.72 0.85 095 085 064 084 093

2.40 3.20 2.60 3.80 3.40 3.70 2.90 7.30 5.70 4.50 3.90 5.20 4.50 6.50 5.00 5.80 5.00 6.20 7.50 7.40 5.90 7.60 600 600 6.40 7.00

2.23 3.72 3.97 3.74 2.12 3.95 4.02 6.33 6.86 4.11 5.00 5.78 5.19 6.53 5.41 5.87 5.35 5.02 6.51 6.63 5.78 6 15 5 50 598 6.03 5.78

4.60 700 570 640

574 688 594 670

6.10 8.10

7 13 8 09

760 630

6 19 697

X3=87.94 (38 items); xa (items < 10) = 70.43 (37 items);S2 = 0.73. 182

X3

0.40 0.69 2.84 0.16 1.45 0.08 0.00 8.30 17.51 2.53 0.04 9.75 0.01 5.91 0.26 0.16 2.37 5.04 3.11 4.68 0.11 0 19 5.37 0.19 0 19 0.90 1 62 1 54 1 46 290 025 1 91 026 039 034 3 49 1 43 0 13

PATRICK SUPPES cess latencies. A rough indication of the goodness of fit of the regression lines is reflected by the multiple correlation coefficient R and its square R2, which is an estimate of the amount of variance accounted for by the regression model. In only one case is less than 40 per cent of the variance in the success latency accounted for by the model. When one takes into account the facts that the two magnitude variables account for a relatively small amount of the variance, and that in setting up the variable NSTEPS we have combined several potentially powerful and probably independent variables, the results are encouraging. Table 3 presents an example of the individual contributions of the problems to x2 when a set of coefficients for response errors given in Table 2 was used to predict the proportions of errors. Included in Table 3 are the rank order of observed problem difficulty, the observed proportion of students making errors (Observed [1 —pi]), the proportion of errors predicted from the linear regression model (Predicted [1 — pi]), and the actual component of the x2 contributed by the problem. Also included in Table 3 are the observed and predicted success latencies for individual problems. The problems in Table 4 constitute one of the eight sets of drills for which variable weights were calculated and presented in Table 2.* Table 4 summarizes the total x2 and S2 for all eight sets of drills. Some of the x2 values obtained in Table 4 are extremely high and would usually be an indication of a poor fit, but a closer look at the components of the X2 showed that a few problems in each set or drill made extremely large contributions to the total x2- In Table 3, for instance, problem 9 contribTable 4. Total x2 and S2 Obtained as a Measure of Fit of Predicted versus Observed Proportion of Errors and Success Latency for Addition

Grade 4 4 4 4 4 4 4 5

No. of Concept Block Level Problems

Sz

x2

2 3 4 5 2 3 4 3&4

.65 1.29 .73 1.17 2.29 .62 1.04 2.32

18.03 233.91 87.94 24.69 97.02 391.87 225.08 64.00

1 1 1 1 3 3 3 3

19 38 38 19 57 95 76 57

No. of Reduced Items in a Reduced x Xs

18.03 83.78 70.43 24.69 66.31 156.75 134.90 64.00

33 37 55 83 70

* Complete data on individual problems may be found in the Institute's Technical Report No. 100, Linear Structural Models for Response and Latency Performance in Arithmetic.

183

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY uted 20 per cent of the total x2 obtained. In several of the other sets of drills two or three particular problems contributed as much as 70 per cent of the total x2. In some of the sets of drills, as in the one in Table 3, the reduction in x2 obtained by deleting a few extreme problems is still insufficient to yield a value of x2 such that the model would normally be accepted. When we do reduce the x2 values presented in Table 4 by removing the few extreme components whose individual contributions are equal to or greater than 10, we find that in four of the eight cases we obtain a x2 value whose probability is such that .l