Statistical inference based on ranks

This paper develops a unified approach, based on ranks, to the statistical analysis of data arising from complex experimental designs. In this way we answer a major objection to the use of rank procedures as a major methodology in data analysis. We show that the rank procedures, including testing, estimation and multiple comparisons, are generated in a natural way from a robust measure of scale. The rank methods closely parallel the familiar methods of least squares, so that estimates and tests have natural interpretations.This research was supported in part by grant MCS76-07292 from the National Science Foundation.     

Best univocal estimates of orthogonal common factors

A general formulation is presented for obtaining conditionally unbiased, univocal common-factor score estimates that have maximum validity for the true orthogonal factor scores. We note that although this expression is formally different from both Bartlett's formulation and Heermann's approximate expression, all three, while developed from very different rationales, yield identical results given that the common-factor model holds for the data. Although the true factor score validities can be raised by a different non-orthogonal transformation of orthogonalized regression estimates—as described by Mulaik—the resulting estimates lose their univocality.     

Verbal self-reports about matching to sample: effects of the number of elements in a compound sample stimulus.

Adults' self-reports about their choices in a delayed matching-to-sample task were studied as a function of the number of elements (one, two, or three) in a compound sample stimulus. Signal-detection analyses were used to examine control of self-reports by the number of sample elements, by the speed and accuracy of choices reported about, and by several events contingent on self-reports. On each matching-to-sample trial, a sample element appeared as one of two comparison stimuli. Choice of the matching element, if made within 500 ms of the onset of the comparison stimuli, produced points worth money or chances in a drawing for money, depending on the subject. After each choice, subjects pressed either a "yes" or "no" button to answer a computer-generated query about whether the choice met the point contingency. The number of sample elements in the matching-to-sample task varied across trials, and events contingent on self-reports varied across experimental conditions. In Experiment 1, the conditions were defined by different combinations of feedback messages and point consequences contingent on self-reports, but self-reports were systematically influenced only by the sample-stimulus manipulation. Self-report errors increased with the number of sample elements. False alarms (inaccurate reports of success) were far more common than misses (inaccurate reports of failure), and false alarms were especially likely after choices that were correct but too slow to meet the point contingency. Sensitivity (A') of self-reports decreases as the number of sample elements increased. In addition, self-reports were more sensitive to choice accuracy than to choice speed. All subjects showed a pronounced bias (B'H) for reporting successful responses, although the bias was reduced as the number of sample elements increased and successful choices became less frequent. Experiment 2 demonstrated that the failure of point contingencies to influence self-reports in the first experiment was not due to a general ineffectiveness of the point consequences. Rates of inaccurate self-reports decreased when they resulted in point losses and increased when they resulted in point gains.     

The effect of increased response requirements on discriminative performance of the domestic hen in a visual acuity task.

Six domestic hens were trained in a spatial discrimination task. A controlled reinforcement procedure insured that the ratio of scheduled and obtained reinforcement remained equal. Gray stimuli and gratings ranging in spatial frequency from 1 to 10 cycles per millimeter were presented in seven descending series of probes. The response requirement to the sample key was varied from fixed ratio 1 to fixed ratio 40 in seven experimental conditions. An increase in response requirements from fixed ratio 1 to fixed ratio 5 and fixed ratio 10 resulted in significantly higher accuracy at discriminable grating values. Further increases in response requirements did not consistently improve performance. Generally, response biases increased and occasionally became extreme for probes at finer gratings with increased response requirements.     

The transfer of specific and general consequential functions through simple and conditional equivalence relations

The purpose of this study was to examine the transfer of consequential (reinforcement and punishment) functions through equivalence relations. In Experiment 1, 9 subjects acquired three three-member equivalence classes through matching-to-sample training using arbitrary visual forms. Comparison stimuli were then given conditioned reinforcement or punishment functions by pairing them with verbal feedback during a sorting task. For 8 of the 9 subjects, trained consequential functions transferred through their respective equivalence classes without additional training. In Experiment 2, transfer of function was initially tested before equivalence testing per se. Three of 4 subjects showed the transfer without a formal equivalence test. In Experiment 3, 3 subjects were given training that gave rise to six new three-member conditional equivalence classes. For 2 of the subjects, the same stimulus could have either a reinforcement or punishment function on the basis of contextual cues that defined its class membership. Experiment 4 assessed whether equivalence training had established general or specific consequential functions primarily by adding novel stimuli in the transfer test. Subjects treated even novel feedback stimuli in the transfer test as consequences, but the direction of consequential effects depended upon the transfer of specific consequential functions through equivalence relations.     

Transient effects of acquisition history on generalization in a matching-to-sample task

This study examined the role of learning history on the acquisition of a matching-to-sample task. Twelve preschool children learned four stimulus classes through instructions, shaping, or imitation. After reaching criterion, the subjects were exposed to changed discrimination contingencies to determine how each learning history affected the acquisition of responses appropriate to the new contingencies. All subjects reached criterion on the new relations, although the subjects with a shaping history adapted slightly more quickly than those subjects with a history of instructions or imitation. Given sufficient exposure to changed contingencies, rule-driven insensitivity to contingencies was overcome by experience with consequences. This result may be specific to younger subjects, but it suggests that instructions can be used in education without creating insensitivity to contingencies.     

THE FORMATION OF VISUAL STIMULUS EQUIVALENCES IN CHILDREN

Four normal children were presented a series of matching-to-sample tasks, using five sets of visual stimuli designated A, B, C, D, and E. Stimulus equivalences were established by matching stimuli from one set to those from another set. Each set consisted of three stimuli, so matching set A to set D meant that each stimulus in set A served as a sample with all three stimuli in set D as comparisons. Subjects were first taught AD and DC matching and were then able to perform AC/CA matching without additional training. After ED was taught directly, CE/EC and AE/EA performances emerged. Following CB training, three new equivalences were demonstrated: AB/BA, EB/BE, and DB/BD. Oral naming of each stimulus showed that subjects had not assigned a common label to stimuli in the same class, indicating that naming is not necessary for the formation of stimulus equivalences. The absence of response mediation suggests that matching to sample can form direct stimulus-stimulus associations. The data also provide support for the notion that generative performances are outcomes of existing stimulus-control relationships.     

Food wrenching and dodging: Eating time estimates influence dodge probability and amplitude

Eating rats dodge conspecifics, who are trying to steal their food, by making a somewhat stereotyped 180° turn and step movement to block the robber's approach. This experiment examined the effect of food features on the form and vigor of the dodging movement. Dodge probability and its amplitude were measured as a function of food size, elapsed eating time, food hardness, and the way in which food theft was attempted. Under all conditions dodge probability and its amplitude were directly related to the time necessary to complete eating. Thus, rats estimated the time required to complete eating and adjusted the size of their evasive movements to gain this time. The results show that although dodging has the appearance of a fixed-action pattern, it is influenced by cognitive processes that may be similar to those that direct other aspects of foraging behavior. © 1994 Wiley-Liss, Inc.     

Intuitions about sample size: the empirical law of large numbers

According to Jacob Bernoulli, even the ‘stupidest man’ knows that the larger one's sample of observations, the more confidence one can have in being close to the truth about the phenomenon observed. Two-and-a-half centuries later, psychologists empirically tested people's intuitions about sample size. One group of such studies found participants attentive to sample size; another found participants ignoring it. We suggest an explanation for a substantial part of these inconsistent findings. We propose the hypothesis that human intuition conforms to the ‘empirical law of large numbers’ and distinguish between two kinds of tasks–one that can be solved by this intuition (frequency distributions) and one for which it is not sufficient (sampling distributions). A review of the literature reveals that this distinction can explain a substantial part of the apparently inconsistent results. © 1997 John Wiley & Sons, Ltd.     

Testing Measurement Invariance of the Dark Triad Dirty Dozen in a Belgian Adult Sample

The Dirty Dozen (Jonason & Webster, 2010) is a frequently used concise version of the Dark Triad to measure three socially aversive personality traits: Machiavellianism, psychopathy and, narcissism. The present study has examined measurement invariance in a sample of Belgian adults. The present study aims to assess measurement invariance of the Dutch version of the Dirty Dozen measure across gender in a large city-based representative adult sample in Belgium (N = 1587). Multi-group first-order confirmatory factor analysis for categorical indicators was utilized. In addition, unique associations between Dirty Dozen traits, trait self-control and, acceptance of illegitimate norms were examined in a series of structural equation models. Results indicated that the internal consistency of the Dirty Dozen subscales was good for Machiavellianism (α = 0.80) and narcissism (α = 0.80), but modest for psychopathy (α = 0.64). The hypothesized three correlated factors model with separate factors for Machiavellianism, psychopathy and, narcissism provided a poor fit for men and women. Invariance testing across gender showed evidence for weak invariance only, indicating that the underlying latent factors are measured the same way with the same metric in the two populations. However, we were not able to establish strong measurement invariance. Observed group differences should be interpreted with caution. Furthermore, Machiavellianism and psychopathy were strongly associated with trait self-control in both men and women. Strong correlations were found between acceptance of illegitimate norms and Dirty Dozen traits, Machiavellianism and, psychopathy, but not with narcissism.