Idealization and factualization in science

Summary This paper considers the method of idealization and factualization as the main method of all advanced empirical sciences. The procedure is as follows. Some idealizing conditions are assumed: the vanishing of factors (p _i=0) which never vanish in the real world. An idealization law is formulated — a law which is exactly (non-vacuously) fulfilled only in an ideal model, not in any real system. Then the idealizing assumptions are abrogated one by one-it is a process of gradual factualization, of the transition to the factual laws which are fulfilled in real systems. These laws may be directly applied and tested by experience.     

Lower bounds for the reliability of the total score on a test composed of non-homogeneous items: I: Algebraic lower bounds

Let Σ _x be the (population) dispersion matrix, assumed well-estimated, of a set of non-homogeneous item scores. Finding the greatest lower bound for the reliability of the total of these scores is shown to be equivalent to minimizing the trace of Σ _x by reducing the diagonal elements while keeping the matrix non-negative definite. Using this approach, Guttman's bounds are reviewed, a method is established to determine whether his λ₄ (maximum split-half coefficient alpha) is the greatest lower bound in any instance, and three new bounds are discussed. A geometric representation, which sheds light on many of the bounds, is described. Present affiliation of the second author: Department of Statistics, University of Nigeria (Nsukka Campus). Work on this paper was carried out while on study leave in Aberystwyth.     

Reliability formulas that do not assume experimental independence

Tautologies are established for the reliability coefficient ² _t of the sum ofn part scores. It is not assumed that the part scores are experimentally independent of each other nor that the parts are equivalent to each other. The tautologies show the exact role played by experimental dependence and nonequivalence of parts, respectively, in the reliability of the sum. The formal algebra is appropriate to reliability in the sense of repeated trials of the same test, as well as in the sense of a universe of parallel tests, although the empirical meanings are different. Emphasis is on practical formulas that require information from only a single experiment (or test). These can take the form only of lower bounds to ² _t , four of which are developed.     

Estimation of the reliability of ratings

A procedure for estimating the reliability of sets of ratings, test scores, or other measures is described and illustrated. This procedure, based upon analysis of variance, may be applied both in the special case where a complete set of ratings from each ofk sources is available for each ofn subjects, and in the general case wherek ₁,k ₂, ...,k _n ratings are available for each of then subjects. It may be used to obtain either a unique estimate or a confidence interval for the reliability of either the component ratings or their averages. The relations of this procedure to others intended to serve the same purpose are considered algebraically and illustrated numerically.The writer wishes to acknowledge the helpful comments and suggestions of Professors E. E. Cureton, Harold Gulliksen, and E. F. Lindquist.     

The selection of judges for preference testing

A scheme for choosing a few individuals whose preferences for given objects are most representative of those of a larger group of individuals is proposed. The method involves (a) quantifying the preferences of each individual so as to discriminate optimally among objects, (b) testing statistically whether or not a common preference continuum may be assumed for the quantified preferences, (c) constructing a linear estimator of values for the objects on this continuum, if it may be assumed, and (d) selecting as judges the least number of individuals whose quantified preferences, when used with this estimator, determine values for the objects with acceptable accuracy. A numerical example based on food preferences is presented. Preparation of this paper has been supported in part by the Quartermaster Food and Container Institute for the Armed Forces. Views or conclusions expressed herein are those of the author and do not necessarily reflect the views or indorsement of the Department of Defense.     

A quasi-nonmetric method for multidimensional scaling VIA an extended euclidean model

An Extended Two-Way Euclidean Multidimensional Scaling (MDS) model which assumes both common and specific dimensions is described and contrasted with the standard (Two-Way) MDS model. In this Extended Two-Way Euclidean model then stimuli (or other objects) are assumed to be characterized by coordinates onR common dimensions. In addition each stimulus is assumed to have a dimension (or dimensions) specific to it alone. The overall distance between objecti and objectj then is defined as the square root of the ordinary squared Euclidean distance plus terms denoting the specificity of each object. The specificity,s _j , can be thought of as the sum of squares of coordinates on those dimensions specific to objecti, all of which have nonzero coordinatesonly for objecti. (In practice, we may think of there being just one such specific dimension for each object, as this situation is mathematically indistinguishable from the case in which there are more than one.)We further assume that _ij =F(d _ij ) +e _ij where _ij is the proximity value (e.g., similarity or dissimilarity) of objectsi andj,d _ij is the extended Euclidean distance defined above, whilee _ij is an error term assumed i.i.d.N(0, ²).F is assumed either a linear function (in the metric case) or a monotone spline of specified form (in the quasi-nonmetric case). A numerical procedure alternating a modified Newton-Raphson algorithm with an algorithm for fitting an optimal monotone spline (or linear function) is used to secure maximum likelihood estimates of the paramstatistics) can be used to test hypotheses about the number of common dimensions, and/or the existence of specific (in addition toR common) dimensions.This approach is illustrated with applications to both artificial data and real data on judged similarity of nations.     

Does Drawing Attention to the Referent Constrain the Way in Which Children Construct Verbal Messages?

Tasks which assess children's speaker skills in the referential communication paradigm frequently mark the target item in some way to indicate which picture should be described. It was hypothesized that this procedure would interfere with effective scanning of the visual array (comparison processing) assumed to be necessary for the production of accurate messages. It was also predicted that, when one item was highlighted, more redundant features would be included in messages. An experiment which compared a marked with an unmarked target condition across three age ranges (6, 8, 10 years) found that message accuracy was not affected by highlighting. But significantly more redundant features were reported in the marked condition, indicating that, where redundancy is the focus of interest, a highlighting procedure should be avoided. Two age effects were also found: Message accuracy improved with age, while redundancy reduced with age.     

Choice reactions with a null stimulus event

A procedure for producing a null stimulus (S₀) in a CRT task is described. The S₀ produced is shown to elicit reactions that have characteristics of responses given to stimuli (S₁) that appear in regular CRT tasks. It was also discovered that, in this procedure, the initiation of S₀ sampling comes earlier than that of S₁ when S₀ and S₁ appear in the same CRT task. The nature of S₀ as well as the apparent reasons for its early sampling are discussed.     

The relationship between factorial composition of test items and measures of test reliability

For continuous distributions associated with dichotomous item scores, the proportion of common-factor variance in the test,H ², may be expressed as a function of intercorrelations among items.H ² is somewhat larger than the coefficienta except when the items have only one common factor and its loadings are restricted in value. The dichotomous item scores themselves are shown not to have a factor structure, precluding direct interpretation of the Kuder-Richardson coefficient,r _K-R, in terms of factorial properties. The value ofr _K-R is equal to that of a coefficient of equivalence,H ² , when the mean item variance associated with common factors equals the mean interitem covariance. An empirical study with synthetic test data from populations of varying factorial structure showed that the four parameters mentioned may be adequately estimated from dichotomous data.This study was supported in part by an Air Force project (Contract Number AF18(600-170), monitored by the Crew Research Laboratory, Air Force Personnel and Training Research Center, Randolph Air Force Base, Randolph Field, Texas. Permission is granted for reproduction, translation, publication, use and disposal in whole and in part by or for the United States Government. Further support was given by the Northwestern University Graduate School. The computational assistance of Mr. Norman Miller is acknowledged. Professor Meyer Dwass provided mathematical advice both directly and indirectly relevant to the paper.     

Social identification and depression: A meta-analysis

A meta-analysis of 76 studies (N = 31,016) examined the relationship between social identification and depression. Overall, individuals who identify highly with a group tend to report less depression (average r_z = −.15). However, a large amount of variability between studies was observed. The 95% prediction interval, which indicates the true effect size that can be expected in future research, ranged from r_z = −.50 to .19. The relationship between depression and social identification is more complex than previously assumed. Some variability is related to the social identification measure used. Studies that focused on identification with interactive groups (r_z = −.28) had larger effect sizes than studies that focused on social categories (r_z = −.11). Moreover, studies of non-stigmatized groups (r_z = −.24) had larger effect sizes than studies of stigmatized groups (r_z = −.10). In conclusion, the structure and social identity content of groups appear to play an important role in the relationship between depression and social identification.     

Estimating population or group sensitivity and its precision from a set of individual d′

A commonly used method of estimating population sensitivity is the so‐called averaged d ′ method. In this method, the arithmetic mean of a set of individual d ′ is usually taken as a population sensitivity estimator. This practice ignores the fact that the individual d ′ itself is an estimator with an inherent variance. For observations with different levels of precision, the arithmetic mean is not the best estimator of a population parameter. It may lead to an estimate with a large variation. Another fact, which is often ignored, is that the variance of individual d ′ involves both between‐ and within‐subject variations in a random effects model when population sensitivity and its level of precision are estimated. Failing to account for both components of variance leads to an underestimate of variation and an overestimate of precision for the estimator. In this paper a lognormal distribution rather than a normal distribution is assumed for individual sensitivity. An iterative weighting procedure is proposed for estimating population sensitivity on the log scale on the basis of a random effects model. An ordinary weighting procedure is proposed for estimating group sensitivity on the log scale on the basis of a fixed effects model. The levels of precision of population and group sensitivity estimators are also given. Numerical examples illustrate the estimation procedures.     

More than,less than,or minimum,maximum: how upper and lower bounds determine subjective interval estimates

Uncertain quantities can be described by single‐point estimates of lower interval bounds (X₁), upper interval bounds (X₂), two‐bound estimates (separate estimates of X₁ and X₂), and by ranges (X₁?X₂). A price estimation task showed that single‐bound estimates phrased as “T costs more than X₁” and “T costs less than X₂,” yielded much larger intervals than “minimum X₁” and “maximum X₂.” This difference can be attributed to exclusive interpretations of X₁ and X₂ in the first case (X₁ and X₂ are unlikely values), and inclusive interpretations in the second (X₁ and X₂ are likely values). This pattern of results was replicated in other domains where participants estimated single targets. When they estimated a distribution of targets, the pattern was reversed. “Minimum” and “maximum” values of variable quantities (e.g., flight prices) were found to delimit larger intervals than “more than” and “less than” estimates. Copyright © 2006 John Wiley & Sons, Ltd.     

Orthorhombic approximant phases and their relation to quasicrystals in mechanically alloyed Al–Cu–Fe–Si alloys

The possibility of synthesis of quasicrystalline and associated approximant phases during mechanical alloying and subsequent heat treatment of Al₆₅Cu₂₀Fe₁₀Si₅ alloy powders has been investigated. It is shown that, in addition to the stable ordered quasicrystal and 1/1 cubic approximant, two more phases having orthorhombic symmetry coexist. The a and c parameters of both these phases are similar to the lattice parameters of the cubic approximant, whereas their b parameters are, respectively, three and four times larger than the c parameters. It is suggested that these phases evolve on account of local symmetry breaking of the cubic approximant phase, possibly due to ordering.     

Coordination dynamics of rhythmical and discrete prehension movements: Implications of the scanning procedure and individual differences

The aim of this study was to compare the coordination dynamics of discrete and rhythmical reaching and grasping movements from a dynamical systems perspective. Previous research from this theoretical perspective had focused on rhythmical actions and it is unclear to what extent discrete movements are amenable to a similar dynamical systems analysis. Six adult subjects performed prehension in two conditions: a discrete, non-continuous mode and a rhythmical, continuous mode. A `scanning procedure' was implemented between pre- and post-tests in which the required time of final relative hand closure (T_rfc) was systematically varied. It was shown that the error in the reaching and grasping pattern was least at an attractor region and systematically increased with deviation from the attractor. Results also indicated that there were no differences between condition or trial block for the group. However, there were several within-subject effects of interest. The validity of the scanning procedure was found to be questionable in the discrete condition, where four subjects showed differences in T_rfc between pre- or post-test and the predicted T_rfc of the scanning procedure. Four out of six subjects also had different preferred T_rfc values for discrete and rhythmical movement, indicating that individual specific models might need to be constructed for future dynamical modelling of discrete movement.PsycINFO classification: 2330     

Influence of mechanical factors on movement units in infant reaching

In a number of studies it is assumed that movement units (combinations of an acceleration and a deceleration in the tangential velocity profile) are a reflection of the control process. In this study, we investigated to what extent movement units reflect the oscillatory mechanics of the arm. At the ages of 16 and 20 weeks, the age range in which infants just begin to reach, a toy rattle was presented in three conditions, with varying external forces acting on the arm: sitting, sitting with masses on the forearms, and supine.The tangential velocity profile of the wrist during successful reaching attempts was decomposed to a gravity-dependent (φ_v), and a gravity-independent component (φ_h), and movement units were determined in the total velocity profile and in its components. Significant effects of experimental condition, but not age, were found for movement time, number of movement units and duration ofphi;_hcomponent units. It was shown that these effects can be accounted for by a simple mechanical model, in which the arm is approximated as a harmonic oscillator governed by, gravity, the moment of inertia of the arm, and the stiffness of the shoulder joint. Stiffness values, derived from fitting the model to the data, were in the order of 1 Nm/rad.From these results we conclude that movement units in an infant's initial attempts at reaching are to a large extent a reflection of the mechanical context.     

Temporal, but not spatial, context modulates a masked prime's effect on temporal order judgment, but not on response latency

Three experiments investigated a dissociation originally described by Neumann, Esselmann, and Klotz. Stimuli were geometric shapes, preceded by similar shapes that were masked by metacontrast. Each experiment consisted of three parts. In the reaction time (RT) part, participants saw an array of geometric shapes, one of which was marked by bars, and had to respond to the marked shape's position by pressing an appropriate button. A prime (a similar, but smaller stimulus) preceded either the marked or an unmarked stimulus. In the temporal order judgment (TOJ) part, the task was to judge the temporal order of the marked and the unmarked stimulus. In the detection part, detectability of the prime was tested. Although its detectability was zero or close to zero, the prime affected both RT and the apparent onset as measured by TOJ. The effect on RT was significantly larger than the effect on TOJ (Exp. 1). Increasing the spatial context (number of non-target stimuli in the display) did not affect this pattern (Exp. 2). By contrast, reducing the temporal context (range of stimulus onset asynchronies) abolished the prime's effect in the TOJ task, although the prime affected RT under identical conditions. It is concluded that partially different mechanisms mediate the prime's effect in the two tasks and that the effect of stimulus context on TOJ found in the Neumann et al. study was due to temporal, not spatial context. Received: 17 December 1997 / Accepted: 15 December 1998     

MCMC estimation for the p2 network regression model with crossed random effects

The p₂ model is a statistical model for the analysis of binary relational data with covariates, as occur in social network studies. It can be characterized as a multinomial regression model with crossed random effects that reflect actor heterogeneity and dependence between the ties from and to the same actor in the network. Three Markov chain Monte Carlo (MCMC) estimation methods for the p₂ model are presented to improve iterative generalized least squares (IGLS) estimation developed earlier, two of which use random walk proposals. The third method, an independence chain sampler, and one of the random walk algorithms use normal approximations of the binary network data to generate proposals in the MCMC algorithms. A large‐scale simulation study compares MCMC estimates with IGLS estimates for networks with 20 and 40 actors. It was found that the IGLS estimates have a smaller variance but are severely biased, while the MCMC estimates have a larger variance with a small bias. For networks with 20 actors, mean squared errors are generally comparable or smaller for the IGLS estimates. For networks with 40 actors, mean squared errors are the smallest for the MCMC estimates. Coverage rates of confidence intervals are good for the MCMC estimates but not for the IGLS estimates.     

‘Our way of life is worth defending’: testing a model of attitudes towards superordinate group membership through a study of Scots' attitudes towards Britain

This research used a survey design (N = 227) to investigate Scottish people's support or opposition to independence from Britain. It was hypothesised that political attitudes towards supra‐national bodies are not a direct function of the degree of ingroup (Scottish) identification, but are moderated by the extent to which the expression of ingroup identity is seen as being undermined within the larger entity. This feeling of identity undermining is assumed to arise from perceptions of incompatibility with the outgroup and ingroup powerlessness within the common group. The results provided support for these hypotheses. Only for those participants who had high feelings of identity undermining did identification lead to stronger separatist attitudes. Moreover, incompatibility with the outgroup and ingroup powerlessness predicted feelings of identity undermining while this latter mediated their impact on attitudes to being part of Britain. These findings underline the importance of taking into account (a) the contents ascribed to identities and their relations, and (b) the practical ability to pursue a way of live based on these contents in order to understand the way identity processes shape attitudes towards superordinate groups. Copyright © 2008 John Wiley & Sons, Ltd.     

Attunement and Affordance Learning in Infants

ABSTRACT

From a perceptual learning perspective, infants use social information (like gaze direction) in a similar way as other information in our physical environment (like object movements) to specify action possibilities. In the current study, we assumed that infants are able to learn an affordance upon observing an adult failing to act out that affordance, without appreciating object-directed intentions, or, communicative intent towards the infant. Using a variation of the Re-enactment procedure, we found that when the attention of infants (N = 46, M_age = 20 months) was drawn towards the eyes of the person before she acted out the failed attempt, either by ostensive cues or non-ostensive cues, infants achieved more affordances than when their attention was not directed towards the eyes. As directing the attention of infants to the eyes of another person frequently results in gaze following, this suggests that infants use the gaze direction of another person in order to learn what affordance that other person is trying to realize. In addition, the results of a spatiotemporal analysis on the eye-movements of infants suggest that the gaze and the object movements of the person facilitate learning by directing the attention of infants towards important object-directed actions on crucial moments during the failed attempt demonstrations. These results are discussed in terms of perceptual attunement and affordance learning.     

The detailed method of optimal regions

The detailed method of optimal regions is an extended form of the method of optimal regions which has been found effective in solving the personnel classification problem when the number of job categories is small. The automatic determination of the successive values of thev _i , made possible by the more exact techniques of the detailed method, provide easier solutions for the more complex problems and provide solutions, which, for the most part, can be mechanized. In a sense the detailed method of optimal regions is more than a detailed form of the method of optimal regions. It is essentially a method of transformations by which the original matrix is reduced to a matrix from which the solution is easily obtained.Much of the basic research covered in this paper was carried out while the author was working on the problem of personnel classification in his capacity as Consultant, Personnel Research Branch, Department of the Army. The author wishes to express his appreciation to the Department of the Army for permission to use these materials in this paper. The opinions expressed are those of the author and are not to be construed as official or as those of the Department of the Army.