Biased estimators, biased experts, and the Ivory Tower: a reply to Grove (2001)

This reply responds to W. M. Grove's (2001) critique of H. O. F. Veiel and R. F. Koopman's (2001) article on bias in widely used methods of estimating premorbid IQ. In this reply, the authors show that Grove is misrepresenting part of Veiel and Koopman's arguments, extend them to show that the proposed adjustment to regression estimates of IQ not only is unbiased but also is the maximum-likelihood estimate of the true IQ, and argue that Grove's notion of the acceptability of biased methods in judicial proceedings reflects a fundamental misapprehension of their nature and purpose.     

Evaluating socioeconomic status bias in the WISC-R

The use of intelligence tests in making special education placement decisions for children has come under repeated scrutiny in recent years. Arguments for and against the use of IQs have centered around the issue of test bias. In California a permanent moratorium on the use of intelligence tests in placing minority group children into classes for the educable retarded has been handed down by the court. One defense proposed by advocates of mental testing has been that the tests are biased against socially and economically disadvantaged groups irrespective of race. According to Clarizio (1978), if a test predicts equally well for two groups it can not legitimately be described as biased. The purpose of this investigation was to evaluate the test bias of the Verbal IQ as measured by the Wechsler Intelligence Scale for Children-Revised in relation to predictions of academic achievement in two different socioeconomic status groups. The results indicated that Verbal IQs are not biased with respect to socioeconomic status. Derived regression equations are presented along with an analysis to inspect the statistical power of the original tests.     

Robust inference with binary data

In this paper robustness properties of the maximum likelihood estimator (MLE) and several robust estimators for the logistic regression model when the responses are binary are analysed. It is found that the MLE and the classical Rao's score test can be misleading in the presence of model misspecification which in the context of logistic regression means either misclassification's errors in the responses, or extreme data points in the design space. A general framework for robust estimation and testing is presented and a robust estimator as well as a robust testing procedure are presented. It is shown that they are less influenced by model misspecifications than their classical counterparts. They are finally applied to the analysis of binary data from a study on breastfeeding.The author is partially supported by the Swiss National Science Foundation. She would like to thank Rand Wilcox, Eva Cantoni and Elvezio Ronchetti for their helpful comments on earlier versions of the paper, as well as Stephane Heritier for providing the routine to compute the OBRE.     

The regression equation method of determining academic discrepancy

This article discusses the regression equation approach to quantifying academic discrepancy, which is an aspect of most generally accepted learning disability definitions. The concept of regression toward the mean and its relevance to determining underachievement is presented. Variations of the expectancy formula and IQ-achievement difference approaches fail to fully consider regression effects and therefore will produce the serious identification errors of including too many children with above-average IQs and too few with below-average IQs. The parameter estimation variation of the regression equation approach is advocated as the best method for quantifying the academic discrepancy aspect of learning disabilities.     

Noniterative estimation and the choice of the number of factors in exploratory factor analysis

Based on the usual factor analysis model, this paper investigates the relationship between improper solutions and the number of factors, and discusses the properties of the noniterative estimation method of Ihara and Kano in exploratory factor analysis. The consistency of the Ihara and Kano estimator is shown to hold even for an overestimated number of factors, which provides a theoretical basis for the rare occurrence of improper solutions and for a new method of choosing the number of factors. The comparative study of their estimator and that based on maximum likelihood is carried out by a Monte Carlo experiment.The author would like to express his thanks to Masashi Okamoto and Masamori Ihara for helpful comments and to the editor and referees for critically reading the earlier versions and making many valuable suggestions. He also thanks Shigeo Aki for his comments on physical random numbers.     

Discrepancies between premorbid and current IQ as a function of progressive mental deterioration

The declining cognitive functioning typically found in patients with Alzheimer's disease presents an opportunity to study that decline. The changing magnitude of ever widening discrepancies between premorbid estimators of IQ and observed IQ increases as severity of the disease increases. Premorbid IQs estimated by these scores (the National Adult Reading Test-Revised, the reading tests of the Revised and Third Editions of the Wide Range Achievement Test, and a demographically based regression index for the Wechsler Adult Intelligence Scale-Revised) had relatively similar discrepancies from obtained WAIS-R Full Scale IQs in samples of normal elderly (n = 30), and elderly patients diagnosed with mild (n = 30) and moderate Alzheimer's disease (n = 30) dementia. The discrepancies became larger, regardless of premorbid estimator, as disease severity progressed from none to mild to moderate across the samples.     

Self-selection biases in correlational studies based on questionnaires

It is commonly held that even where questionnaire response is poor, correlational studies are affected only by loss of degrees of freedom or precision. We show that this supposition is not true. If the decision to respond is correlated with a substantive variable of interest, then regression or analysis of variance methods based upon the questionnaire results may be adversely affected by self-selection bias. Moreover such bias may arise even where response is 100%. The problem in both cases arises where selection information is passed to the score indirectly via the disturbance or individual effects, rather than entirely via the observable explanatory variables. We suggest tests for the ensuing self-selection bias and possible ways of handling the ensuing problems of inference.The author would like to thank members of the Psychology Department at UWA for references on the illustrative example, namely the effects of sex-stereotyping on achievements in mathematics; thanks are also due to the anonymous reviewers whose comments resulted in material improvements to the paper.     

A comparison of generalized and modified sample biserial correlation estimators

In a recent paper, Bedrick derived the asymptotic distribution of Lord's modified sample biserial correlation estimator and studied its efficiency for bivariate normal populations. We present a more detailed examination of the properties of Lord's estimator and several competitors, including Brogden's estimator. We show that Lord's estimator is more efficient for three nonnormal distributions than a generalization of Pearson's sample biserial estimator. In addition, Lord's estimator is reasonably efficient relative to the maximum likelihood estimator for these distributions. These conclusions are consistent with Bedrick's results for the bivariate normal distribution. We also study the small sample bias and variance of Lord's estimator, and the coverage properties of several confidence interval estimates.The author would like to thank the referees for several suggestions that improved the paper.     

SIMSTAT: Bootstrap computer simulation and statistical program for IBM personal computers

SIMSTAT is a computer program that provides bootstrap confidence intervals and estimates distribution parameters for 27 univariate and bivariate statistics. Because it permits variation of the bootstrap sample size, it is a convenient tool for research planning, allowing comparison of power estimates and estimator precision for various estimators and/or sample sizes. SIMSTAT also is a useful tool for studying the robustness of various statistics on real-world data and may be helpful in teaching statistical principles.     

Different WAIS-R short forms and their relation to ethnicity

Potential racial bias on commonly used WAIS-R short forms was examined in a group of 201 African-Americans matched with Caucasians in terms of age, education, gender, and occupational status. Within racial groups, all short form IQs correlated highly with the WAIS-R IQs (all rs 0.87). Although relatively large racial differences emerged on the Block Design, Vocabulary, and Arithmetic subtests, only mild racial discrepancies emerged for three out of the seven short forms investigated. While the magnitude of the results for the short forms was mild, based on these findings it was suggested that certain short forms not be used with African-Americans in order to minimize the potential influence of racial basis.     

Non-equivalence of WPPSI,WPPSI-R,and WISC-R scores

The WPPSI-R, WISC-R, and WPPSI were administered in a counterbalanced design to 72 children, between the ages of 5 years, 11 months and 6 years, 8 months, in order to determine their equivalence by testing the equality of means, variances, and covariances based on scaled scores and IQs. The results indicated that the three scales were not equivalent with respect to any of the IQs because they did not meet one or more of the criteria. The relative magnitudes of the mean IQs on the three scales were in accord with the predicted order: highest IQs on WPPSI, next highest on WISC-R, and the lowest on WPPSI-R. Results were discussed in the context of the secular inflation in IQs and the corresponding compensatory deflation built into the normative data of the new versions.     

Islamic law and human rights: A contribution to an ongoing debate

In this essay the author criticizes two opposite approaches to the relationship between Islam and human rights: the incriminating and the apologetic approach. They are either anachronistic in that they judge the rules of classical Islamic jurisprudence by present‐day standards, or they entirely ignore its heritage. The author attempts instead to develop a new approach whereby classical Islamic jurisprudence is analyzed in its historical context. In order to examine whether Islam recognized a notion of fundamental rights, the author first tries to establish to what extent the notion of legal equality is recognized in Islamic law. Secondly, he examines two hierarchical legal relationships, viz. that between master and slave and that between husband and wife, in order to find which basic and inalienable rights Islamic law assigns to the weaker party in these relationships. His conclusion is that classical Islamic law offers points of departure for the development of a modern theory of human rights rooted in Islamic notions.>     

Non-equivalence of WPPSI, WPPSI-R, and WISC-R scores

The WPPSI-R, WISC-R, and WPPSI were administered in a counterbalanced design to 72 children, between the ages of 5 years, 11 months and 6 years, 8 months, in order to determine their equivalence by testing the equality of means, variances, and covariances based on scaled scores and IQs. The results indicated that the three scales were not equivalent with respect to any of the IQs because they did not meet one or more of the criteria. The relative magnitudes of the mean IQs on the three scales were in accord with the predicted order: highest IQs on WPPSI, next highest on WISC-R, and the lowest on WPPSI-R. Results were discussed in the context of the secular inflation in IQs and the corresponding compensatory deflation built into the normative data of the new versions.     

The mystery of the Polish soul. B. W. Johnson's effect à rebours

Studies conducted in Poland replicated a not very-well known effect discovered by B. W. Johnson (1937). In his study students estimated their mood on several successive days each time comparing it to the mood they usually have. The results revealed a peculiar positive bias in that the students usually defined their mood as ‘better than usual’. Johnson's study was replicated in Poland, where demonstration of optimism is not a cultural norm. The results suggest that Polish subjects ‘usually define their mood as worse than usual’. The generalization and limitation of this negative bias is discussed in the light of the Pollyanna Principle and related empirical studies involving Polish subjects.     

The Socialization of Highly Intelligent Boys: Case Material from Terman's Correspondence

Lewis M. Terman's letters to the parents of 42 boys with childhood IQs greater than 170 were examined and contrasted with those sent to parents of 42 boys with IQs between 135 and 159. Parents of boys with very high IQs were more frequently advised to restrain academic acceleration and to encourage mixing with agemates. The author places this advice in its historical context, suggests that the social needs of many highly intelligent children can best be satisfied in peer groups consisting of children of similar ability and interests, and concludes with a brief discussion of current options for jointly facilitating social and intellectual development.     

Local warming: daily temperature change influences belief in global warming

Although people are quite aware of global warming, their beliefs about it may be malleable; specifically, their beliefs may be constructed in response to questions about global warming. Beliefs may reflect irrelevant but salient information, such as the current day's temperature. This replacement of a more complex, less easily accessed judgment with a simple, more accessible one is known as attribute substitution. In three studies, we asked residents of the United States and Australia to report their opinions about global warming and whether the temperature on the day of the study was warmer or cooler than usual. Respondents who thought that day was warmer than usual believed more in and had greater concern about global warming than did respondents who thought that day was colder than usual. They also donated more money to a global-warming charity if they thought that day seemed warmer than usual. We used instrumental variable regression to rule out some alternative explanations.     

Judicial Wisdom: The Process of Constructing Wise Decisions

Surprisingly little research exists on the role of wisdom within legal decision making. To shed light on this topic, we interviewed 11 U.S. judges who were nominated by their peers for their legal wisdom. They were asked to describe their experience of wise legal decision making and the qualities and processes they felt characterize wise judges. Their interviews were subjected to a grounded theory analysis to develop an understanding of the psychological processes and interpersonal performances that constitute wise legal decision making. Among other findings, results identified attitudes in judges that were thought to lead to better decisions, such as an attitude of curiosity. They identified courtroom management styles that were characterized by magnanimity and compassion as instilling public faith in the system, in contrast to a distant or overly adversarial tone. They tended to agree that, when possible and within the confines of the law, rulings oriented toward rehabilitation were preferable to punitive ones. As well, wise judges described the ways they managed personal challenges arising from value conflicts or ambiguous evidence when making decisions. The article provides clarity on the meanings of the term wisdom within the judicial profession and its construction within the alternative discourses of retributive and procedural justice.     

Forming subjective representations of subjective representations: evidence of a subjective status bias

In 3 studies and 2 pilot experiments, the author examined whether attending to the subjective status of mental representations would affect the ways humans view representational contents. The author found that simple drawing tasks were executed differently depending on whether or not the subject of the drawing was defined as a mental content (belief, imagination, perception). The results challenged particular lay epistemological concepts. They were partly accounted for by Gricean conversational rules (H. P. Grice, 1975), but the author postulated a subjective status bias to fully explain them. The discussion and recommendations for research center on the nature of this bias and relate it either to a tendency to conceive subjective representations as vague shadows of reality, or to an increased impact of the law of pregnance.     

How the 2SLS/IV estimator can handle equality constraints in structural equation models: A system‐of‐equations approach

Parameters in structural equation models are typically estimated using the maximum likelihood (ML) approach. Bollen (1996) proposed an alternative non‐iterative, equation‐by‐equation estimator that uses instrumental variables. Although this two‐stage least squares/instrumental variables (2SLS/IV) estimator has good statistical properties, one problem with its application is that parameter equality constraints cannot be imposed. This paper presents a mathematical solution to this problem that is based on an extension of the 2SLS/IV approach to a system of equations. We present an example in which our approach was used to examine strong longitudinal measurement invariance. We also investigated the new approach in a simulation study that compared it with ML in the examination of the equality of two latent regression coefficients and strong measurement invariance. Overall, the results show that the suggested approach is a useful extension of the original 2SLS/IV estimator and allows for the effective handling of equality constraints in structural equation models.     

A computational technique for improving estimates of discriminability and bias across multiple dimensions of choice

Brown and White (2009) proposed measures of discriminability and bias that accommodate additional dimensions of choice—and hence, bias—in conditional discriminations such as matching-to-sample and the yes-no signal detection task. Their proposed measures increase the statistical independence of discriminability and bias estimates, thus improving their accuracy. Because Brown and White’s (2009) equations partition response data more than do standard equations, however, their measures have a slightly lower ceiling. Consequently, measurements can be less accurate when there are few trials and discriminability and bias are extreme. We introduce a computational estimation technique that overcomes this limitation. It estimates Brown and White’s (2009) discriminability and bias measurements from an array of related measures that have a higher ceiling. Simulations show that resulting estimates of discriminability and bias are either comparable to or more accurate than measurements calculated from traditional equations or Brown and White’s (2009) direct measures, even with few trials. A worked example of our technique may be downloaded from brm.psychonomic-journals.org/ content/supplemental.