Some results on extensions and modifications of the Theil — Sen regression estimator

Many robust regression estimators have been proposed that have a high, finite‐sample breakdown point, roughly meaning that a large porportion of points must be altered to drive the value of an estimator to infinity. But despite this, many of them can be inordinately influenced by two properly placed outliers. With one predictor, an estimator that appears to correct this problem to a fair degree, and simultaneously maintain good efficiency when standard assumptions are met, consists of checking for outliers using a projection‐type method, removing any that are found, and applying the Theil — Sen estimator to the data that remain. When dealing with multiple predictors, there are two generalizations of the Theil — Sen estimator that might be used, but nothing is known about how their small‐sample properties compare. Also, there are no results on testing the hypothesis of zero slopes, and there is no information about the effect on efficiency when outliers are removed. In terms of hypothesis testing, using the more obvious percentile bootstrap method in conjunction with a slight modification of Mahalanobis distance was found to avoid Type I error probabilities above the nominal level, but in some situations the actual Type I error probabilities can be substantially smaller than intended when the sample size is small. An alternative method is found to be more satisfactory.     

Testing whether independent treatment groups have equal medians

The paper suggests new methods for comparing the medians corresponding to independent treatment groups. The procedures are based on the Harrell-Davis estimator in conjunction with a slight modification and extension of the bootstrap calibration technique suggested by Loh. Alternatives to the Harrell-Davis estimator are briefly discussed. For the special case of two treatment groups, the proposed procedure always had more power than the Fligner-Rust solution, as well as the procedure examined by Wilcox and Charlin. Included is an illustration, using real data, that comparing medians, rather than means, can yield a substantially different conclusion as to whether two distributions differ in terms of some measure of central location.     

Bradley — Terry — Luce models to incorporate within‐pair order effects: Representation and uniqueness theorems

The paper presents different representation theorems for the Bradley — Terry — Luce (BTL) models of Beaver and Gokhale and of Davidson and Beaver. In particular, algorithms that can be used in constructing BTL scales are provided. The uniqueness theorems show that the Davidson — Beaver model should be preferred to the Beaver — Gokhale model since the multiplicative order effect parameter is uniquely determined whereas the additive effect parameter is merely a ratio scale. Finally, a relationship to the simple BTL model is established. Let p(a, b) denote the probability that a is chosen when (a, b) is presented in a fixed order. Then the probabilities p(a, b) satisfy the Beaver — Gokhale model if and only if the balanced probabilities p_b(a, b):= ½ (p(a, b) + 1–p (b, a)) satisfy the simple BTL model.     

Differential use of partial information by good and poor readers

Two interpretations of the poor readers' deficit are examined. According to one interpretation, poor readers are primarily deficient in use of phonetic information, and, thus, their deficit is specific to reading or at least to use of language. A second interpretation is that good and poor readers differ in their ability or tendency to use stimulus attributes—that is, partial information for stimulus identity—and, thus, their deficit is not specific to reading. Three experiments provide evidence favoring the second interpretation. Good and poor readers perform differently in tests of memory—whether or not the stimulus items are coded phonetically—when information about stimulus identity is incomplete due to memory loss and the response measure is sensitive to partial-information use in guessing. Likewise, the two groups perform differently in a perceptual task when information for stimulus identity is partial, but they perform at similar levels when information is complete.     

Self-estimates of intelligence: interaction effects of the comparison to a specific reference group and neuroticism

An experiment that investigated the interaction effect of Neuroticism and the comparison to different reference groups on self-estimates of intelligence is reported. University students (100 men, 15 women) were randomly assigned to two experimental groups and asked to rate their own intelligence on a one-item measure, in IQ points, having been provided with reference values for either the general population or a student sample. Analysis of data confirmed that the accuracy of self-estimates of intelligence was influenced by the variation of the instruction. Participants provided more accurate estimations when confronted with comparison information about fellow students than about the general population. Persons scoring high on Neuroticism estimated their intelligence lower, but only when their estimation was based on a general reference group. Theoretical and practical implications were discussed.     

Comparing one-step m-estimators of location corresponding to two independent groups

Experience with real data indicates that psychometric measures often have heavy-tailed distributions. This is known to be a serious problem when comparing the means of two independent groups because heavy-tailed distributions can have a serious effect on power. Another problem that is common in some areas is outliers. This paper suggests an approach to these problems based on the one-step M-estimator of location. Simulations indicate that the new procedure provides very good control over the probability of a Type I error even when distributions are skewed, have different shapes, and the variances are unequal. Moreover, the new procedure has considerably more power than Welch's method when distributions have heavy tails, and it compares well to Yuen's method for comparing trimmed means. Wilcox's median procedure has about the same power as the proposed procedure, but Wilcox's method is based on a statistic that has a finite sample breakdown point of only 1/n, wheren is the sample size. Comments on other methods for comparing groups are also included.     

Majority — minority status and perceived ingroup variability revisited

Social identity theory predicts that ingroup members should see their group as more homogeneous when confronted by a large and presumably dominant outgroup. This prediction has been supported in a series of recent studies, all of which purport to show that the usual ingroup—outgroup difference in perceived variability, i.e. outgroup homogeneity, is reversed when the ingroup is in a minority position. In all of these studies, however, the ingroup—outgroup distinction has been confounded with the size of the target group judged. The present study was conducted to overcome this confound. Subjects judged both the ingroup and outgroup, under one of two different orders, and the first group judged varied in size across subjects while the size of the second group was held constant. This permitted comparisons of the perceived variability of the second judged group (be it the ingroup or outgroup) when it followed the judgment of either a larger or equal size first group. Consistent with social identity theory, ingroups were judged as less variable when judged after a large outgroup than after a small one. This was true, however, only on measures of perceived dispersion and not on measures of perceived stereotypicality. On both sorts of measures, however, overall outgroup homogeneity was found, over and above the difference due to the comparison of the ingroup with a large or small outgroup.     

THE ‘EXTENDEDNESS’ OF SCIENTIFIC EVIDENCE

In recent years, the idea has been gaining ground that our traditional conceptions of knowledge and cognition are unduly limiting, in that they privilege what goes on inside the ‘skin and skull’ (Clark 1997: 82) of an individual reasoner. Instead, it has been argued, knowledge and cognition need to be understood as embodied (involving both mind and body), situated (being dependent on the complex interplay between the individual and its environment), and extended (that is, continuous with, rather than separate from, the world ‘outside’). Whether these various interrelations and dependencies are ‘merely’ causal, or are in a more fundamental sense constitutive of knowledge and cognition, is as much a matter of controversy as the degree to which they pose a challenge to ‘traditional’ conceptions of cognition, knowledge and the mind. In this paper we argue that when the idea of ‘extendedness’ is applied to a core concept in epistemology and the philosophy of science—namely, scientific evidence—things appear to be on a much surer footing. The evidential status of data gathered through extended processes—including its utility as justification or warrant—do not seem to be weakened by virtue of being extended, but instead are often strengthened because of it. Indeed, it is often precisely by virtue of this extendedness that scientific evidence grounds knowledge claims, which individuals may subsequently ascribe to themselves. The functional equivalence between machine‐based gathering, filtering, and processing of data and human interpretation and assessment is the crucial factor in deciding whether evidence has been gathered, rather than the distinction between intra‐ and extracranial processes or individual and social processes (or combinations thereof). To prioritize biological processes here, and to assert the superiority of human cognitive capacities seems both arbitrary and unwarranted with respect to gathering evidence, and ultimately would lead to an unattractive skepticism about many of the methods used in science to gather evidence. In other words, conceiving of scientific evidence as ‘impersonal’ (or at least not necessarily personal) not only better captures the character of evidence‐gathering in practice, but also makes sense of a large amount of evidence‐gathering that ‘personal’ accounts fail to either acknowledge or accurately describe. Whilst we suggest it is likely that all internally‐distributed evidence‐gathering processes are merely contingently internal processes, a significant number of externally‐distributed evidence‐gathering processes are necessarily externally‐distributed. Some evidence can only be gathered by extended epistemic agents.     

Comparing measures of the ‘typical’ score across treatment groups

Researchers can adopt one of many different measures of central tendency to examine the effect of a treatment variable across groups. These include least squares means, trimmed means, M‐estimators and medians. In addition, some methods begin with a preliminary test to determine the shapes of distributions before adopting a particular estimator of the typical score. We compared a number of recently developed adaptive robust methods with respect to their ability to control Type I error and their sensitivity to detect differences between the groups when data were non‐normal and heterogeneous, and the design was unbalanced. In particular, two new approaches to comparing the typical score across treatment groups, due to Babu, Padmanabhan, and Puri, were compared to two new methods presented by Wilcox and by Keselman, Wilcox, Othman, and Fradette. The procedures examined generally resulted in good Type I error control and therefore, on the basis of this critetion, it would be difficult to recommend one method over the other. However, the power results clearly favour one of the methods presented by Wilcox and Keselman; indeed, in the vast majority of the cases investigated, this most favoured approach had substantially larger power values than the other procedures, particularly when there were more than two treatment groups.     

A Follow-up Study of Counseling Effectiveness in Placement Outcomes—Data for Fiscal Years 1973 and 1976

A comparison was made of data from fiscal years 1973 and 1976 to determine if the findings of a study made in 1973 were true also in 1976. Basic findings of the 1973 study were “Your chances of being placed on a job by the Employment Service in Utah are greater if you receive assistance from counseling”; “The chances are even greater when you have more than one counseling interview”; “Personalizing the services seems to be the key to being placed on a job.” Other findings of the 1973 study regarding applicant characteristics often considered barriers to placement were not treated in the present study because of difficulties in obtaining the information from fiscal 1976 records. Results of the current study of 1976 data indicate: Although the advantage in favor of counseled applicants being placed was somewhat less in fiscal year 1976 than in fiscal 1973, counseled applicants' percentage-of-placement rate was still higher than that for all applicants in general, and increased numbers of counseling interviews did seem to have a positive effect on the placement rates of counseled applicants but at a slower rate than was found for fiscal 1973. In the current study an additional factor—renewals—was investigated to determine if higher placement rates accompanied higher numbers of renewals. The findings were positive but deemed inconclusive. Since renewals indicate repeated use of the service, they can be considered to be another measure of the effect of satisfactory service, like placement, rather than a cause of increased placement rates. This additional investigation did determine, however, that at all levels of renewal (except no renewal) the placement rate of counseled applicants was significantly higher than the placement rate of applicants who did not receive counseling.     

Fitting the factor analysis model in ℓ1 norm

The well‐known problem of fitting the exploratory factor analysis model is reconsidered where the usual least squares goodness‐of‐fit function is replaced by a more resistant discrepancy measure, based on a smooth approximation of the ?₁ norm. Fitting the factor analysis model to the sample correlation matrix is a complex matrix optimization problem which requires the structure preservation of the unknown parameters (e.g. positive definiteness). The projected gradient approach is a natural way of solving such data matching problems as especially designed to follow the geometry of the model parameters. Two reparameterizations of the factor analysis model are considered. The approach leads to globally convergent procedures for simultaneous estimation of the factor analysis matrix parameters. Numerical examples illustrate the algorithms and factor analysis solutions.     

Circular interpretation of regression coefficients

The interpretation of the effect of predictors in projected normal regression models is not straight-forward. The main aim of this paper is to make this interpretation easier such that these models can be employed more readily by social scientific researchers. We introduce three new measures: the slope at the inflection point (b_c), average slope (AS) and slope at mean (SAM) that help us assess the marginal effect of a predictor in a Bayesian projected normal regression model. The SAM or AS are preferably used in situations where the data for a specific predictor do not lie close to the inflection point of a circular regression curve. In this case b_c is an unstable and extrapolated effect. In addition, we outline how the projected normal regression model allows us to distinguish between an effect on the mean and spread of a circular outcome variable. We call these types of effects location and accuracy effects, respectively. The performance of the three new measures and of the methods to distinguish between location and accuracy effects is investigated in a simulation study. We conclude that the new measures and methods to distinguish between accuracy and location effects work well in situations with a clear location effect. In situations where the location effect is not clearly distinguishable from an accuracy effect not all measures work equally well and we recommend the use of the SAM.     

Rape — Relationships and Recovery

Rape—Relationships and Recovery is a group counseling model designed to intercede when crisis-oriented rape counseling ends. Major aspects of the model include (a) giving factual information and dispelling common myths surrounding rape; (b) recognizing and working through the grief process following rape; and (c) aiding the expression of the intrapersonal and interpersonal feelings that result from rape.     

Tracing the Path from Personality — via Cooperativeness — to Conservation

Ecological behaviour is often conceptualized as an instance of cooperating in a social dilemma situation. Thus, it has been argued to relate to dispositional tendencies of moral virtue and pro‐social orientation. To embed such notions in models of basic personality, we herein predicted that the recently proposed sixth basic personality factor, Honesty–Humility — which specifically pertains to individual differences in cooperativeness — is linked to environmental attitudes and ecological behaviour. Results from two studies (N = 137 and N = 531, respectively) supported these hypotheses and showed that Honesty–Humility explains incremental variance beyond the remaining, more classical five factors of personality. In addition, mediation analyses revealed that Honesty–Humility exerts part of its influence via individual differences in pro‐social value orientations. Individual tendencies to cooperate in social dilemma situations could thus be shown to form a bridge between basic personality dimensions and ecological behaviour. Copyright © 2012 John Wiley & Sons, Ltd.     

Individual differences in spatial mental imagery

In this article, we report a new image-scanning paradigm that allowed us to measure objectively individual differences in spatial mental imagery—specifically, imagery for location. Participants were asked to determine whether an arrow was pointing at a dot using a visual mental image of an array of dots. The degree of precision required to discriminate “yes” from “no” trials was varied. In Experiment 1, the time to scan increasing distances, as well as the number of errors, increased when greater precision was required to make a judgement. The results in Experiment 2 replicated those results while controlling for possible biases. When greater precision is required, the accuracy of the spatial image becomes increasingly important—and hence the effect of precision in the task reflects the accuracy of the image. In Experiment 3, this measure was shown to be related to scores on the Paper Folding test, on the Paper Form Board test, and on the visuospatial items on Raven's Advanced Progressive Matrices—but not to scores on questionnaires measuring object–based mental imagery. Thus, we provide evidence that classical standardized spatial tests rely on spatial mental imagery but not object mental imagery.     

Contrasts and correlations in effect-size estimation

This article describes procedures for presenting standardized measures of effect size when contrasts are used to ask focused questions of data. The simplest contrasts consist of comparisons of two samples (e.g., based on the independent t statistic). Useful effect-size indices in this situation are members of the g family (e.g., Hedges's g and Cohen's d ) and the Pearson r . We review expressions for calculating these measures and for transforming them back and forth, and describe how to adjust formulas for obtaining g or d from t , or r from g , when the sample sizes are unequal. The real-life implications of d or g calculated from t become problematic when there are more than two groups, but the correlational approach is adaptable and interpretable, although more complex than in the case of two groups. We describe a family of four conceptually related correlation indices: the alerting correlation, the contrast correlation, the effect-size correlation, and the BESD (binomial effect-size display) correlation. These last three correlations are identical in the simple setting of only two groups, but differ when there are more than two groups.     

God,Purpose in Life,and Mental Well‐Being Among Older Adults

This research note uses mixed methods on data from a nationwide sample of 1,525 Americans age 40 and older to make two theoretical contributions to the literatures on purpose and religion. First, by categorizing open‐ended responses to an item asking “Please describe a few of the things, feelings, ideas, etc. that give you a sense of purpose in your life,” we present a categorization framework to group sources of purpose (SPs) in life. Next, we run multivariate models, using mental well‐being as a dependent measure, which simultaneously enter dummy variables reflecting each of the SPs categories within our framework. We hypothesize no relative differences in the effect that any specific source of purpose category would have on mental well‐being. This prediction is undercut by finding a positive link between mental well‐being and a single SP—citing one's “relationship with God”—although this relationship is noted only among respondents age 60 and older. Beyond this research's theoretical contributions, we offer some practical guidance in arguing that research on SPs, particularly when claiming comprehensiveness or examining mental well‐being, should not preclude religious measures and should consider that SPs may have differing effects between age groups.     

Stereotypical behavioural cues — but not their order — influence credibility judgements

To what extent stereotypical deceptive behaviours such as gaze aversion and fidgeting actually influence people's credibility judgements remain largely unknown. In this study, we directly manipulated the presence/absence of such behaviours to investigate this. Participants were shown four truthful videos in which we manipulated the presence of stereotypical cues and asked them to judge how credible the person in each video is. Moreover, research consistently shows that decision making is influenced by various cognitive biases. One example is the primacy effect, which implies that people form an opinion early in the decision process. Information acquired early will have the largest influence on how subsequent information will be interpreted. To investigate a possible primacy effect, we also manipulated whether these cues were present towards the beginning or the end of the video (i.e. the timing of the manipulation). In line with our expectations, the presence of stereotypical cues significantly lowered the observed credibility, showing that the presence of these cues indeed influences credibility judgements. The timing of the cues had no effect.