bluuebunny/crossref_metadata_2025 huggingface dataset:
FACTOR INTERACTION IN NONLINEAR FACTOR ANALYSIS
Authors: McDonald Roderick P.
Published: August 2011

Factor interaction models are defined as those cases in nonlinear factor analysis in which the specification equation contains products of two or more latent variables or functions of latent variables. A complete algebraic treatment is given for the case of a product of two latent variables, and certain more general cases are briefly outlined.
THE PERFORMANCE OF THE LINEAR DISCRIMINANT FUNCTION IN TWO VARIABLES
Authors: Davies M. G.
Published: August 2011

The discriminant function is presented in unnormalized and in normalized form. For the two‐variable case, certain parameter‐dependent features are discussed in Section 2, and sampling features (expectations and variances of various statistics) in Section 3. Section 4 comments on the usefulness of the discriminant function for classification.
QUANTITATIVE INTERPRETATION OF STRESS IN KRUSKAL'S MULTIDIMENSIONAL SCALING TECHNIQUE
Authors: Wagenaar W. A. , Padmos P.
Published: August 2011

Some aspects of the quantitative interpretation of stress are discussed on the basis of random sets of synthetic dissimilarity matrices. In Section 1 the relation between measurement error and stress is studied. Synthetic dissimilarities are obtained starting from a random configuration of n points (n = 8, 10, and 12) in t dimensions (1 ≤ t ≤ 3), and adding a fractional error to the interpoint distances. These dissimilarity sets are then analysed in m dimensions (1 ≤ m ≤ 5). The results give an idea of how the stress is influenced by measurement error and the chosen dimensionality of the analysis. In practice, the results can be used for estimating both the true dimensionality and the measurement error of a set of data. In Section 2 the probability distribution of the stress‐percentages in m dimensions (1 ≤ m ≤ 5) is estimated in cases of randomly chosen dissimilarities among n points (7 ≤ n ≤ 12). The results can be an aid in determining the significance of a multidimensional representation of experimental data.
BINAURAL ADDITIVITY OF LOUDNESS
Authors: Levelt W. J. M. , Riemersma J. B. , Bunt A. A.
Published: August 2011

A definition of binaural additivity is given in terms of the theory of simultaneous conjoint measurement. Additivity is then tested and verified by a conjoint measurement procedure. Methods for deriving psychophysical scales from such procedures are discussed, and the experimental scales are compared with the usual ratio scales for loudness, derived from extensive measurement such as magnitude estimation. The functions are in good agreement and it is concluded that binaural additivity of loudness holds for non‐zero stimulation of the ears.
ORTHOGONAL ROTATION TO A PARTIALLY SPECIFIED TARGET
Authors: Browne M. W.
Published: August 2011

This paper presents an iterative procedure for rotating a factor matrix orthogonally to a least squares fit to a target matrix which need not be fully specified. Applications of the procedure are discussed.
SPANNING TREES AND ASPECTS OF CLUSTERING
Authors: Hubert Lawrence
Published: August 2011

The concept of a spanning tree for a weighted graph is used to characterize several methods of clustering a set of objects. In particular, most of the paper is devoted to stating relationships between spanning trees, single‐link and complete‐link hierarchical clustering, network flow and two divisive clustering procedures. Several related topics using the notion of a spanning tree are also mentioned.
DIFFICULTY FACTORS IN BINARY DATA
Authors: McDonald Roderick P. , Ahlawat Kapur S.
Published: August 2011

A number of writers have regarded difficulty factors as arising from the misbehaviour, in some sense, of correlation coefficients for binary data when the binary variables have varying difficulty levels. McDonald (1965) argued that difficulty factors are due to non‐linear item characteristic curves rather than difficulty per se, but did not give an example using binary data. An artificial experiment is described in which non‐linear item characteristic curves yield a difficulty factor, whereas linear item characteristic curves do not, even when in the latter case the items differ markedly in difficulty and phi coefficients are employed.
ITEM SAMPLING AND DECISION‐MAKING IN ACHIEVEMENT TESTING
Authors: Fhanér Stig
Published: August 2011

An item‐sampling approach is used to develop a probabilistic model for achievement testing. The model is applied to the problem of deciding whether an examinee should pass or fail, given an observed test score. Provided certain specifications are made, it is possible to estimate the number of items necessary to make this decision with prescribed precision.
USE OF THE BONFERRONI INEQUALITY FOR MULTIPLE COMPARISONS AMONG MEANS WITH POST HOC CONTRASTS
Authors: Ury Hans K. , Wiggins Alvin D.
Published: August 2011

Ury & Wiggins (1971) have used the Bonferroni inequality to obtain shorter confidence intervals for multiple comparisons among means, for most situations of interest, than those proposed by Marascuilo (1966). Their attempt to extend this technique to contrasts chosen post hoc has been shown to be not generally valid by Rodger (1973). A valid extension is given here.
MEASURING THE RELATIONSHIP BETWEEN TWO SETS OF VARIABLES
Authors: Coxhead Peter
Published: August 2011

A number of methods of measuring the relationship between two sets of variables are discussed. A coefficient is suggested which may be more suitable in those cases where the direction of the relationship is important.
A GENERAL METHOD FOR STUDYING DIFFERENCES IN FACTOR MEANS AND FACTOR STRUCTURE BETWEEN GROUPS
Authors: Sörbom Dag
Published: August 2011

A statistical model is developed for the study of similarities and differences in factor structure between several groups. The model assumes that the observed variables satisfy a factor analysis model in each group. A method of data analysis is presented which, in contrast to earlier work, makes use of information in the observed means as well as the observed variances and covariances to estimate the parameters in each group, i.e. factor means, factor loadings, factor variances and covariances and unique variances. Usually the units of measurement in the observed variables have no intrinsic meaning and therefore it is only meaningful to compare the relative magnitudes of the parameters for the different groups. The method estimates the parameters for all groups simultaneously and can take into account a priori information about factorial invariance of various degrees.
AN EMPIRICAL EVALUATION OF AN APPROXIMATE RESULT IN RANDOM GRAPH THEORY
Authors: Schultz James , Hubert Lawrence
Published: August 2011

A technique for evaluating the non‐randomness of a proximity matrix prior to a cluster analysis has been suggested by Ogilvie which incorporates an asymptotic result developed by Erdös & Rényi for the size of the largest connected component in a random graph. On the basis of Ogilvie's Monte Carlo comparisons, the use of Erdös & Rényi's asymptotic formula appears justified even when the number of objects in the set to be clustered is small. Several additional empirical comparisons are given in this paper that would indicate a more cautious attitude toward the use of the Erdös‐Rényi asymptotic formula in a non‐asymptotic context.
THE DISTRIBUTION OF PROBLEM‐SOLVING TIMES: AN EXAMINATION OF THE STAGES MODEL
Authors: Brée David S.
Published: August 2011

A proposal by Restle & Davis, that the times taken by subjects to solve a problem are distributed as a gamma function, is examined. The original data are found to be inadequate for testing the proposition, but data from 73 subjects solving the Missionaries and Cannibals (MAC) problem give strong support. In the Restle‐Davis model a problem is considered as being made up of a number of equally difficult stages. The MAC data suggest two stages, but a search in the subjects' problem‐solving protocols for the divide between the two stages fails. Two alternative models are proposed. The first is a simple birth process coming into effect after a fixed minimum solution time, which predicts a negative exponential distribution with shift of location. The second alternative is non‐stochastic and assumes that a solution time is produced by the multiplicative interaction of uncorrelated properties of subjects, leading to a lognormal distribution. The MAC data fit both these distributions as well. A Bayesian analysis strongly favours the negative exponential distribution, but it is argued that the lognormal distribution should continue to be considered.
SERIATION USING ASYMMETRIC PROXIMITY MEASURES
Authors: Hubert Lawrence
Published: August 2011

The data analysis problem of ordering or sequencing a set of objects using an asymmetric proximity function is reviewed, with an emphasis on literature not generally referenced in psychology. In particular, an attempt is made to present some of the more important approaches to the asymmetric seriation task that have been developed independently under a number of different names, for instance, the triangularization of input‐output matrices, minimum feedback arc sets, maximum likelihood paired comparison ranking, majority rule under transitivity constraints, and so on. A simple numerical example that illustrates some of the basic concepts is presented in the course of the discussion.
REGRESSION COMPONENT ANALYSIS
Authors: Schönemann Peter H. , Steiger James H.
Published: August 2011

Regression component decompositions (RCD) are defined as a special class of component decompositions where the pattern contains the regression weights for predicting the observed variables from the latent variables. Compared to factor analysis, RCD has a broader range of applicability, greater ease and simplicity of computation, and a more logical and straightforward theory. The usual distinction between factor analysis as a falsifiable model, and component analysis as a tautology, is shown to be misleading, since a special case of regression component decomposition can be defined which is not only falsifiable, but empirically indistinguishable from the factor model.
QUADRATIC ASSIGNMENT AS A GENERAL DATA ANALYSIS STRATEGY
Authors: Hubert Lawrence , Schultz James
Published: August 2011

The quadratic assignment paradigm developed in operations research is discussed as a general approach to data analysis tasks characterized by the use of proximity matrices. Data analysis problems are first classified as being either static or non‐static. The term ‘static’ implies the evaluation of a detailed substantive hypothesis that is posited without the aid of the actual data. Alternatively, the term ‘non‐static’ suggests a search for a particular type of relational structure within the obtained proximity matrix and without the statement of a specific conjecture beforehand. Although the static class of problems is directly related to several inference procedures commonly used in classical statistics, the major emphasis in this paper is on applying a general computational heuristic to attack the non‐static problem and in using the quadratic assignment orientation to discuss a variety of research tactics of importance in the behavioral sciences and, particularly, in psychology. An extensive set of numerical examples is given illustrating the application of the search procedure to hierarchical clustering, the identification of homogeneous object subsets, linear and circular seriation, and a discrete version of multidimensional scaling.
A MONTE CARLO AID TO THE EVALUATION OF MAXIMUM LIKELIHOOD FACTOR ANALYSIS SOLUTIONS
Authors: Heeler Roger M. , Whipple Thomas W.
Published: August 2011

Monte Carlo determined factor structures are used to derive the basic random level of fit when restricted maximum likelihood factor analysis is used to evaluate the fit of a particular hypothetical model. The performance of the hypothesized model is then assessed in relation to the maximal fit obtainable and the basic random level of fit.
A test of finite‐state theories of memory
Authors: Richardson John T. E.
Published: August 2011

Two general classes of theory have been proposed to handle data in signal detection and recognition memory. Previous research has considered that one might test such theories by considering the shape of the receiver operating characteristic (ROC) curve, but this has not proved to be helpful. Similarly, the question of the invariance of the ROC curve under different testing procedures is shown to be incidental to this task. It does not appear to be possible to generate empirical predictions peculiar to continuous theories, but various predictions have been extracted from discrete, or finite‐state, theories. Previous results favour a special case of discrete theory in both detection and recognition. However, results are presented which appear to offer a conclusive refutation of finite‐state theory as a model for recognition memory of unrelated words.
Nominal scale response agreement as a generalized correlation
Authors: Hubert Lawrence
Published: August 2011

A further discussion of Brennan & Light's (1974) measure of nominal scale response agreement between two raters is given. Specifically, a monotonic function of Brennan & Light's statistic is obtained in terms of a generalized correlation coefficient and provided with a descriptive probabilistic interpretation. Under the different assumptions of fixed and variable marginal frequencies, simple numerical illustrations of the appropriate mean and variance formulae are included. The fixed marginal assumption was used by Brennan & Light, and thus our formulae in this case merely suggest convenient algebraic simplifications.
Spearman‐like computation of Kendall's tau
Authors: Stuart Alan
Published: August 2011

Two new methods for calculating Kendall's tau from rank differences are shown to be valid if neither or one of the rankings contains tied ranks, but not if both do.
Pairwise comparisons involving unequal sample sizes associated with correlations, proportions or variances
Authors: Levy Kenneth J.
Published: August 2011

Attention is drawn to a procedure advocated by Spjøtvoll & Stoline (1973) for making pairwise contrasts among k independent normal moans arising from samples with unequal sample sizes. The generality of the procedure is pointed out using transformations given by Levy (1975) for making comparisons among correlations, proportions or variances. An example is also provided.
A note on local identifiability and degrees of freedom in the asymptotic likelihood ratio test
Authors: McDonald Roderick P. , Krane William R.
Published: August 2011

It is pointed out that both the degrees of freedom in the chi‐square asymptotic likelihood ratio test and the local identifiability of the parameters in the model can be determined unambiguously from the ranks of certain matrices.
Repeated cuing and the structure of recall
Authors: Jones Gregory V.
Published: August 2011

Theoretical controversy attends the question of whether the recall process is in some fundamental way consistent rather than probabilistic. The question was investigated here by examining memory for series of pictures each containing three independently specified elements: colour, location and object type. After a delay, the recall of each item was assessed in a series of separate, well‐spaced tests by providing each of its elements in turn as a retrieval cue. The results were accurately represented by a model which proposes that recall of the functional memory trace (or ‘fragment’) is indeed primarily consistent, although deviations may occur for secondary reasons.
A short note on a method of seriation
Authors: Defays D.
Published: August 2011

The classical problem of the sequencing of objects along a continuum may be solved in a rather elegant way, by means of linear algebra.
The effect of poorly conditioned data on multiple regression procedures
Authors: Goldstein Michael
Published: August 2011

A non‐technical discussion is given of the effects of ill‐conditioning on multiple regression. The informal treatment of prediction and interpretation is considered, and the motivations underlying some estimation procedures in the literature are discussed.
Estimating effect size: Bias resulting from the significance criterion in editorial decisions
Authors: Lane David M. , Dunlap William P.
Published: August 2011

Experiments that find larger differences between groups than actually exist in the population are more likely to pass stringent tests of significance and be published than experiments that find smaller differences. Published measures of the magnitude of experimental effects will therefore tend to overestimate these effects. This bias was investigated as a function of sample size, actual population difference, and alpha level. The overestimation of experimental effects was found to be quite large with the commonly employed significance levels of 5 per cent and 1 per cent. Further, the recently recommended measure, ω2, was found to depend much more heavily on the alpha level employed than the true population ω2 value. Hence, it was concluded that effect size estimation is impractical unless scientific journals drop the consideration of statistical significance as one of the criteria of publication.
Latent Markov chain analysis of a value conflict in Prisoner's Dilemma Games
Authors: van der Sanden Antoine L.
Published: August 2011

If a subject's opponent in iterated plays of the Prisoner's Dilemma Game is non‐responsive and 100 per cent cooperative, the subject is in conflict between reciprocating the cooperative acts of the other and choosing the ‘rational’ alternative which maximizes his pay‐off at the cost of the other. It is assumed that this is a conflict between opposed values which a subject can hold. The process of decision‐making in this value conflict is described in a Markov model, which relates non‐observable value states to the observable behaviour. The relationships between the parameters of the model and a new parameterization of the Prisoner's Dilemma Game are examined to add more content to the constructs of value states and to gain more insight of the dynamics of the decision‐making process in the game.
Generalized proximity function comparisons
Authors: Hubert Lawrence J.
Published: August 2011

Generalizations are given for a simple cross‐product statistic that has been used to compare two proximity functions defined on the Cartesian product of a given set S. The extensions developed here are based on a similar cross‐product form but rely on two functions defined either on S × S × S or on S × S × S × S. Typically, the latter are obtained in some way from the original proximity measures. A variety of these indices, suggested by the recent literature on cluster analysis and seriation, are mentioned explicitly along with a discussion of an approximate permutation test for assessing their relative size. Finally, a representative application of two generalized cross‐product statistics is presented in terms of a data analysis problem that requires the comparison of a partition of S against a proximity function denned on S × S.
Scale invariance and the factor analysis of correlation matrices
Authors: Krane William R. , McDonald Roderick P.
Published: August 2011

The traditional treatment of estimators in factor analysis as scale free versus not scale free is compared to the results that can be obtained on scale invariance. A theorem is given to the effect that we can obtain scale‐invariant estimators of the parameters in any model that prescribes the structure of a correlation matrix, rather than a covariance matrix, by maximum likelihood and by generalized least squares both in the metric of the sample covariance matrix and in the metric of the sample variances. An examination is made of the conditions under which we may properly neglect the scaling parameters connecting the model describing the correlation matrix with the fitted covariance matrix.
Distribution‐free methods for non‐parametric problems: A classified and selected bibliography
Authors: Singer Bernard
Published: August 2011

A bibliography of distribution‐free methods and associated topics of interest to researchers in psychology and related fields is given. Sources from biology and other areas have also been included to extend the range of coverage. References are classified into 15 main sections and 21 subsections with some cross‐referencing. The majority of papers have been published since 1961 but some earlier major studies are included. The list ends around April 1978 but late additions are also appended. The introductory sections contain a note on common misconceptions about distribution‐free methods and also a brief account of the historical connexions between the study of such statistical methods and the study of psychological processes.
A note on estimation of the autocovariance function in the analysis of timing of repetitive responses
Authors: Wing Alan M.
Published: August 2011

The estimator of the interresponse‐interval autocovariance function used by Wing (1977) is defined and its bias noted. The implications of the bias for the conclusions arrived at by Wing (1977) concerning models of response timing are discussed.
A psychological scaling model for testing order hypotheses
Authors: Davison Mark L.
Published: August 2011

This paper describes a scaling model which is based on Goodman's concept of quasi‐independence and which can be used to test an a priori order hypothesis for dichotomous or rank order data. The order hypothesis may be unidimensional or multidimensional. Methods based on the model provide a means of investigating Guttman scales, Thurstone scales, developmental stage sequences, first‐in‐first‐out developmental sequences and Coombs' unfolding theory for preferences. The methods are designed to assess whether or not there are dependencies among a set of response variables which go beyond those imposed by the experimental task and, if so, whether or not those dependencies can be accounted for by the hypothesized orderings of the variables. The methods are unique in that they are applicable to both ipsative and non‐ipsative data.
Testing and obtaining fit of data to the Rasch model
Authors: Gustafsson Jan‐Eric
Published: August 2011

Problems and procedures in assessing and obtaining fit of data to the Rasch model are treated in the paper. The assumptions embodied in the model are made explicit and it is concluded that statistical tests are needed which are sensitive to deviations such that more than one item parameter would be needed for each item, and such that more than one person parameter would be needed for each person. Statistical goodness‐of‐fit tests, based on the conditional maximum‐likelihood estimates of the item parameters, which can detect these two kinds of deviation are presented. Common sources of deviation are also identified, as are the tests needed to detect them. Problems in the use of statistical tests to assess fit are discussed and some investigations of power are presented. In relation to a distinction between use of the Rasch model as a criterion and as an instrument the treatment of the goodness‐of‐fit problem in different measurement contexts is discussed. Finally it is concluded that items which can be identified as misfitting should not be routinely excluded to obtain fit to the model; instead other actions should often be taken such as grouping of the items into homogeneous subsets.
Dimensionality, bias, independence and measurement scale problems in latent trait test score models
Authors: Goldstein Harvey
Published: August 2011

It is argued that latent trait models used in the analysis of test scores, in particular the Rasch model, suffer from serious defects. They assume implicitly a measurement scale model for which little substantive justification seems to be available and they make the assumption of ‘local independence’ which enjoys little empirical support. Perhaps their most serious drawback, which is illustrated with the fixed effects' Rasch model, is that the individual ability estimates obtained are always biased. This bias is not constant but depends upon an individual's true ability, the number of items in the test and their difficulty values. Moreover, there is no way to obtain an unbiased estimate in the typical case when only one administration of a test is given to individuals. This result suggests that the use of such models needs to be critically examined, especially in connection with so‐called ‘item banks’. The paper also discusses the dimensionality of the latent space, and shows how multidimensional models may be specified.
On taking up position in a group: A continuous‐time Markov model for biased random movement
Authors: Grimmett Geoffrey , Treisman Michel
Published: August 2011

A model is developed for movement by members of a group when this movement is random but is affected by a preference for a particular region of the space occupied by the group. Asymptotic distributions are derived from a continuous‐time Markovian model for the case in which a group member may move to any unoccupied location in one jump, and a method for estimating the degree of attraction of the preferred region is given. Such a group is described as ‘fluid’. A viscous' group is defined as one in which interchanges take place one step at a time. Movement in such groups was simulated on a computer and some results are given, including the apparently paradoxical finding that an approach tendency will be more strongly evident at asymptote if access to the preferred region is difficult than if it is easy.
Model evaluation via stochastic parameter convergence as on‐line system identification
Authors: Gregson Robert A. M.
Published: August 2011

The comparative testing of models of cognitive judgements has previously been done by post hoc parameter estimation on data gathered without feedback. If on any trial within an experiment responses are tested against competing models, and feedback is provided to the subject on his partial consistency with a currently best‐fitting model, then under some conditions behavioural and parameter convergence may be stochastically achieved. An algorithm SIMFBS with parameter convergence potential is described and its performance examined on up to five models of similarity, with various forms of memory built into the algorithm.
On how to test threshold models of detection without making assumptions about the response rule
Authors: Dusoir A. E.
Published: August 2011

Threshold models assume J discrete sensory states, which are related to responses by a probabilistic response rule. The paper discusses how we can refute threshold models with J small without imposing a priori constraints on the response rule. An argument due to Krantz is extended and applied to a sinusoid‐in‐noise detection task with randomly varying signal strengths. When five subjects are tested in this task, it is shown that J needs to be at least 3 for four subjects and at least 4 for one.
On the relative power of the U and t tests
Authors: Blair R. Clifford , Higgins J. J. , Smitley William D. S.
Published: August 2011

Boneau (1962) concluded that there is little difference between the power of the Mann–Whitney U test and the t test when samples are drawn from non‐normal populations. He further concluded that, in the long run, the t statistic does hold a slight power advantage over the Mann–Whitney statistic in the non‐normal population situation. These conclusions are not supported by the asymptotic results obtained by Hodges & Lehmann (1956).

In this study, computer simulation techniques were used to re‐examine a portion of Boneau's work. As a result of this re‐examination, it was demonstrated that Boneau erred in his conclusions and that the Mann–Whitney test may indeed show large power advantages over the t test.
On the early history of ANOVA in the analysis of repeated measure designs in psychology
Authors: Lovie A. D.
Published: August 2011

Newcomers to experimental psychology might be forgiven for thinking that the flurry of interest in repeated measure designs and their problems is of recent vintage only and that, prior to 1900, most psychologists experienced little or no difficulty with their use or analysis. This is not the case, however, and an interest in their problems and analyses can be detected even in the earliest applications of analysis of variance to psychology. The purpose of this paper, therefore, is to survey critically work on repeated measure designs and their analysis over the period 1940 to 1950. During this decade it is possible to discover the beginnings of all of the approaches and attitudes that colour contemporary thinking, from the outright radicalism of those who would reject the use of repeated measure designs almost completely, to those who view the problem as one of adapting existing techniques in design and analysis to take account of the specific features of such designs. The keys to understanding the work are the degree of insight into the structure of the designs exhibited by the people involved and their attitudes to subjects as a factor.
Search effort and the detection of faults
Authors: Smith J. Q.
Published: August 2011

A Bayes decision approach is adopted to give predictive models for the behaviour of an inspector or inspectors searching for an unlikely fault. The associated probability of the detection of such an unlikely fault is found and is related to the inspector's prior beliefs, losses and personal model when he or she is in various environments. These theoretical probabilities of detection that assume ‘sensible’ action from the inspector are found, generally, to be dramatically smaller than the probabilities obtained from the assumption of efficient search. Thus the paper explains why events with associated minute ‘probabilities’ seem to occur regularly in practice.
Statistical and metastatistical considerations in analysing the desirability of human Bayesian conservatism
Authors: Navon David
Published: August 2011

Goldstein (1979) showed that interdependence of Bernoulli data can lead to either overestimation or underestimation of odds depending on the type of interdependence, and inferred that conservative behaviour is not a necessary outcome of interdependence. It is argued here that the effect of data interdependence on posterior odds in the real world cannot be determined by pure statistical reasoning. Logical arguments suggest that interdependence which requires conservative revisions is most typical. Thus, a Bayesian processor acting on the assumption that data are conditionally independent is likely to end up with inflated posterior odds.
Appropriateness measurement: Review, critique and validating studies
Authors: Levine Michael V. , Drasgow Fritz
Published: August 2011

The test‐taking behaviour of some examinees may be so unusual that their test scores cannot be regarded as appropriate measures of their ability. Appropriateness measurement is a model‐based approach to the problem of identifying these test scores. The intuitions and basic theory supporting appropriateness measurement are presented together with a critical review of earlier work and a series of interrelated experiments. We conclude that appropriateness measurement techniques are robust to errors in parameter estimation and robust to the presence of unidentified aberrant examinees in the test norming sample. In addition, the frequently criticized ‘three‐parameter logistic’ latent trait model was found to be adequate for the detection of spuriously low scores in actual test data.
Differential coupling of sensory discriminations inferred from a survey of stable decision models for Weber's Law
Authors: Laming Donald
Published: August 2011

Differential coupling of sensory discriminations to the physical stimuli is here established by showing that the contrary supposition, direct coupling, leads to empirical predictions which are at variance with well‐established experimental findings.

Certain plausible assumptions about the initial stages of sensory processing suggest that the distributions to be combined in a statistical model for sensory discrimination should be stable; these assumptions are first set out together with the experimental evidence which gives them plausibility. The notion of direct coupling to the physical stimuli suggests, in addition, that the stable distributions should be unidimensional. A survey of stable decision models shows that, to accommodate Weber's Law, the distributions must be either Cauchy distributions or strictly stable. The unidimensional Cauchy model is shown to be incompatible with the typical shape of the psychometric function for a discrimination between two separate stimuli; and unidimensional, strictly stable, decision models are shown to have inadequate resolving power in relation to the discriminative sensitivity of human subjects. The suggestion that the decision variables should be unidimensional is thereby shown to be untenable.

Sensory discriminations can be satisfactorily represented by a strictly stable model with an unspecified, possibly large, number of independent components, and an example (the normal model) is given to show what such a model might look like. Estimates are given with respect to this model of the numbers of independent components required to support the accuracy of discrimination typically achieved with different stimulus attributes.
The decomposition of multitrait‐multimethod matrices
Authors: Browne M. W.
Published: August 2011

Existing models for multitrait‐multimethod matrices are evaluated and a new composite direct product model with a multiplicative property is proposed. The estimation of parameters in the composite direct product model is considered and an example of its application is provided. A cross‐validation to compare models is reported.
A review of exact hypothesis testing procedures (and selection techniques) that control power regardless of the variances
Authors: Wilcox Rand R.
Published: August 2011

When testing hypotheses, two important problems that applied statisticians must consider are whether a large enough sample was used, and what to do when the frequently adopted homogeneity of variance assumption is violated. The first goal in this paper is to briefly review exact solutions to these problems. In the one‐way ANOVA, for example, these procedures tell an experimenter whether enough observations were sampled so that the power will be at least as large as some pre‐specified level. If too few observations were sampled, the procedure indicates how many more observations are required. The solution is exact, which is in contrast to another well‐known procedure described in the paper. Also, the variances are allowed to be unequal. The second goal is to review how the techniques used to test hypotheses have also been used to solve problems in selection.
Some algebraic properties of the Reticular Action Model for moment structures
Authors: McArdle J. Jack , McDonald Roderick P.
Published: August 2011

A number of models for the analysis of moment structures, such as LISREL, have recently been shown to be capable of being given a particularly simple and economical representation, in terms of the Reticular Action Model (RAM). In contrast to previous treatments, a formal algebraic treatment is provided which shows that RAM directly incorporates many common structural models, including models describing the structure of means. It is also shown here that RAM treats coefficient matrices with patterned inverses simply and generally.
Statistical properties of staircase estimates from two interval forced choice experiments
Authors: Kershaw C. D.
Published: August 2011

Wetherill & Levitt (1965) suggested a class of sequential procedures for estimating points on a psychometric function. They investigated the properties of staircase estimators in yes‐no experiments. Such procedures have been used widely in two interval forced choice (21FC) experiments. In this paper large sample properties of estimators from yes‐no and 2IFC experiments are compared. These estimators are also compared by computer simulation. Results indicate that estimates from 2IFC experiments can have much greater biases and mean squared errors than those from yes‐no experiments.
Towards a general model of non‐random sampling and the impact on population correlation: Generalizations of Berkson's Fallacy and restriction of range
Authors: Alexander Ralph A. , Barrett Gerald V. , Alliger George M. , Carson Kenneth P.
Published: August 2011

A long history of restriction of range research has developed in the psychometric literature under the assumption of strict truncation. A conceptualization of the general problem of non‐random sampling is proposed leading to a model of which both restriction of range and Berkson's Fallacy (Berkson, 1946) are special cases. Cast in the framework of unequal sampling probabilities operating separately on the variables of interest, two major forms of the model are investigated: an additive and an interactive (multiplicative) form. The influence of unequal selection probabilities on population values of the bivariate normal correlation (ρ) is described and findings from other research on restriction of range are shown to be special cases of these results. Implications for inferences from data and evaluation of research designs are discussed.
Sample size determination in replication attempts: The standard normal z test
Authors: Gillett Raphael
Published: August 2011

In the light of evidence suggesting that replication attempts are often markedly deficient in power, a case can be made for a more rigorous approach to sample size determination in such studies. A method is proposed which uses information provided by the original experiment to arrive at a distribution of probable effect sizes. The sample size to be employed in a replication attempt is that which supplies an expected power of the desired amount over the distribution of probable effect sizes. To facilitate the application of the method, formulae arc developed which provide a rapid, straightforward means of establishing the appropriate sample size when the significance test employed is the standard normal z test. Examples of sample size determination using the formulae are presented for replication studies investigating the difference between two means, the difference between two correlations, and the difference between two proportions.
A more generally useful measure of the weight of examination components
Authors: Cresswell M. J.
Published: August 2011

A variety of measures of the weight of examination components are discussed in the measurement literature. Those which have been widely used are based upon considerations of candidate rank orders or the variance of the total scores. The appropriateness of such measures to examinations which are not norm‐referenced is questioned and a new measure based upon the notion of mark values is proposed which is appropriate to both norm‐ and criterion‐referenced examinations. The new measure has a number of other properties which make it generally preferable to traditional ones.
Pairwise comparisons of J independent regression lines over a finite interval, simultaneous pairwise comparison of their parameters, and the Johnson‐Neyman procedure
Authors: Wilcox Rand R.
Published: August 2011

Consider J regression lines, each with one predictor, corresponding to J independent treatment groups. The purpose of this paper is to address two related problems when comparing these J lines. Using a proposed ‘bivariate’ analogue of the Studentized range distribution, the paper notes that it is possible to get Tukey‐Kramer type simultaneous confidence intervals on both the J(J – 1)/2 pairwise differences of the intercepts and the J(J – 1)/2 pairwise differences of the slopes. That is, simultaneous confidence intervals are obtained for all J(J – 1) differences. The first goal is to provide the percentage points needed to implement the procedure. The second goal is to describe a method for obtaining simultaneous 1 – α confidence intervals for the distance between all pairs of regression lines at the end points of a finite interval. Advantages over the Johnson–Neyman procedure are noted, and certain improvements in the Johnson–Neyman procedure are described as well.
Type I error control and the power to detect factorial effects
Authors: Keselman H. J. , Keselman Joanne C.
Published: August 2011

The probability of detecting factorial effects (main, interaction, simple) with experimentwise and per hypothesis Type I error protection are compared. The effects of level of significance, sample size and size of the true factorial effect are discussed. For researchers working in the personality, social or clinical area, where effects are presumed to be small, the power to detect treatment effects is very low. On the other hand, investigations of large factorial effects in such areas as experimental and physiological psychology are likely to have reasonable power even if a 0·01 per hypothesis criterion of significance is adopted.
Simple tests implied by a genetic X‐linked model
Authors: Thomas Hoben
Published: August 2011

Suppose performance on a task is facilitated by the recessive form of an X‐linked gene in two alleles. Let the gene action be modelled by a random variable B. Let other sources of influence be modelled by a random variable N at least uncorrelated with B. Assume observations are made on a random variable W = B + N. A variety of implications of models of this form suggest many simple tests in data, several of which are apparently unfamiliar. Bivariate, univariate, discrete and continuous versions of the model are considered.
Factor indeterminacy: The saga continues
Authors: Rozeboom William W.
Published: August 2011

The much‐discussed prevailing failure of a moment decomposition Mzz = AM0A to identify just one factor tuple F such that Z = AF and MFF = M0 is only one of many ways in which a selected fragment of a complete factor solution generally specifies the solution's remainder only imperfectly. Precise ranges are worked out here for the main varieties of such indeterminacies, together with the special conditions, if any, under which they shrink to unique determinations.
Tobit factor analysis†
Authors: Muthén Bengt O.
Published: August 2011

A new approach is proposed for data which are skewed and have a sizeable proportion of observation at variable end points. Using a covariance structure modelling framework, the new approach assumes censored multivariate normal variables. Using bivariate information, this leads to the use of ‘tobit’ correlations in weighted least squares estimation. The behaviour of the tobit approach is compared to that of normal theory estimation and ADF estimation.
The 1/kn rules in the minimum logit chi‐square estimation procedure when small samples are used
Authors: Kim Seock‐ho , Baker Frank B. , Subkoviak Michael J.
Published: August 2011

Under the minimum logit chi‐square item parameter estimation procedure, observed proportions of correct response of zero or unity result in infinite logits and estimates cannot be obtained. The paper examines the application of three rules (l/2n, l/4n and elimination) for dealing with such cases. A simulation study is conducted in which sample size, number of grouping intervals, underlying item discrimination and difficulty are varied. The outcome variables are the square of the difference between the estimates and the underlying parameter values for item discrimination and difficulty. The results indicate that a complex set of interactions exist among the factors employed in the study. Overall, the 1/4n rule is preferred over the other two rules as it generally yields the smallest RMSE for both item discrimination and difficulty. However, as sample size increases the differences among the three rules decreased.
An approximately standardized person test for assessing consistency with a latent trait model
Authors: Klauer Karl Christoph , Rettig Klaus
Published: August 2011

Latent trait models predict that an examinee's ability level is invariant over subtests of the total test, that is, that all subtests measure the same latent trait. Three statistics are proposed and evaluated as significance tests of this invariance hypothesis. They are computed on the basis of a single response vector and are asymptotically standardized, that is, their conditional distributions given a particular level of ability do not depend upon the absolute value of the examinee's ability parameter. In a Monte Carlo study, one of the statistics turned out to perform satisfactorily for test lengths of 80 items. The use of the test statistic is illustrated in two applications.
A repeated measurements model with applications in psychology
Authors: Kimber Alan C. , Crowder Martin J.
Published: August 2011

The multivariate Burr distribution is discussed in relation to the analysis of repeated measures data in psychology. The ease of coping with censored and missing observations is particularly highlighted. A numerical example involving test scores of low IQ institutional patients is used to illustrate the method.
Finite state polynomic item characteristic curves
Authors: García‐Pérez Miguel A. , Frary Robert B.
Published: August 2011

A new approach to the development of the item characteristic curve (ICC) is presented, in which knowledge states, decision processes and other circumstances underlying responding to objective tests receive a priori consideration. Earlier work on finite state models of objective test performance provides the basis for deriving expressions for ICCs that directly account for factors such as examinee willingness to guess, mode of test administration, number of options per item, and the response strategy of the examinees. This approach utilizes a parameterization of ability different from that used in conventional item response theory (IRT) and yields ICCs that are polynomial functions of ability. The degree and coefficients of these polynomials depend in part on psychological/circumstantial factors such as those just mentioned or others that may readily be introduced. Examples are provided to show how differing assumptions about objective test responding lead to variation in the shapes of the resulting ICCs. The advantages that IRT could gain from adoption of these ICCs are discussed, and the work that remains to be done before finite state polynomic ICCs can be used in practice is outlined. Some possible extensions to the finite state approach are also discussed.
The importance of being OSCAR or Balance and the analysis of factorial designs
Authors: Macdonald Ranald Roderick
Published: August 2011

It is often assumed that balanced factorial designs are desirable as they result in hypotheses to be tested in an analysis of variance which are independent of each other. It is also a consequence of balance that, with the exception of the highest‐order interaction, significant analysis of variance effects derived from balanced designs generalize only to differences between linear functions of cell means with fixed weights. Such generalizations are therefore restricted to replications of complete studies including all the factors not involved in the significant effects. When dealing with non‐experimental factors, e.g. sex, age, etc., there are distinct advantages to designs in which the Observations are Sampled Completely At Random (OSCAR designs). Though this leads to unbalanced designs, analyses can be performed which treat each observation equally. In this way any significant effect generalizes both to the population sampled and to partial replications of the study which omit factors not involved in the particular significant effect. These unconstrained generalizations require that each effect is tested against its within‐effect variance, thus separate error terms are required for each test. Unweighted (equally weighted) means analyses when applied to OSCAR designs suffer from the same demerits as balanced designs and lower‐order effects do not generalize to differences between means in naturally occurring populations.