bluuebunny/crossref_metadata_2025 huggingface dataset:
The MacQuarrie Test for Mechanical Ability
Authors: Chapman Robert L.
Published: January 2006

Data originally analyzed by Charles H. Goodman on the MacQuarrie Test for Mechanical Ability are subjected to the principal axes factoring method. The maximum variance was extracted with three factors. Rotation to an oblique simple structure yielded a factor pattern which satisfies the simple structure concept more adequately than the orthogonal factor matrix, thus leading to greater clarity of interpretation of the factors.
An Algebraic Solution for the Communalities
Authors: Rosner Burt
Published: January 2006

Factorial analysis begins with an n × n correlation matrix R, whose principal diagonal entries are unknown. If the common test space of the battery is under investigation, the communality of each test is entered in the appropriate diagonal cell. This value is the portion of the test's variance shared with others in the battery. The communalities must be so estimated that R will maintain the rank determined by its side entries, after the former have been inserted. Previous methods of estimating the communalities have involved a certain arbitrariness, since they depended on selecting test subgroups or parts of the data in R. A theory is presented showing that this difficulty can be avoided in principle. In its present form, the theory is not offered as a practical computing procedure. The basis of the new method lies in the Cayley-Hamilton theorem: Any square matrix satisfies its own characteristic equation.
Who Belongs in the Family?
Authors: Thorndike Robert L.
Published: January 2006

I was sitting before my TV set, a while back, watching Captain Video and pondering the organizational problems of psychologists, psychometricians, psychodiagnosticians, psycho-somatists, psychosomnabulists, and psychoceramics (crack-pots to you). Wondering what I might do, in my small way, to help out, I decided to enlist Captain Video's help to bring me from the Black Planet that superogalactian hypermetrician, Dr. Idnozs Hcahscror-Tenib, cosmos-famous discoverer of Serutan.

Why delay? The Galaxy was on its way. and in half a light year Dr. Tenib was at my side prepared to devote his gargantuan talents to the task.

Seeing no point in confusing the good doctor by trying to describe to him the present administrative hodgepodge, I said, “Doctor, let's start from scratch. I want you to find out for me how these good people who are present at the annual meeting of the APA structure themselves? What families are represented? How many, or better, how few? And who belongs to each?”
Maximizing the Discriminating Power of a Multiple-Score Test
Authors: Loevinger Jane , Gleser Goldine C. , DuBois Philip H.
Published: January 2006

Maximizing the discriminating power of a multiple-score test involves maximizing the homogeneity of each subtest and minimizing the correlations between subtests. A method is presented for constructing such tests from items whose intercorrelations are not too high. Under certain restrictions the saturation, defined as the proportion of inter-item covariance to total variance, is maximized for each subtest. The nucleus of each subtest is three items with high covariances inter se. All items which will lower the saturation are discarded; the one item is added which will maximize the saturation of the resultant test. This process is repeated until all the items are included or discarded for that subtest. If the correlation between any such subtests approaches the geometric mean of their saturations, their items form a new pool for one or more subtests. Formulas are presented for deciding which items to eliminate in order to reduce further the correlations between subtests.
On the Sampling Errors of Factor Loadings
Authors: McNemar Quinn
Published: January 2006

The results of three empirical studies on the sampling fluctuation of centroid factor loadings are reported. The first study is based on data which happened to be available on 8 variables for 700 cases and which were factored to three factors for subsamples. The second study is based on fictitious data for 2500 cases which provided separate analyses on 25 samples for each of three situations: 5 variables, one factor; 5 variables, two factors; and 6 variables, three factors. The third study, based on real data for 9 variables and 7000 cases, involves separate factorization for 35 samples of 200 cases. The three studies agree in showing that the sampling behavior of first centroid factor loadings is much like that of correlation coefficients, whereas the sampling fluctuations for loadings beyond the first are disturbingly large.
Test Reliability Estimated by Analysis of Variance
Authors: Hoyt Cyril
Published: January 2006

A formula for estimating the reliability of a test, based on the analysis of variance theory, is developed and illustrated. The data needed for the required computation are the number of correct responses to each item and the score for each subject. The results obtained from this formula are identical with those from one of the special cases of the Kuder-Richardson formulation. The relationships of the new procedure to other approaches to the problem are indicated.
The Evaluation of Determinants
Authors: Dwyer P. S.
Published: January 2006

The numerical evaluation of determinants with a modern computing machine is discussed. Various methods are presented and their relations to each other are indicated. The methods presented parallel those developed in the previous paper on “The Solution of Simultaneous Equations.” Especially emphasized are the Abbreviated Doolittle and the Compact methods. Additional topics include the evaluation of partially symmetric determinants by means of symmetric methods and the evaluation of determinantal ratios.
Test “Reliability”: Its Meaning and Determination
Authors: Cronbach Lee J.
Published: January 2006

The concept of test reliability is examined in terms of general, group, and specific factors among the items, and the stability of scores in these factors from trial to trial. Four essentially different definitions of reliability are distinguished, which may be called the hypothetical self-correlation, the coefficient of equivalence, the coefficient of stability, and the coefficient of stability and equivalence. The possibility of estimating each of these coefficients is discussed. The coefficients are not interchangeable and have different values in corrections for attentuation, standard errors of measurement, and other practical applications.
The Relation of Multiserial Eta to other Measures of Correlation
Authors: Wherry Robert J. , Taylor Erwin K.
Published: January 2006

Ordinary product-moment correlation and regression methods are frequently not immediately applicable to qualitative data, whereas multiserial r, point-multiserial r, and multiserial eta can be easily applied. The multiserial r is rejected for prediction since it tells us only what the correlation might be if certain assumptions were true and if we could measure what is not now measured. The point-multiserial r and multiserial eta are identical when the number of categories is two but differ when it is three or greater. The multiserial eta is identical with the product-moment r when categories are assigned scale values equal to their means on the continuous variable. With three or more categories, the point-multiserial r, which assumes linearity with equal step intervals, is always lower than the multiserial eta, which forces linearity by adoption of unequal step intervals based upon difference in criterion attainment. While the multiserial eta expends one degree of freedom with the weighting of each category, this is known and correctable, whereas the vague partial loss of degrees of freedom due to the ordering of categories in the point-multiserial is not correctable.
A Comparison of the Thurstone Method of Multiple Factors with the Hotelling Method of Principal Components
Authors: McCloy C. H. , Metheny Eleanor , Knott Virginia
Published: January 2006

The factors found by the Hotelling method of principal components present the same necessity for rotation as those found by the Thurstone method of multiple factors.

The Thurstone method of multiple factors is here found superior to the Hotelling method of principal components, and is suggested as the method of choice for all problems requiring the determination of elemental components from a group of related variables, since it was found on every point of comparison that, when applied to a correlation matrix of unknown communalities, the Thurstone method was more accurate than the Hotelling method, and also required much less time.
A Contribution to the Mathematical Biophysics of Psychophysical Discrimination
Authors: Landahl H. D.
Published: January 2006

The properties of a simple neural mechanism are developed theoretically and interpreted in terms of observable variables. The results are discussed in connection with experimental data in cases for which the latter are available.
An Extension of Item Analysis Procedures to the Case of Polychotomous Response
Authors: Baker Frank B. , Gurland John
Published: January 2006

Classical item analysis procedures were developed for dichotomously scored items and do not apply to items allowing multiple correct responses. Maximum likelihood procedures analogous to those employed in polychotomous bio-assay are presented which yield estimates of the sets of parameters for items having multiple nonordered responses. Expressions for the estimates of the asymptotic variances of the item parameters and on overall chi-square goodness of fit test are also provided.
A Unified Treatment of the Weighting Problem
Authors: McDonald Roderick P.
Published: January 2006

A general procedure is described for obtaining weighted linear combinations of variables. This includes as special cases, multiple regression weights, canonical variate analysis, principal components, maximizing composite reliability, canonical factor analysis, and certain other well-known methods. The general procedure is shown to yield certain desirable invariance properties, with respect to transformations of the variables.
Multidimensional Scaling: Combining Observations when Individuals have Different Perceptual Structures
Authors: Horan C. B.
Published: January 2006

The usual methods of combining observations to give interpoint distance estimates based on interstimulus differences are shown to lead to a distortion of the stimulus configuration unless all individuals in a group perceive the stimuli in perceptual spaces which are essentially the same. The nature of the expected distortion is shown, and a method of combining individual distance estimates which produces only a linear deformation of the stimulus configuration is given.
Average Exponent from Magnitude Production
Authors: Rule Stanley J.
Published: January 2006

When magnitude production is used to obtain a psychophysical power function for a group of Ss, the group exponent is shown to be the harmonic mean of individual-S exponents under the conditions usually employed in empirical research. The conditions are (a) the same numbers are presented to each S, (b) responses to each number are pooled over Ss by taking geometric means, and (c) the function is fit by the method of least squares in which regression is of the logarithm of Ss' responses upon the logarithm of numbers presented by E.
Univariate Selection: The Effects of size of Correlation, Degree of Skew, and Degree of Restriction
Authors: Brewer James K. , Hills John R.
Published: January 2006

Pearson's formula for univariate selection was derived with the assumption of normality of variates before and after selection. This study examined the influence of skew upon estimates from Pearson's formula under certain conditions. It was found that even with essentially symmetric distributions, a large proportion of the data is necessary to obtain reasonably precise estimates of low correlations. With increasing skew, estimates become increasingly erroneous, the direction of the error depending upon which tail of the distribution is the basis of the estimates. Difficulties in applying correction for univariate selection in several studies of the predictability of college-grades for Negroes from scores on standard aptitude tests are discussed.
Fitting the Factor Analysis Model
Authors: Browne Michael W.
Published: January 2006

When the covariance matrix Σ(p×P) does not satisfy the formal factor analysis model for m factors, there will be no factor matrix Λ(p×m) such that γ=(Σ-ΛΛ′) is diagonal. The factor analysis model may then be replaced by a tautology where γ is regarded as the covariance matrix of a set of “residual variates.” These residual variates are linear combinations of “discarded” common factors and unique factors and are correlated. Maximum likelihood, alpha and iterated principal factor analysis are compared in terms of the manner in which γ is defined, a “maximum determinant” derivation for alpha factor analysis being given. Weighted least squares solutions using residual variances and common variances as weights are derived for comparison with the maximum likelihood and alpha solutions. It is shown that the covariance matrix γ defined by maximum likelihood factor analysis is Gramian, provided that all diagonal elements are nonnegative. Other methods can define a γ which is nonGramian even when all diagonal elements are nonnegative.
A Latent Structure for the Simplex
Authors: Gibson W. A.
Published: January 2006

A perfect Guttman scale generates a perfect Guttman simplex. This is capitalized on to get a transformation useful in a kind of non-linear factor analysis applicable to empirical correlations resembling but not necessarily conforming to a perfect simplex.

A Gramian factorization—square, symmetric, possibly of low rank but with no negative characteristic roots—of empirical correlations is transformed into latent information about nonlinear regressions of tests on a single underlying dimension. Class intervals on that continuum are defined in terms of their standard score profiles on the tests. Each class interval exhibits “local independence,” so that individual members may vary but may not covary in their profiles.

The method is flexible as to choice of diagonals, fitted rank, and exact shape of resulting non-linear regressions, so long as those regressions are essentially monotonic and have a proper progression of curvatures. Construction of the needed transformation for data of any size is outlined, and the problem of metric for the latent continuum is given several solutions.

An empirical example is provided with full and low rank solutions involving different diagonal choices.
Developing Prediction Weights by Matching Battery Factorings
Authors: Lunneborg Clifford E.
Published: January 2006

Between-sample shrinkage of validity from sample errors is compounded when usual multiple regression techniques are employed to estimate weights for new battery components. A rationale is described for increasing prediction weight validity through a combination of a reduced-rank regression technique and a method for determining maximal factored congruence between two sets of measures. A numerical illustration is based on data drawn from a problem in academic prediction.
Orthogonal Inter-Battery Factor Analysis
Authors: Kristof Walter
Published: January 2006

It is the purpose of this paper to present a method of analysis for obtaining (i) inter-battery factors and (ii) battery specific factors for two sets of tests when the complete correlation matrix including communalities is given. In particular, the procedure amounts to constructing an orthogonal transformation such that its application to an orthogonal factor solution of the combined sets of tests results in a factor matrix of a certain desired form. The factors isolated are orthogonal but may be subjected to any suitable final rotation, provided the above classification of factors into (i) and (ii) is preserved. The general coordinate-free solution of the problem is obtained with the help of methods pertaining to the theory of linear spaces. The actual numerical analysis determined by the coordinate-free solution turns out to be a generalization of the formalism of canonical correlation analysis for two sets of variables. A numerical example is provided.
A Theory of Appropriate Statistics
Authors: Adams Ernest W. , Fagot Robert F. , Robinson Richard E.
Published: January 2006

A formal theory of appropriateness for statistical operations is presented which incorporates features of Stevens’ theory of appropriate statistics and Suppes’ theory of empirical meaningfulness. It is proposed that a statistic be regarded as appropriate relative to statements made about it in case the truths of these statements are invariant under permissible transformations of the measurement scale. It is argued that the use of inappropriate statistics leads to the formulation of statements which are either semantically meaningless or empirically nonsignificant.
A Probability Model for Errors of Classification. II. Particular Cases
Authors: Sutcliffe J. P.
Published: January 2006

General features of a probability model for errors of classification are recapitulated as an introduction to particular cases and applications. Several models for dichotomous and nondichotomous systems are examined in sufficient detail to elaborate a procedure for dealing with any particular case. The system O = f(T, E) has empirical reference where, as statistic or parameter, probability of occasional subclass membership is given by observation, and one seeks to recover T and E values from O. A procedure for relating models and data is described. Applications of the concepts and methods are illustrated for several areas of psychological research.
Latency Models for Reaction Time Distributions
Authors: Taylor D. H.
Published: January 2006

This paper presents an adaptation of the method of moments for comparing observed and theoretical distributions of reaction time. By using cumulants in place of moments, considerable simplification of the treatment of convoluted distributions is obtained, particularly if one of the components is normally distributed. Stochastic latency models are often poorly fitted by reaction time data. This may be because a simple latency distribution is convoluted with a normal or high-order gamma distribution. The comparison method described will assist investigation of this and other interpretations of reaction time distributions.
A Remark on Tucker and Messick's “Points of View” Analysis
Authors: Ross John
Published: January 2006

It is shown that to combine readings from “points of view” configurations as assumed in Tucker and Messick's model is not to combine configurations in any simple way. Both empirical and logical consequences of the disparity are discussed.
Derivation of Likelihood-Ratio Tests for Guttman Quasi-Simplex Covariance Structures
Authors: Mukherjee Bishwa Nath
Published: January 2006

In this paper, maximum-likelihood estimates have been obtained for covariance matrices which have the Guttman quasi-simplex structure under each of the following null hypotheses: (a) The covariance matrix Σ, can be written asTΔT′ + Γ where Δ and Γ are both diagonal matrices with unknown elements andT is a known lower triangular matrix, and (b) the covariance matrix Σ*, is expressible asTΔ*T′ + γI where γ is an unknown scalar. The linear models from which these covariance structures arise are also stated along with the underlying assumptions. Two likelihood-ratio tests have been constructed, one each for the above null hypotheses, against the alternative hypothesis that the population covariance matrix is simply positive definite and has no particular pattern. A numerical example is provided to illustrate the test procedure. Possible applications of the proposed test are also suggested.
Some Mathematical Notes on Three-Mode Factor Analysis
Authors: Tucker Ledyard R
Published: January 2006

The model for three-mode factor analysis is discussed in terms of newer applications of mathematical processes including a type of matrix process termed the Kronecker product and the definition of combination variables. Three methods of analysis to a type of extension of principal components analysis are discussed. Methods II and III are applicable to analysis of data collected for a large sample of individuals. An extension of the model is described in which allowance is made for unique variance for each combination variable when the data are collected for a large sample of individuals.
Rotation for Simple Loadings
Authors: Jennrich R. I. , Sampson P. F.
Published: January 2006

Existing analytic oblique rotation schemes proceed by optimizing a simplicity function applied to the reference structure. This article suggests optimizing a simplicity function applied to primary loadings directly. The feasibility of the suggestion is demonstrated using the quartimin criterion. An algorithm to implement the optimization is derived and the existence of an admissible solution proved. Practical comparisons with the biquartimin method are made using Thurstone's Box Problem and Holzinger and Swineford's Twenty-Four Psychological Tests Problem.
Experimental Design Symbolization and Model Derivation
Authors: Lee Wayne
Published: January 2006

A method of design symbolization (DS) is given for a class of designs in which all factors are related by complete crossing or by nesting. Characterization of acceptable DS's, and logical relational properties are given. It is shown how the design model can be obtained from the DS.
Simultaneous Factor Analysis of Several Gramian Matrices
Authors: Levin Joseph
Published: January 2006

Given several Gramian matrices, a least-square fit to all the matrices by one factor matrix, with a predetermined number of factors, is shown to be the principal axes solution of the average of the matrices.
Obtaining Maximum-Likelihood Estimates of Factor Loadings and Communalities Using an Easily Implemented Iterative Computer Procedure
Authors: Hemmerle W. J.
Published: January 2006

This paper considers the problem of computing estimates of factor loadings, specific variances, and communalities for a factor analytic model. The equations for maximum-likelihood estimators are discussed. Iterative formulas are developed to solve the maximum-likelihood equations and a simple and efficient method of implementation on a digital computer is described. Use of the iterative formulas and computing techniques for other estimators of factor loadings and communalities is also considered to provide a very general approach for this aspect of factor analysis.
A Note on Some Modifications of Latent Roots and Vectors
Authors: Cartwright Desmond S.
Published: January 2006

When an arbitrary positive scalar matrix is added to a correlation matrix the latent roots of the sum are equal to the corresponding roots of the correlation matrix plus an amount equal to the scalar number of the scalar matrix. The latent vectors of the sum are identical with those of the correlation matrix. An approximation to these relationships is suggested for the case in which the sum is of a correlation matrix and of a positive semidefinite diagonal matrix. The approximation is used to allow the solution of a characteristic problem for a correlation matrix with unities in the main diagonal to provide a family of solutions for the same correlation matrix.
Testing a Simple Structure Hypothesis in Factor Analysis
Authors: Jöreskog K. G.
Published: January 2006

It is assumed that the investigator has set up a simple structure hypothesis in the sense that he has specified the zero loadings of the factor matrix. The maximum-likelihood method is used to estimate the factor matrix and the factor correlation matrix directly without the use of rotation methods, and the likelihood-ratio technique is used to test the simple structure hypothesis. Numerical examples are presented.
The Number of Paths and Cycles in a Digraph
Authors: Cartwright Dorwin , Gleason Terry C.
Published: January 2006

An algorithm is presented for constructing from the adjacency matrix of a digraph the matrix of its simple n-sequences. In this matrix, the i, j entry, i ≠j, gives the number of paths of length n from a point vi to a point vj; the diagonal entry i, i gives the number of cycles of length n containing vi. The method is then generalized to networks—that is, digraphs in which some value is assigned to each line. With this generalized algorithm it is possible, for a variety of value systems, to calculate the values of the paths and cycles of length n in a network and to construct its value matrix of simple n-sequences. The procedures for obtaining the two algorithms make use of properties of a line digraph—that is, a derived digraph whose points and lines represent the lines and adjacency of lines of the given digraph.
Alternative Power Laws for Ratio Scaling
Authors: Fagot Robert F.
Published: January 2006

To take account of the observed lack of fit of the power law near thresh-old intensities, two different modifications of the power law have been proposed by various investigators. In this paper, both of these two laws are derived as a special case of a generalized power function for ratio scaling. A method is presented for discriminating between the special laws which provides (i) a prescription for the manipulation of independent variables, and (ii) specification of theoretical curves to which empirical curves are to be compared. Maximum-likelihood estimators are derived for the exponents of the special laws under the assumption that the observed subjective ratios are log normal.
An Individual Differences Model for Multiple Regression
Authors: Cleary T. Anne
Published: January 2006

A model for multiple regression was developed which allows individual differences to emerge empirically. The model encompasses as special cases several of the previous attempts to improve psychological prediction by deviating from the usual linear multiple regression model. The model is tested with both artificial and real data. The results indicate that the model effectively reduces the variance of the error of prediction, and that the weights obtained are stable over different samples, and, to some extent, over different sets of predictors.
Derivation of Learning Process Statistics for a General Markov Model
Authors: Bernbach Harley A.
Published: January 2006

A Markov learning model may be stated in the form of a transition matrix, starting vector, and response probability vector. Utilizing these and some general properties of absorbing Markov chains, general expressions are derived for several statistics of the learning process which can be applied to any model of this form. Included are derivations for the mean learning curve, number of total errors, trial numbers of the first success and the last error, and the number of error runs. As an illustration, all derivations are worked out for the simple two-state one-element model.
Simultaneous Nonlinear Prediction
Authors: Fortier Jean J.
Published: January 2006

A previous article was concerned with simultaneous linear prediction. There one was given a set of predictor tests or items and one predicted a set of predictands (also tests or items, or perhaps criteria.) We proposed a simultaneous prediction which was a certain weighted sum of the predictors. In the present article the constraint that the prediction be a weighted sum is relaxed. We seek a general function of the predictors which will maximize the quantity chosen for measuring prediction efficiency. This quantity is the same as the one used in linear prediction and we justify this approach by showing it is the appropriate one when there is only one predictand. In order to solve the problem we restrict consideration to a vector of predictors having only a finite number of possible values, i.e., it possesses discrete probability distribution weights. This can be applied in the case of dichotomous items for instance. It may also be used in continuous distributions as an approximation, by first dividing the original range of values into a finite number of intervals. Then one attributes to the interval the weight corresponding to the probability mass it underlies in the original distribution.
Classical and Bayesian Inference in Certain Latency Processes
Authors: Bechtel Gordon G.
Published: January 2006

Certain aspects of point estimation are treated for two kinds of exponential latency processes. The first unitary process is represented by a simple exponential density in which the rate parameter may be viewed as an unknown constant or as a random variable. If a second, slower exponential process is grafted onto the first, there results a postulated two-component latency between stimulus and response. Moments estimators are derived for the two parameters of this latter density, and the relevance of the second parameter to decision time is emphasized.
The Algebra of Factorial Indeterminancy
Authors: Heermann Emil F.
Published: January 2006

Certain properties and consequences of factor indeterminancy are deduced from an orthogonal transformation derived by Ledermann. The first deduction is the matrix of cosines between maximally distinct factor axes which represent the same factor solution. This result is used to investigate the indeterminancy of factor extensions.
Resolution of the Heywood Case in the Minres Solution
Authors: Harman Harry H. , Fukuda Yoichiro
Published: January 2006

In the course of developing the minres method of factor analysis the troublesome situation of communalities greater than one arose. This problem—referred to as the generalized Heywood case—is resolved in this paper by means of a process of minimizing the sum of squares of off-diagonal residuals. The resulting solution is superior to the otherwise very efficient original minres method without requiring additional computing time.
Generalizability of Scores Influenced by Multiple Sources of Variance
Authors: Gleser Goldine C. , Cronbach Lee J. , Rajaratnam Nageswari
Published: January 2006

Generalizability theory concerns the adequacy with which a “universe” score can be inferred from a set of observations. In this paper the theory is applied to a universe in which observations are classifiable according to two independent variable aspects of the measuring procedure. Several types of universe scores are developed and the variance components ascertained for each type. The composition of expected observed-score variance and the adequacy of inference to a particular type of universe score is a function of the procedure used in gathering data. A generalizability study provides estimates of variance components which can be used in designing an efficient procedure for a particular decision purpose.
A Method of Successive Cumulations for the Scaling of Pair-Comparison Preference Judgments
Authors: Greenberg Marshall G.
Published: January 2006

The present model treats the scaling of pair-comparison preference judgments among a unidimensional set of stimuli across a population of individuals. Given a set S of n stimuli, S = {S1, S2, …, Sn}, the model yields a partially ordered metric on the interstimulus distances which may be used to construct an interval scale of values forS. Obtained also are a set of predictions P = {P1, P2, …, Pn} wherePi is the proportion of individuals in the population whose first choice among the elements of S is Si. A numerical illustration is offered and comparisons are drawn with Coombs' unfolding technique.
A Sensitive Rank Test for Comparing the Effects of Two Treatments on a Single Group
Authors: Cronholm James N. , Revusky Samuel H.
Published: January 2006

By taking advantage of an experimental design which increases the number of observations per subject, the sensitivity of the proposed test is increased. In the first of a series of subexperiments, the score of a randomly selected experimentalS is ranked with the scores of the remaining (control) Ss, and the experimental S is discarded. This procedure is repeated until one S remains. The test criterion, Rn, is the sum of ranks of the experimental Ss; its exact sampling distribution, a normal approximation, and the sensitivity of the test relative to the Wilcoxon T, are described. Because of the large number of scores obtained, the test is particularly useful when preparing Ss is more costly than testing them, e.g., in tests following involved conditioning procedures. Since each S is discarded after experimental treatment, the test fills a real need in studies involving radiation, ablation, or other irreversible treatments.
Geometric Vector Orthogonal Rotation Method in Multiple-Factor Analysis
Authors: Kashiwagi Shigeo
Published: January 2006

An objective method for the orthogonal rotation of factors which gives results closer to the graphic method is proposed. First, the fact that the varimax method does not always satisfy simple-structure criteria, e.g., the positive manifold and the level contributions of all factors, is pointed out. Next, the principles of our method which are based on “geometric vector” are discussed, and the computational procedures for this method are explained using Harman and Holzinger's eight physical variables. Finally, six numerical examples by our method are presented, and it is shown that they are very close to the factors obtained from empirical studies both in values and in signs.
Correcting Correlation Coefficients for Group Heterogeneity When One Variable is a Dichotomy
Authors: Tupes Ernest C.
Published: January 2006

A method is illustrated for estimating correlation coefficients and mean criterion scores in a full-range population from bivariate distributions available in a selected sample when the criterion is a dichotomy. The proposed method requires only the assumptions needed for use of formulas for correcting correlation coefficients for restriction of range when both variables are continuous and is suitable for use when restriction is due to either direct or indirect selection.
A Factor Analytic Method for Investigating Differences between Groups of Individual Learning Curves
Authors: Weitzman R. A.
Published: January 2006

In this method of analyzing learning data, entire learning curves are described quantitatively by single numbers which are used in a statistical test to determine whether two or more groups of learning curves are significantly different. The method has some logical advantages over prevailing methods in that it avoids the use of average learning curves and of arbitrary measures of slope and asymptote. Its disadvantage is computational. Since it involves the use of factor analytic procedures, it may be tedious to apply unless computation is carried out on a high-speed computer.
Biserial Estimates of Correlation
Authors: Lord Frederic M.
Published: January 2006

Brogden's coefficient of selective efficiency and Clemans' λ are more efficient than biserial r when the correlation is high. Some empirical sampling studies are reported comparing the standard errors of these statistics.
Note on Use of Extreme Criterion Groups in Item Discrimination Analysis
Authors: Feldt Leonard S.
Published: January 2006

The purpose of this note is to reconsider the Kelley-Cureton definition of optimal extreme groups for estimating item-criterion correlations. Optimal tail per cents are derived, using the criterion of minimum sampling variance of the tetrachoric correlation coefficient, and the findings are related to earlier work of Mosteller. It is shown that upper and lower 27 per cent groups yield the most precise estimate of the tetrachoric coefficient only when the population correlation is close to zero. When the population value is .4, extreme 20 per cent groups provide estimates with the smallest sampling error variance. It is further shown, however, that 27 per cent extremes yield highly efficient estimates. Thus no change is recommended in traditional item analysis procedures.
The Stochastic Model of Mental Testing Theory and an Application
Authors: Woodbury Max A.
Published: January 2006

An axiomatization of mental test theory is presented. The presentation deals explicitly with the following concepts: true score, parallel forms, reliability, validity, and combined test score.
A General Method of Obtaining Exact Sampling Probabilities of the Shannon-Wiener Measure of Information Ĥ
Authors: Cronholm James N.
Published: January 2006

A two-variable generating function is described which yields the sampling probabilities of the Shannon-Wiener information measure. Expansion and collection of terms in like powers of the first variable imposes the restriction that the sum of the k category frequencies equal n; collection of terms in like powers of the second variable then produces terms whose coefficients are the required probabilities. The method may be used with either equal or unequal category probabilities for any finite n and k, and thus represents a general solution to the small sample problem. Tables of sampling probabilities are presented.
Powered Vector Method of Factor Analysis
Authors: Overall John E. , Porterfield James L.
Published: January 2006

The powered vector method of factor analysis yields directly and without rotation factors satisfying objectives of parsimony, orthogonality, and meaningfulness. The method is objective, computationally efficient, and easily programmed for digital computers. The computational procedure is described. Illustrative analyses are presented. Results of applications of the powered vector method are compared with results obtained using the principal axes solution followed by orthogonal rotation.
Multidimensional Scaling by Optimizing Goodness of Fit to a Nonmetric Hypothesis
Authors: Kruskal J. B.
Published: January 2006

Multidimensional scaling is the problem of representing n objects geometrically by n points, so that the interpoint distances correspond in some sense to experimental dissimilarities between objects. In just what sense distances and dissimilarities should correspond has been left rather vague in most approaches, thus leaving these approaches logically incomplete. Our fundamental hypothesis is that dissimilarities and distances are monotonically related. We define a quantitative, intuitively satisfying measure of goodness of fit to this hypothesis. Our technique of multidimensional scaling is to compute that configuration of points which optimizes the goodness of fit. A practical computer program for doing the calculations is described in a companion paper.
Informational Models and Their Uses
Authors: Binder Arnold , Wolin Burton R.
Published: January 2006

An analysis of the selection and use of informational models in psychological research is undertaken. The axioms of different informational models are presented together with the deductions which have direct empirical application. The models are used to demonstrate many of the inadequacies and inaccuracies involved in the use of information theory in the psychological literature. It is also shown that certain related conceptual ambiguities are understandable in terms of confusions among various models.
On the Interaction of the Subject and the Experiment in the Matching Model
Authors: Swentzell Ralph , Roberts Alan H.
Published: January 2006

Two types of matching designs, static and dynamic, are differentiated. While all matching designs are logically the same in terms of the probability model which determines chance level of performance, an attempt is made to demonstrate that there is an interaction between the tactics, strategies, and actual knowledge of S and the type of design used which will, in turn, lead to different results even when S's knowledge is held constant. It is suggested that analogous situations may exist within the framework of the traditional psychometric model.
J Scale Models for Preference Behavior
Authors: Greenberg Marshall G.
Published: January 2006

Three models for preference behavior are developed within the framework of Coombs' theory of data, an absolute difference model, a ratio model, and a two-stage model. Each of these models describes a mechanism by which unilateral preferences may be determined on a unidimensional J scale. Differential implications of the models for response latencies are derived, and some early data employing an application of the unfolding technique are presented in support of the two-stage model.
Test Reliability and Practice Effects
Authors: Hoffman Paul J.
Published: January 2006

The purpose of this paper is to develop mathematical formulations of test reliability when the estimation of reliability requires successive observations and these observations are not independent of the process (or act) of measurement. The specific application of concern arises in performance testing where performance varies as a function of practice and where practice accrues as a result of measurement. Repeated measures are experimentally nonindependent in such cases. Formulations for the estimation of reliability are developed for each of two cases. The first of these assumes a linear model for acquisition; the second assumes a nonlinear (quadratic) model. Illustrative data are presented whereby insights may be gained as to the inadequacy of the models.
Asymptotic Sampling Variances for Factor Analytic Models Identified by Specified Zero Parameters
Authors: Lockhart R. S.
Published: January 2006

Formulas are derived for the asymptotic variances and covariances of the maximum likelihood estimators for oblique simple structure models which are identified by prior specification of zero elements in the factor loading matrix. The formulas are expressed in terms of the various submatrices of the inverse of the required variance-covariance matrix. A numerical example using artificial data is given and problems in the application of the formulas discussed.
On a New Property of Partially Balanced Association Schemes useful in Psychometric Structural Analysis
Authors: Srivastava J. N. , Maik R. L.
Published: January 2006

In an earlier paper [Psychometrika, 31, 1966, p. 147], Srivastava obtained a test for the Hypothesis H0 : Σ =α0Σ0 + ... +αlΣl, where Σi are known matrices,αi are unknown constants and Σ is the unknown (p × p) covariance matrix of a random variablex (withp components) having ap-variate normal distribution. The test therein was obtained under (p × p) covariance matrix of a random variablex (with p components) the condition that Σ0, Σ1, ..., Σl form a commutative linear associative algebra and a certain vector θ, dependent on these, has non-negative elements. In this paper it is shown that this last condition is always satisfied in the special situation (of importance in structural analysis in psychometrics) where Σ0, Σ1, ..., Σl are the association matrices of a partially balanced association scheme.
A Note on a Matrix Criterion for Unique Colorability of a Signed Graph
Authors: Gleason Terry C. , Cartwright Dorwin
Published: January 2006

A signed graph,S, is colorable if its point set can be partitioned into subsets such that all positive lines join points of the same subset and all negative lines join points of different subsets.S is uniquely colorable if there is only one such partition. Developed in this note is a new matrix, called the type matrix of S, which provides a classification of the way pairs of points are joined in S. Such a classification yields a criterion for colorability and unique colorability.
Estimates of Test Size for Several Test Procedures based on Conventional Variance Ratios in the Repeated Measures Design
Authors: Collier Raymond O. , Baker Frank B. , Mandeville Garrett K. , Hayes Thomas F.
Published: January 2006

Estimates of test size (probability of Type I error) were obtained for several specific repeated measures designs. Estimates were presented for configurations where the underlying covariance matrices exhibited varying degrees of heterogeneity. Conventional variance ratios were employed as basic statistics in order to produce estimates of size for a conventional test, an ∊-adjusted test, and ∊-adjusted test and a conservative test. Indices for empirical distributions of two estimators of ∊j, a measure of covariance heterogeneity, were also provided.
Markovian Processes with Identifiable States: General Considerations and Application to All-or-None Learning
Authors: Greeno James G. , Steiner Theodore E.
Published: January 2006

It often happens that a theory specifies some variables or states which cannot be identified completely in an experiment. When this happens, there are important questions as to whether the experiment is relevant to certain assumptions of the theory. Some of these questions are taken up in the present article, where a method is developed for describing the implications of a theory for an experiment. The method consists of constructing a second theory with all of its states identifiable in the outcome-space of the experiment. The method can be applied (i.e., an equivalent identifiable theory exists) whenever a theory specifies a probability function on the sample-space of possible outcomes of the experiment. An interesting relationship between lumpability of states and recurrent events plays an important role in the development of the identifiable theory. An identifiable theory of an experiment can be used to investigate relationships among different theories of the experiment. As an example, an identifiable theory of all-or-none learning is developed, and it is shown that a large class of all-or-none theories are equivalent for experiments in which a task is learned to a strict criterion.
Nominally and Rigorously Parallel Test Forms
Authors: Lord Frederic M.
Published: January 2006

When several test forms are used interchangeably, they will not in practice, despite all efforts, be rigorously parallel. A definition of the standard error of measurement appropriate for this type of situation can be provided; however, it will be different from the definition in classical test theory. Appropriate formulas for the standard error of measurement and for other related quantities under both definitions are derived and compared; also sample statistics for estimating these quantities.
Oblique Factor Analytic Solutions by Orthogonal Transformations
Authors: Harris Chester W. , Kaiser Henry F.
Published: January 2006

A general framework for obtaining all possible factor analytic solutions, orthogonal and oblique, for a given common factor space is developed in detail. Interestingly, and seemingly paradoxically, any one of these solutions may be obtained by orthogonal transformations of selected matrices; thus an oblique solution may be determined by orthogonal transformations. Within the possible oblique solutions, two distinct categories of solutions emerge, a special case of the simpler of which apparently provides a definitive solution to the problem of independent, but correlated, clusters. Possible further specializations of the general approach to specific problems are discussed.
On the Psychophysical Law and Estimation Procedures in Psychophysical Scaling
Authors: Fagot Robert F.
Published: January 2006

A general formulation of the power law is presented which has two special features: (1) negative exponents are admissible; and (2) the log law is a special limiting case. Estimation procedures, which provide joint estimates of the exponent and the absolute threshold, are derived for the direct ratio scaling methods. A solution is provided for the averaging problem for ratio production and bisection scaling, two methods generating observations on the physical scale, and Monte Carlo methods are used to evaluate the resulting estimators.
Univocal or Orthogonal Estimators of Orthogonal Factors
Authors: Heermann Emil F.
Published: January 2006

The defects of the least-squares or multiple-regression equation approach to estimating orthogonal factors are discussed and transformations of the beta weights are derived which remove these defects with minimum loss in correlations between estimators and true factor scores.
Some Possible Forms of Lexicographic Evaluation
Authors: Gregson R. A. M.
Published: January 2006

A set of definitions leading to an axiom set which makes possible distinction between two or more forms of lexicographic choice is offered. It is shown that, by treating value as quantized and only taking a finite number of levels for each attribute of a multi-attribute choice situation, lexicographic evaluation might be subsumed under more familiar forms of choice model. Special cases and implications are discussed.