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.     

Measuring nominal scale agreement between a judge and a known standard

Two designs for comparing a judge's ratings with a known standard are presented and compared. Design A pertains to the situation where the judge is asked to categorize each ofN subjects into one ofr (known) classes with no knowledge of the actual number in each class. Design B is employed when the judge is given the actual number in each class and is asked to categorize the individuals subject to these constraints. The probability distribution of the total number of correct choices is developed in each case. A power comparison of the two procedures is undertaken.     

The approximation of a group stimulus space by averaging responses to selected subsets of the stimuli

This paper presents a simple random procedure for selecting subsets of stimulus pairs for presentation to subjects. The resulting set of ratings from the group of subjects allows the construction of a group (average) space through the use of the computer program TORSCA-9 or equivalent programs. The procedure is applied to both real and simulated data. It is found that subjects need only make between 20% and 50% of the usual judgements to reconstruct a reasonably accurate group space.     

A thurstonian pairwise choice model with univariate and multivariate spline transformations

A probabilistic choice model is developed for paired comparisons data about psychophysical stimuli. The model is based on Thurstone's Law of Comparative Judgment Case V and assumes that each stimulus is measured on a small number of physical variables. The utility of a stimulus is related to its values on the physical variables either by means of an additive univariate spline model or by means of multivariate spline model. In the additive univariate spline model, a separate univariate spline transformation is estimated for each physical dimension and the utility of a stimulus is assumed to be an additive combination of these transformed values. In the multivariate spline model, the utility of a stimulus is assumed to be a general multivariate spline function in the physical variables. The use of B splines for estimating the transformation functions is discussed and it is shown how B splines can be generalized to the multivariate case by using as basis functions tensor products of the univariate basis functions. A maximum likelihood estimation procedure for the Thurstone Case V model with spline transformation is described and applied for illustrative purposes to various artificial and real data sets. Finally, the model is extended using a latent class approach to the case where there are unreplicated paired comparisons data from a relatively large number of subjects drawn from a heterogeneous population. An EM algorithm for estimating the parameters in this extended model is outlined and illustrated on some real data.The first author is supported as Bevoegdverklaard Navorser of the Belgian Nationaal Fonds voor Wetenschappelijk Onderzoek. The authors are indebted to Ulf Böckenholt and Yoshio Takane for useful comments on an earlier draft of this paper.     

Paired comparison,triple comparison,and ranking experiments as generalized linear models,and their implementation on GLIM

A wide variety of paired comparison, triple comparison, and ranking experiments may be viewed as generalized linear models. These include paired comparison models based on both the Bradley-Terry and Thurstone-Mosteller approaches, as well as extensions of these models that allow for ties, order of presentation effects, and the presence of covariates. Moreover, the triple comparison model of Pendergrass and Bradley, as well as models for complete rankings of more than three items, can also be represented as generalized linear models. All such models can be easily fit by maximum likelihood, using the widely available GLIM computer package. Additionally, GLIM enables the computation of likelihood ratio statistics for testing many hypotheses of interest. Examples are presented that cover a variety of cases, along with their implementation on GLIM.     

Global and appearance-contingent self-esteem: Associations with health and attractiveness exercise reasons

Whilst some individuals exercise for health-related reasons, others appear to exercise to bolster physical attractiveness. For the latter, this is often attributed to dissatisfaction with appearance. Few studies, however, have explored if differences in self-esteem may relate to diverse exercise reasons. The present study investigated whether global self-esteem, appearance-contingent self-worth, and appearance satisfaction may be differentially associated with health and attractiveness exercise reasons. It was further sought to explore whether these relations coincided with different motivational regulations. Adults from the east midlands of the United Kingdom (N = 209; 75% female, 25% male; mean age = 29.77 years) completed measures relating to their global and appearance-contingent self-esteem, appearance satisfaction, exercise intentions, and motivations. Structural equation modelling revealed that global self-esteem was positively associated with appearance satisfaction and health reasons for exercise, whereas appearance-contingent self-esteem related to lower appearance satisfaction and attractiveness reasons. Appearance satisfaction had no association with either exercise reason but was associated with intrinsic motivation and lower controlled exercise motivations. Health exercise reasons were positively associated with intrinsic, identified, and introjected motivation, whereas attractiveness reasons were exclusively related to external motivation. The findings highlight the conceptual importance of differentiating the level and contingency of exercisers’ self-esteem. The findings may also have substantive value for exercise practitioners in understanding different reasons for exercise.     

Maternal perinatal representations and their associations with mother–infant interaction and attachment: A longitudinal comparison of Portuguese and Brazilian dyads

Prior research in Western countries (mostly the US, Canada and northern Europe) indicates that mothers' representations are associated with mother–infant interaction quality and their child's attachment security later in the first year. Fewer studies, however, have evaluated whether these associations hold for mother–infant dyads in other countries, such as Brazil and Portugal. Although these countries share a similar language and culture, they differ on societal dimensions that may affect parenting attitudes and mother–infant relationships, such as economic stress, social organisation, social policy, and the availability of services for young families. In this longitudinal study, we followed two independent samples of Brazilian and Portuguese mother–infant dyads from the perinatal period to 12 months post-partum. We assessed mothers' perinatal representations using semi-structured interviews in the first 48 hours after the infant's birth, and evaluated the associations of these representations with mother interaction quality at 9 months and infant attachment at 12 months. Results were similar in each country, corroborating prior research in single Western countries: Mothers with more positive perinatal representations were more sensitive to their infants during free play at 9 months and were more likely to have infants classified as securely attached at 12 months.     

Patterns of agonistic interactions in three species of macaque (Macaca mulatta,M fascicularis,M tonkeana)

Patterns of aggression and response to aggression were studied in three groups of macaques living in semiliberty, each group representing a different species: Macaca mulatta, M fascicularis, and M tonkeana. In Macaca mulatta, intensity of aggression is high (biting is frequent) and symmetry in aggression is low: the aggressee most often flees or submits. In Macaca tonkeana, in contrast, biting is exceptional, aggression is very often bidirectional, and appeasement behaviors are frequently observed. Intermediate patterns are found in Macaca fascicularis with, in addition, especially frequent mild forms of submission. It is argued that relationships exist between intensity of aggression, symmetry in aggression, and development of behaviors controlling aggresssion. Whether balances between these variables are species-specific is discussed.     

The Multiplicative AHP,SMART and ELECTRE in a Common Context

This paper presents a comparative study of three popular methods for multicriteria decision analysis based on a particular model of human preferential judgement. Since decisions are invariably made within a given context, we model relative preferences as ratios of increments or decrements in an interval on an axis of desirability. Next we sort the ratio magnitudes into a small number of categories, represented by numerical values on a geometric scale. We explain why the analytic hierarchy process (AHP) and the French collection of ELECTRE methods, typically based on pairwise comparison methods, are concerned with categories of ratio magnitudes, whereas the simple multiattribute rating technique (SMART) essentially uses orders of magnitude of these ratios. This phenomenon provides a common basis for the analysis of the methods in question and for a cross-validation of their results. We illustrate the approach via a well-known case study, the choice of a location for a nuclear power plant. We conclude by discussing the scope of the comparative study. © 1997 John Wiley & Sons, Ltd.     

Invidious Comparisons: Imagining a Psychology of Race and Gender Beyond Differences

Within psychology there is a longstanding debate concerning whether large, fundamental differences between races and genders exist. Much of this research involves comparisons that are invidious (offensively discriminating) and supports a political ideology in which members of different groups are held to be fundamentally different, alien, and therefore destined to different spheres. In this paper, specific factors are identified that make research on group differences more likely to produce distorted and partial findings. In addition, studies are cited whose methodological strategies offer insight into the processes that create and maintain group differences. Such research may illuminate not only the differences between groups, but also the very meaning of group categories. The process of scholarly peer review should become sensitive to the features that make comparisons invidious, so as to incorporate them into the criteria used to evaluate research.