Four bootstrap confidence intervals for the binomial-error model

Confidence intervals for the mean function of the true proportion score ( _x ), where andx respectively denote the true proportion and observed test scores, can be approximated by the Efron, Bayesian, and parametric empirical Bayes (PEB) bootstrap procedures. The similarity of results yielded by all the bootstrap methods suggests the following: the unidentifiability problem of the prior distributiong() can be bypassed with respect to the construction of confidence intervals for the mean function, and a beta distribution forg() is a reasonable assumption for the test scores in compliance with a negative hypergeometric distribution. The PEB bootstrap, which reflects the construction of Morris intervals, is introduced for computing predictive confidence bands for x. It is noted that the effect of test reliability on the precision of interval estimates varies with the two types of confidence statements concerned.The Authors are indebted to the Editor and anonymous reviewers for constructive suggestions and comments. The authors wish to thank Min-Te Chao and Cheng-Der Fuh for some useful suggestions at earlier stages of writing this paper.     

The transfer of contextual control over equivalence classes through equivalence classes: a possible model of social stereotyping.

In Experiment 1, subjects acquired conditional equivalence classes controlled by three male and three female names as contextual stimuli. When equivalence relations were tested using new names not used in training (three male and three female), contextual control remained intact. Thus, generalized control of the composition of conditional equivalence classes by characteristically gender-identified names was shown. A basic analysis of this finding was tested in Experiment 2. Contextual equivalence classes were established using as contextual stimuli nonrepresentational visual figures that were members of additional pretrained three-member equivalence classes. When other stimuli in the pretrained equivalence classes were used as contextual stimuli, the conditional equivalence classes remained intact. Control subjects showed that this effect depended on the equivalence relations established in pretraining. The results show that contextual control over equivalence classes can transfer through equivalence classes. The implications of this phenomenon for social stereotyping are discussed.     

The simplicity of theories: Its degree and form

Almost all commentators acknowledge that among the grounds on which scientists perform theory-choices are criteria of simplicity. In general, simplicity is regarded either as only a logico-empirical quality of a theory, diagnostic of the theory's future predictive success, or as a purely aesthetic or otherwise extra-empirical property of it. This paper attempts to demonstrate that the simplicity-criteria applied in scientific practice include both a logicoempirical and a quasi-aesthetic criterion: to conflate these in an account of scientists' theory-choice is to court confusion.     

Extending sequence-class membership with matching to sample

Three normal adults were first trained to point sequentially to each member of several pairs of visual stimuli. This baseline training established one class of stimuli to which subjects responded first, and another class of stimuli to which they responded second. Then, in a matching-to-sample procedure, baseline-sequence stimuli served as samples and new visual stimuli served as comparisons. Subjects were trained to choose one group of new comparisons when the sample was a "first" stimulus from the sequence baseline, and to choose the other new comparison stimuli when the sample was a "second" from the sequence baseline. When the new stimuli were then presented as pairs in the posttest, two subjects pointed to them in sequences predictable on the basis of the stimulus-class membership established during matching to sample. The failure of one subject to demonstrate sequential transfer was shown to be a consequence of the failure of the matching-to-sample procedure to establish stimulus classes. The production of sequences that were not directly trained suggested an empirical approach to the analysis of simple grammatical behavior.     

Using the simultaneous protocol to study equivalence class formation: the facilitating effects of nodal number and size of previously established equivalence classes

The emergence of equivalence classes in college students is unlikely when all baseline relations are trained concurrently and all probes for emergent relations are then introduced concurrently (the simultaneous protocol). This experiment showed how the number of nodes and the size of previously established equivalence classes enhanced the emergence of new equivalence classes under the simultaneous protocol. First, one-node three-, five-, or seven-member classes or three-node five- or seven-member classes were established with college students. A sixth group received no pretraining. Then, the simultaneous protocol was used to establish new three-node five-member equivalence classes with all students. The speed and variability with which the baseline relations were established in the simultaneous protocol were inverse functions of number of nodes in the previously established classes, but not of their size. The percentage of subjects who showed the emergence of new equivalence classes under the simultaneous protocol was a direct function of number of nodes and size of pretrained classes. The additional time spent for pretraining greatly reduced the total training time needed to produce individuals who showed the emergence of classes under the simultaneous protocol. The total time saved was a direct function of number of nodes and number of stimuli in the pretrained classes.     

Incongruous stimulus pairing and conditional discrimination training: effects on relational responding

In Experiment 1, 5 subjects were exposed to a stimulus-pairing procedure in which two nonsense syllables, identified by a letter-number code as A1 and C2, each predicted the onset of a sexual film clip, and the nonsense syllables A2 and C1 each predicted the onset of a nonsexual film clip. Subjects were then exposed to a matching-to-sample test in which the nonsense syllables A1 and A2 were presented as sample stimuli and C1 and C2 were presented as comparison stimuli and vice versa (i.e., C stimuli as samples and A stimuli as comparisons). All subjects matched A1 with C2 and A2 with C1. Subjects were then trained on the conditional discriminations A1-B1, A2-B2, B1-C1, B2-C2, after which the matching-to-sample test was again administered. All subjects continued to match A1 with C2 and A2 with C1 in accordance with the earlier stimulus-pairing contingencies. An additional 5 subjects were exposed first to conditional discrimination training and testing before being exposed to the incongruous stimulus pairing and matching-to-sample testing. Under these conditions, 4 of the 5 subjects always matched A1 with C1 and A2 with C2. Experiment 2 replicated Experiment 1, except that a matching-to-sample test was not administered following the initial training procedure. Under these conditions, matching-to-sample test performances were controlled by the contingencies that had immediately preceded the test. Experiment 3 indicated that initial matching-to-sample test performances were unlikely to change, even after repeated exposure to incongruous training and testing. Experiment 4 demonstrated that pretraining with unrelated stimulus sets increased the sensitivity of matching-to-sample test performances to incongruous contingencies when they were similar in format to those arranged during pretraining. These data may have implications for a behavior-analytic interpretation of attitude formation and change.     

Predicting the extension of equivalence classes from primary generalization gradients: the merger of equivalence classes and perceptual classes.

In Experiment 1, 6 college students were given generalization tests using 25 line lengths as samples with a long line, a short line, and a “neither” option as comparisons. The neither option was to be used if a sample did not go with the other comparisons. Then, four-member equivalence classes were formed. Class 1 included three nonsense words and the short line. Class 2 included three other nonsense words and the long line. After repeating the generalization test for line length, additional tests were conducted using members of the equivalence classes (i.e., nonsense words and lines) as comparisons and intermediate-length lines as samples. All Class 2 comparisons were selected in the presence of the test lines that also evoked the selection of the long line in the generalization test that had been given before equivalence class formation. Class 1 yielded complementary findings. Thus, the preclass primary generalization gradient predicted which test lines acted as members of each equivalence class. Regardless of using comparisons that were nonsense words or lines, the post-class-formation gradients overlapped, showing the substitutability of class members. Experiment 2 assessed the discriminability of the intermediate-length test lines from the Class 1 (shortest) and Class 2 (longest) lines. The test lines that functioned as members of an equivalence class were discriminable from the line that was a member of the same class by training. Thus, these test lines also acted as members of a dimensionally defined class of “long” or “short” lines. Extension of an equivalence class, then, involved its merger with a dimensionally defined class, which converted a close-ended class to an open-ended class. These data suggest a means of predicting class membership in naturally occurring categories.     

Why behavior analysts should study emotion: the example of anxiety.

Historically, anxiety has been a dominant subject in mainstream psychology but an incidental or even insignificant one in behavior analysis. We discuss several reasons for this discrepancy. We follow with a behavior-analytic conceptualization of anxiety that could just as easily be applied to emotion in general. Its primary points are (a) that language-able humans have an extraordinary capacity to derive relations between events and that it is a simple matter to show that neutral stimuli can acquire discriminative functions indirectly with no direct training; (b) that private events can readily acquire discriminative functions; (c) that anxiety disorders seem to occur with little apparent direct learning or that the amount of direct learning is extraordinarily out of proportion with the amount of responding; and (d) that the primary function of anxious behavior is experiential avoidance. We conclude that the most interesting aspects of anxiety disorders may occur as a function of derived rather than direct relations between public events and overt and private responses with avoidance functions. Implicit in this conclusion and explicit in the paper is the assertion that anxiety is a suitable subject for behavior-analytic study.     

The social unconscious in clinical work

An analyst who is unaware of the constraints of social facts and forces will be insensitive to their unconscious recreation within therapeutic situations, and unable to provide space for patients to imagine how their identities have been formed at particular social and political junctures. The concepts of the social unconscious and of equivalence are defined and located within the traditions of Group Analysis and British Object Relations Theory. A model of maturity is outlined, the central element of which is the willingness and ability to take the role of citizen. These ideas are illustrated with clinical vignettes from psychoanalysis and group analysis.