bluuebunny/crossref_metadata_2025 huggingface dataset:
An Investigation of the Sampling Distributions of Item Discrimination Indices
Authors: Baker Frank B.
Published: January 2006

The sampling properties of four item discrimination indices (biserial r, Cook’s index B, the U–L 27 per cent index, and Delta P) were investigated in order to ascertain their sampling properties when small samples drawn from actual test data rather than constructed data were employed. The empirical results indicated that the mean index values approximated the population values and that values of the standard deviations computed from large sample formulas were good approximations to the standard deviations of the observed distributions based on samples of size 120 or less. Goodness of fit tests comparing the observed distributions with the corresponding distribution of the product-moment correlation coefficient based upon a bivariate normal population indicated that this correlational model was inappropriate for the data. The lack of adequate mathematical models for the sampling distributions of item discrimination indices suggests that one should avoid indices whose only real reason for existence was the simplification of computational procedures.
An Alternative Approach to the Method of Correct Matching
Authors: Halevi Hai
Published: January 2006

The correct matching method is treated in a new way which increases its power and enables the results to be expressed by a correlation coefficient. Tables for 3 ≤ n ≤ 7 are included.
A Generalized Solution of the Orthogonal Procrustes Problem
Authors: Schönemann Peter H.
Published: January 2006

A solutionT of the least-squares problem AT=B + E, given A and B so that trace (E′E)= minimum and T′T= I is presented. It is compared with a less general solution of the same problem which was given by Green [5]. The present solution, in contrast to Green's, is applicable to matrices A and B which are of less than full column rank. Some technical suggestions for the numerical computation of T and an illustrative example are given.
Structural Centrality in Communications Networks
Authors: Mackenzie Kenneth D.
Published: January 2006

This paper examines the concept of centrality with respect to small-group communication experiments. An index of centrality is presented which is based on the incidence matrix of actual communications rather than on the deviation matrix of possible communications, as in the Bavelas Index of Centrality. The index takes the value of zero for the homogeneous all-channel graph and the value of unity for the homogeneous wheel graph. The index can be computed for individuals as well as groups. Three examples are computed.
Probability Matching
Authors: Norman M. Frank , Yellott John I.
Published: January 2006

The class of symmetric path-independent models with experimenter-controlled events is considered in conjunction with two-choice probability learning experiments. Various refinements of the notion of probability matching are defined, and the incidence of these properties within this class is studied. It is shown that the linear models are the only models of this class that predict a certain phenomenon that we call stationary probability matching. It is also shown that models within this class that possess an additional property called marginal constancy predict approximate probability matching.
The Minimal Transformation to Orthonormality
Authors: Johnson Richard M.
Published: January 2006

The solution is presented to the problem of finding that orthonormal matrix closest in the least-square sense to a given matrix of full rank. An application is shown to the problem in multiple regression analysis of determining the “importance” of each independent variable.
Accuracy of Maximum-Likelihood Estimates of Correlation for a Biserial Model
Authors: Prince Benjamin M. , Tate Robert F.
Published: January 2006

Tables are given for the calculation of variances of maximum-likelihood estimates in a multiple biserial model. For the estimates of individual correlations between the dichotomized variable and each of the graduated variables additional calculation is necessary; variances for estimates of the multiple correlation and the point of dichotomy are available directly. The required formulas and notation are those of a recent paper by Hannan and Tate.
Corrected Item-Test Correlations
Authors: Cureton E. E.
Published: January 2006

Previous papers on this subject derive the correlation between an item and the remainder of the test. This correlation is unsatisfactory because the reliability of the remainder varies inversely with the reliability of the item omitted. The present paper derives the correlation between an item and the total test, with that item replaced by a rationally equivalent item. The general formula is then modified, for dichotomus items, to give the corrected point-biserial, biserial, and Brogden biserial correlations. The results apply strictly only to factorially homogeneous tests: those in which the same trait or combination of traits is measured (apart from error) by every item.
Factor Analysis by Minimizing Residuals (Minres)
Authors: Harman Harry H. , Jones Wayne H.
Published: January 2006

This paper is addressed to the classical problem of estimating factor loadings under the condition that the sum of squares of off-diagonal residuals be minimized. Communalities consistent with this criterion are produced as a by-product. The experimental work included several alternative algorithms before a highly efficient method was developed. The final procedure is illustrated with a numerical example. Some relationships of minres to principal-factor analysis and maximum-likelihood factor estimates are discussed, and several unresolved problems are pointed out.
Theorems for a Finite Sequence from a Two-State, First-Order Markov Chain with Stationary Transition Probabilities
Authors: Bogartz Richard S.
Published: January 2006

Various theorems are obtained for N-trial sample sequences from the general two-state, first-order Markov chain with stationary transition probabilities. Four lemmas which facilitate the derivations are given. A brief discussion of applications to binary data, estimation, and evaluation is given, including a maximum-likelihood procedure for estimating transition probabilities which are restricted by inequalities.
Estimation of a Correlation Coefficient from an Uncertainty Measure
Authors: Pearson William H.
Published: January 2006

In this paper graphs are given for estimating a correlation ρXY from a double-entry table. 2 Hr, twice the statistic Hr, “relative uncertainty” (the average of the ratios of the conditional uncertainty of each variable to its uncertainty) was computed. Mean 2 Hr's were computed from 100 samples for each of several sample sizes and numbers of categories. Graphs relating mean 2 Hr to \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$\hat r_H$$
\end{document}, the estimated correlation, for 3–17 categories to each variable and 3 sample sizes—50, 100, and 500—were constructed. 2.5 per cent and 97.5 per cent fiducial limits curves were constructed for establishing confidence limits on ρXY and \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$\hat r_H$$
\end{document}.
Generating Multiple Samples of Multivariate Data with Arbitrary Population Parameters
Authors: Wherry Robert J. , Naylor James C. , Wherry Robert J. , Fallis Robert F.
Published: January 2006

A method of generating any number of score and correlation matrices with arbitrary population parameters is described. Either Z scores or stanines are sampled from a normal population to represent factor scores by an IBM 1620 program. These are converted to variates from a population with an a priori factor structure. The effectiveness of the method is illustrated from research data. Some further modifications and uses of the method are discussed.
Another Interpretation of a Model for Paired Comparisons
Authors: Bradley Ralph A.
Published: January 2006

The first contribution of this paper is to demonstrate that the paired-comparison model may be derived from a variety of different initial assumptions about the nature of paired comparisons, some of these assumptions appearing to the author to be more appropriate to a description of the preference-decision process than others. The second contribution of this paper is to note that the generalization of the model to triple comparisons chosen earlier is not the one compatible with the Lehmann model even though it possesses other desirable properties. Limited numerical calculations suggest that both models for triple comparisons give comparable results in applications. Their asymptotic properties should be similar.
An Empirical Study of Item-Test Regression
Authors: Lord Frederic M.
Published: January 2006

Certain questions about the shape of item-test regressions are answered on the basis of data obtained from 103,275 examinees. Ten of the regressions obtained are shown in illustrative plots.
Admissible Probability Measurement Procedures
Authors: Shuford Emir H. , Albert Arthur , Massengill H. Edward
Published: January 2006

Admissible probability measurement procedures utilize scoring systems with a very special property that guarantees that any student, at whatever level of knowledge or skill, can maximize his expected score if and only if he honestly reflects his degree-of-belief probabilities. Section 1 introduces the notion of a scoring system with the reproducing property and derives the necessary and sufficient condition for the case of a test item with just two possible answers. A method is given for generating a virtually inexhaustible number of scoring systems, both symmetric and asymmetric, with the reproducing property. A negative result concerning the existence of a certain subclass of reproducing scoring systems for the case of more than two possible answers is obtained. Whereas Section 1 is concerned with those instances in which the possible answers to a query are stated in the test itself, Section 2 is concerned with those instances in which the student himself must provide the possible answer(s). In this case, it is shown that a certain minor modification of a scoring system with the reproducing property yields the desired admissible probability measurement procedure.
Robustness of the Maximum-Likelihood Estimation Procedure in Factor Analysis
Authors: Fuller E. L. , Hemmerle W. J.
Published: January 2006

In order to determine the robustness of the maximum-likelihood estimation procedure, random variates from six distributions were generated independently on a high speed computer and then used to represent the common and specific factors in a factor analysis model in which the coefficients of these factors had been specified. Using Lawley's approximate x2 statistic in evaluating the estimates obtained, the estimation procedure is found to be insensitive to changes in the distributions considered.
Some Comments in Connection with Rozeboom's Linear Correlation Theory
Authors: Fhanér Stig
Published: January 2006

It is shown that certain correlation measures suggested by information theory are simple functions of the determinants of the correlation matrices involved, if multivariate normality is assumed. This illuminates and in a sense strengthens Rozeboom's point in [3], that information theoretical statistics have “classical” correlational counterparts.
Analysis of Covariance Structures
Authors: Bock R. Darrell , Bargmann Rolf E.
Published: January 2006

A general method is presented for estimating variance components when the experimental design has one random way of classification and a possibly unbalanced fixed classification. The procedure operates on a sample covariance matrix in which the fixed classes play the role of variables and the random classes correspond to observations. Cases are considered which assume (i) homogeneous and (ii) nonhomogeneous error variance, and (iii) arbitrary scale factors in the measurements and homogeneous error variance. The results include maximum-likelihood estimations of the variance components and scale factors, likelihood-ratio tests of the goodness-of-fit of the model assumed for the design, and large-sample variances and covariances of the estimates. Applications to mental test data are presented. In these applications the subjects constitute the random dimension of the design, and a classification of the mental tests according to objective features of format or content constitute the fixed dimensions.
A Matrix Formulation of Kaiser's Varimax Criterion
Authors: Sherin Richard J.
Published: January 2006

Kaiser has given the varimax criterion for the solution of the rotation problem in factor analysis as well as a practical computational procedure for maximizing this criterion. In the present paper, the maximization condition is shown as a matrix equation involving only the unknown orthogonal rotation matrix. This matrix equation can be solved iteratively as a sequence of symmetric eigenproblems.
Alpha Factor Analysis of Infallible Variables
Authors: Glass Gene V
Published: January 2006

The relationship between the factor pattern, F, derived from fallible (containing measurement error) observations on variables and the factor pattern, F*, derived from infallible observations on variables is investigated. A widely believed relationship between F and F*, viz.,F* = AF where A is a diagonal matrix containing the inverses of the square roots of the reliabilities of the variables, is shown to be false for several factor analytic techniques. Under suitable assumptions, it is shown that for Kaiser and Caffrey's “alpha factor analysis”F* and F are related by F* = AF. Empirical examples for which the corresponding elements of F* and AF are equal to two decimal places are presented. The implications of the equality of F* and AF for alpha factor analysis are discussed.
Matching Components of Self-Report and Peer-Nomination Personality Measures
Authors: Norman Warren T. , Harshbarger Thad R.
Published: January 2006

Two common methods of measuring personality variables are examined with respect to the ways in which they control respondent biases. A form of the mental-test theory model is developed which makes explicit differences in score components that result from different methodological constraints imposed by the two methods. From the model, it is possible to specify the operations necessary to provide equivalent information from the two sets of data. Performance of these operations in an empirical test supports the model by producing generally higher correlations between the variables having score components which are more closely matched.
A Direct Method for Multidimensional Ratio Scaling
Authors: Ekman Gösta
Published: January 2006

A generalization of direct ratio scaling methods to multidimensional ratio scaling is described. This method requires an observer to report the proportion of a standard percept that is contained in a given percept and vice versa. The method was developed to meet requirements for experimentation in such areas as color vision, gustation, and olfaction.
Factoring the Circumplex
Authors: Gibson W. A.
Published: January 2006

This paper presents a way of factoring the Guttman circumplex to get factor weights whose pattern is close to that postulated by Guttman for the circumplex. An empirical example, including a crude procedure for diagonal estimation, is shown. Other sources of nonuniqueness are discussed, and the limitation to odd-numbered complexity for the tests is indicated. An orthodox factor analysis is applied to the example, and this provides a basis for comparison of the two opposing models.
An Individual differences Model for Multidimensional Scaling
Authors: Tucker Ledyard R , Messick Samuel
Published: January 2006

A quantitative system is presented to permit the determination of separate multidimensional perceptual spaces for individuals having different viewpoints about stimulus interrelationships. The structure of individual differences in the perception of stimulus relationships is also determined to provide a framework for ascertaining the varieties of consistent individual viewpoints and their relationships with other variables.
A Nonparametric Test for the Two-Sample Problem
Authors: Hollander Myles
Published: January 2006

Moses has proposed a nonparametric test of the null hypothesis that two samples, say a treatment and a control group, have been drawn from the same population; his test is designed to be sensitive to the alternative hypothesis that the treatment group is extreme in either or both directions as compared with the controls. This paper presents a test of similar character, except that rather than being based on a range of the control group ranks, it depends upon the variance of those ranks. This has the advantage of making ties less troublesome. Tables of significance values are presented for some small sample sizes. A normal approximation is developed and seen to be useful.
Canonical Correlations with Fallible Data
Authors: Meredith William
Published: January 2006

The technique of canonical correlation may be used to determine the extent to which two sets of measurements reflect the same underlying traits. However, if the two sets are not perfectly reliable, the unreliability may obscure the fact that they are essentially dependent on similar processes. If we attempt to determine sets of weights so as to maximize the correlation between linear composites after correction for attenuation in the composites, it turns out that the results may be obtained by determining the canonical correlations and canonical regression weights between the true score components of the measures making up the two sets. In addition, formulas are developed for calculating the correlations between the canonical variates and original measures, both corrected and uncorrected for attenuation. A numerical example relating the verbal to the performance subtests of the Wechsler Intelligence Scale for Children is presented.
A New Method for Solving Simultaneous Linear Equations Associated with Multivariate Analysis
Authors: Watson F. R.
Published: January 2006

A method is outlined whereby the equations resulting from multivariate analyses may be solved. Only the upper or lower triangular coefficient matrix need be employed. All solutions involving any combination(s) of the variables represented in the coefficient matrix are readily obtainable without permutation of the matrix. All solutions are given immediately without the need for back solving. One variable is added to or subtracted from the regression equation with each application of the method. The method may be applied as repeatedly as needed for any particular solution.
The Use of Limit Theorems in Paired Comparison Model Building
Authors: Thompson W. A. , Singh Jagbir
Published: January 2006

The Thurstone and the Bradley-Terry models, both initially advanced on intuitive grounds, have proved useful in the analysis of paired comparisons. The psychological meaning of these models and their relation to one another is unclear, but they fit data. Stevens has observed that there may be two basic mechanisms of discrimination 1) additive and 2) substitutive. We advance two corresponding mathematical models: that experienced sensation is 1) the sum of a large number of independent signals and 2) the maximum of a large number of independent signals. These assumptions yield 1) Thurstone's model and 2) the model of Bradley-Terry. Psychological interpretations of the various parameters, in terms of sensation, present themselves in a natural manner. Thus this paper presents a theory which unifies and interprets two paired comparison models that have proved useful in fitting experimental data.
Successive Intervals Scaling of Paired Comparisons
Authors: Sjöberg Lennart
Published: January 2006

In this paper a method is developed for analyzing data resulting from the use of a modification of the usual paired comparisons procedure which allows for ratings of size of difference. The scaling model is essentially an extension of the Thurstonian successive intervals model. The method is applied to scaling of a set of nine “immoral” actions and the results agree rather well with those from conventional successive intervals scaling of the same stimuli.
The Influence of Communality, Factor Strength, and Loading Size on the Sampling Characteristics of Factor Loadings
Authors: Cliff Norman , Pennell Roger
Published: January 2006

A Monte Carlo approach is employed in determining whether or not certain variables produce systematic effects on the sampling variability of individual factor loadings. A number of sample correlation matrices were generated from a specified population, factored, and transformed to a least-squares fit to the population values. Influences of factor strength, communality and loading size are discussed in relation to the statistics summarizing the results of the above procedures. Influences producing biased estimators of the population values are also discussed.
An Estimation of True Scores in the Case of Items Scored on a Continuous Scale
Authors: Srivastava A. B. L. , Webster Harold
Published: January 2006

For the tests in which the score on an item is not restricted to 0 and 1, but is any number on a continuous scale, a procedure for estimating an examinee's true score is given. For the case of 0, 1 item scoring this problem was considered by Lord [1959]. Following Lord, the least squares estimation procedure is used and the regression coefficient is obtained, which is compared with the generalized KR(20) and KR(21) formulas. Also, results are discussed using analysis of variance models.
A Choice Model for Paired Comparison Data based on Imperfectly Nested Sets
Authors: Eisler Hannes
Published: January 2006

A ratio scale of subjective magnitude is developed from paired-comparison data. The model attempts to combine arguments of Restle, Ekman, and Luce relating data obtained from paired comparisons and corresponding data from direct psychophysical scaling methods at the ratio level. The basic set-theoretical model involves the use of imperfectly nested sets. A numerical example illustrates the application of the theory.
The Preliminary Analysis of Emergent Social Structure in Groups
Authors: Davis James H.
Published: January 2006

The problem of detecting emergent social structure in small groups is examined in terms of establishing a baseline or expected structure. The standard proposed here is equalitarianism; that is to say, every member is equally likely to interact with every other member. Using information theory, a formal statement of the equalitarian argument is possible. In addition to detecting a deviation by a single group, the structural tendency of several groups assigned to some experimental condition is discussed. This technique is designed for the preliminary analysis of structure; it deals only with the general character of the total structure.
A Comparison of Graphic and Analytic Solutions for both Oblique and Orthogonal Simple Structures for Factors of Employee Morale
Authors: Baehr Melany E.
Published: January 2006

Solutions for simple structure obtained from empirical data through the use of the Oblimax, Quartimax, and Varimax procedures are matched with independently determined graphic solutions for the same data. The relative merits of the two analytic orthogonal solutions (Quartimax and Varimax) are discussed. Factors of employee morale are interpreted.
Correction of Item-Total Correlations in Item Analysis
Authors: Henrysson Sten
Published: January 2006

The biserial correlation between an item and the total test of which the item is a part tends to be misleadingly high when used in item analysis, since the item is included in the total test. Two formulas with correction for this overlap are derived and compared with Zubin's and Guilford's formulas. One of the new coefficients is invariant to test length.
A Stochastic Model for Free Recall
Authors: Waugh Nancy C. , Keith Smith J. E.
Published: January 2006

A statistical model for verbal learning is presented and tested against experimental data. The model describes a Markov process with a realizable absorbing state, allowing complete learning on some finite trial as well as imperfect retention prior to this trial.
A Comparison of Three Methods of Fitting the Normal Ogive
Authors: Cramer Elliot M.
Published: January 2006

The Mueller-Urban method of fitting the normal ogive is derived, and the inadequacies of its inherent assumptions are discussed. This and the unweighted least squares method are compared to the maximum likelihood solution which is shown to be very close to the “ideal” least squares solution. As an empirical demonstration of the superiority of the maximum likelihood solution, random ogives are fitted by all three methods and they are compared on the basis of the expected values and the standard errors of the estimates. It is concluded that the maximum likelihood solution is uniformly superior to the others in all respects.
A Note on the Derivation of the General Latent Class Model
Authors: McDonald Roderick P.
Published: January 2006

A general formulation of the latent structure principle is suggested, from which it is possible to derive Lazarsfeld’s accounting equations in their most general form. The basic equations of Gibson’s latent profile model can thence be derived in a single step.
A Maximum Likelihood Solution for the Method of Successive Intervals Allowing for Unequal Stimulus Dispersions
Authors: Schönemann Peter H. , Tucker Ledyard R
Published: January 2006

A maximum likelihood solution for the method of successive intervals is presented together with an iterative procedure for obtaining estimates for stimulus scale values, boundary scale values, and stimulus dispersions. The method applies without modification to incomplete data matrices. The method was programmed for ILLIAC and a brief description of the program and a numerical illustration are included.
Note on a Rank Test of Cronholm and Revusky
Authors: Bennett B. M.
Published: January 2006

A rank test Rn has been proposed by Cronholm and Revusky which in effect increases the number of observations per subject by the device of randomly assigning a subject to a treated group in each of a series of sub-experiments. In this note further results on the asymptotic normality of the Rn test are discussed both under the null hypothesis H0 of randomness and under a class of alternatives to H0. The limiting power of the test is also discussed.
Random Fluctuations of Response Rate
Authors: McGill William J.
Published: January 2006

A simple model for fluctuating interresponse times is developed and studied. It involves a mechanism that generates regularly spaced excitations, each of which can trigger off a response after a random delay. The excitations are not observable, but their periodicity is reflected in a regular patterning of responses. The probability distribution of the time between responses is derived and its properties are analyzed. Several limiting cases are also examined.
The Asymptotic Distribution for the Two-Absorbing-Barrier Beta Model
Authors: Kanal Laveen
Published: January 2006

For the two-absorbing-barrier specialization of Luce's beta learning model, the asymptotic distribution of the response probability has all its density at p = 0 and p = 1. The functional equation for the amount of the density at p = 1 is investigated in this paper.
Probabilistic Foundations for Coefficients of Generalizability
Authors: Hunter John Edward
Published: January 2006

This paper explores certain problems which arise within the context of the theory of generalizability put forward by Cornbach, Rajaratnam, and Gleser. In particular, a formal explication of their theory for the single observation is given, and the various coefficients of generalizability which they define are related to the estimation of universe scores.
Fechner: Inadvertent Founder of Psychophysics
Authors: Boring Edwin G.
Published: January 2006

Certainly the most interesting tool that science employs in its perpetual pursuit of knowledge is the scientist, with his enthusiasms, egoisms, and prejudices, his inevitable unconscious attitudinal orientation in the consensus of contemporary opinion, which we call the Zeitgeist. One wonders what science would be like if automation could take over completely. Are there mechanical equivalents for jealousy and pride and pigheadedness and insight, and those other interacting personal forces that contribute to contemporary truth in the scientific field?

Fechner never tried to found psychophysics or a new experimental psychology. He was, in his own estimation in those last forty-five years of his life, a philosopher, fighting what he regarded as the crass materialism of his day, the Nachtansicht or “night view,” as he called it, and promoting the faith that mind and soul are the ultimates of reality, the Tagesansicht or “day view.” This favoring of the clear philosophical vision in the day view as opposed to the materialistic darkness of the night view is Fechner’s panpsychism, a faith that seems mystical to most modern scientists, partly because the German word Seele does not distinguish between mind and soul, between that which compares the sensory intensities of two lifted weights and whatever it is that persists after the body’s death.
New Developments in Statistical Behavior Theory: Differential Tests of Axioms for Associative Learning
Authors: Estes W. K.
Published: January 2006

Several types of new developments in statistical behavior theory deserve attention: (i) attempts at relatively direct empirical tests of basic axioms; (ii) the application of models that survive these tests for purposes of data reduction and analysis; (iii) the extension of extant models, or elaborations of them, to new empirical problems; and (iv) the introduction of new models based primarily on abstract mathematical considerations. The last two of these “new developments” have been well represented in recent books [3, 11]; the first two will be illustrated in the following sections.
Computer Models of Cognitive Processes
Authors: Green Bert F.
Published: January 2006

Twenty-five years ago, when the Psychometric Society was formed, the new developments that were then shaping the course of psychometric research were subjective scaling and factor analysis. Today, a development that seems destined to influence psychometric research in the next twenty-five years is the simulation of cognitive processes on high-speed digital computers. So far, of course, there has been more talk about the potential utility of computers in psychology than there has been accomplishment; nevertheless, what achievements have been made seem to me to imply a bright future.
Instrumental Variables in Factor Analysis
Authors: Madansky Albert
Published: January 2006

The factor analysis model is rewritten as a system of linear structural relations with errors in variables. The method of instrumental variables is applied to this revised form of the model to obtain estimates of the factor loading matrix. The relation between this method and interbattery analysis, proportional profile analysis, and canonical factor analysis is pointed out. In addition, an estimation procedure based on replicated sampling different from proportional profile analysis is given.
A Generalization of the Interpoint Distance Model
Authors: Ross John , Cliff Norman
Published: January 2006

Coombs and Kao have conjectured that, given the distances between a set of points representing persons and another representing objects, factor analytic methods can be used to recover the locations of the persons and objects. In the present paper it is proved that the conjecture applies, with some qualifications, to squared distances rather than distances themselves. Possible applications to scaling and to inventory responses are discussed.
Some Generalizations of a Theoretical Distribution of Mental Test Scores
Authors: Keats John A.
Published: January 2006

The negative hypergeometric distribution may be generalized to provide distributions involving 3, 4, or more parameters. It is shown that, in the case of the binomial error model, such distributions correspond to quadratic, cubic, etc., regressions of true scores on raw scores. Explicit formulas are given for the bivariate moments required to fit these regressions and so estimate the parameters of the generalized hypergeometric distribution. Equations are also developed for fitting the 3- and 4-parameter distributions directly, i.e., without reference to the model, and the method for generalizing these is indicated. The methods developed are applied to objective test data with satisfactory results.
On the Johnson-Neyman Technique and Some Extensions Thereof
Authors: Potthoff Richard F.
Published: January 2006

The Johnson-Neyman technique is a statistical tool used most frequently in educational and psychological applications. This paper starts by briefly reviewing the Johnson-Neyman technique and suggesting when it should and should not be used; then several different modifications and extensions of the Johnson-Neyman technique, all of them conceptually simple, are proposed. The close relation between confidence intervals and regions of significance of the Johnson-Neyman type is pointed out. The problem of what to do when more than two groups are being compared is considered. The situation of more than one criterion variable is also considered.
Analysis of Preferential Experiments
Authors: Ramanujacharyulu C.
Published: January 2006

The problems of selecting the winner in a tournament, a leader in a society, or the most dominating or influential person in a group of individuals are not infrequent. Graph theory is successfully used in such situations in locating, by the use of associated matrices of graphs representing the individuals under the studied relation, the person with the greatest power to influence. In this paper one more important point is brought into consideration before selecting the leader or the most influencing personality—that is the consideration of weakness to be influenced by. The one with a nice blending of these two characters—possessing the highest power to influence a person and simultaneously having the least weakness to be influenced by—is to be selected. But, in practice, to locate such a man in a group is delicate. A solution is presented here by appealing to graph theoretic notions and using them.
On a Connection Between Factor Analysis and Multidimensional Unfolding
Authors: Coombs Clyde H. , Kao Richard C.
Published: January 2006

Given the preference ordering of each of a number of individuals over a set of stimuli, it is proposed that if the preference orderings are generated in a Euclidean space of r dimensions which can be recovered by unfolding the preference orderings, then a factor analysis of the correlations between individual's preference orderings will yield a space of r + 1 dimensions with the original r-space embedded in it, and the additional dimension will be one of social utility. The proposition is clearly shown to be satisfied by means of the Monte Carlo technique for both random and lattice stimuli in three dimensions and for two other examples with random stimuli in one and two dimensions.
Percentage Points of Wilks' Lmvc and Lvc Criteria
Authors: Roy J. , Murthy V. K.
Published: January 2006

Likelihood ratio tests have been proposed by Wilks for testing the hypothesis of equal means, variances, and covariances (Hmvc) and the hypothesis of equal variances and covariances (Hvc) in a p-variate normal distribution. Using exact distributions of the appropriate likelihood ratio statistics, tables of the .05 and .01 points of these distributions are constructed for p = 4, 5, 6, 7 and sample size n = 25 (5) 60 (10) 100. A correction factor is recommended for larger n. Two numerical examples illustrate use of the tables. A nonparametric test is proposed for Hmvc when the multivariate parent population is known to be non-normal.
Models for Choice-Reaction Time
Authors: Stone Mervyn
Published: January 2006

In the two-choice situation, the Wald sequential probability ratio decision procedure is applied to relate the mean and variance of the decision times, for each alternative separately, to the error rates and the ratio of the frequencies of presentation of the alternatives. For situations involving more than two choices, a fixed sample decision procedure (selection of the alternative with highest likelihood) is examined, and the relation is found between the decision time (or size of sample), the error rate, and the number of alternatives.
A Model for Detection and Recognition with Signal Uncertainty
Authors: Shipley Elizabeth F.
Published: January 2006

A model for signal detectability suggested by Luce is extended to situations in which the observer is uncertain of some important characteristic of the signal, such as frequency. By making a single assumption concerning the observer's covert response behavior, two solutions are obtained corresponding to qualitatively different behavior. Decrements in detectability and in recognition with uncertainty are shown to be particular functions of discriminability and detectability of the stimuli in other situations. Relevant experimental data are considered.
A Note on Combining Probabilities
Authors: Adcock C. J.
Published: January 2006

The weakness in the usual application of the Fisher method of combining probabilities is pointed out and a supplementary method is suggested.
Alpha Factor Analysis
Authors: Kaiser Henry F. , Caffrey John
Published: January 2006

A distinction is made between statistical inference and psychometric inference in factor analysis. After reviewing Rao's canonical factor analysis (CFA), a fundamental statistical method of factoring, a new method of factor analysis based upon the psychometric concept of generalizability is described. This new procedure (alpha factor analysis, AFA) determines factors which have maximum generalizability in the Kuder-Richardson, or alpha, sense. The two methods, CFA and AFA, each have the important property of giving the same factors regardless of the units of measurement of the observable variables. In determining factors, the principal distinction between the two methods is that CFA operates in the metric of the unique parts of the observable variables while AFA operates in the metric of the common (“communality”) parts.

On the other hand, the two methods are substantially different as to how they establish the number of factors. CFA answers this crucial question with a statistical test of significance while AFA retains only those alpha factors with positive generalizability. This difference is discussed at some length. A brief outline of a computer program for AFA is described and an example of the application of AFA is given.
A Method for Studying Differences between Groups
Authors: Meredith William
Published: January 2006

The researcher in behavioral or biological science has available a large arsenal of methods for studying the nature and statistical significance of differences between various groups of individuals. He may use any of a wide variety of univariate methods to test hypotheses about differences in location, in dispersion, in correlation between pairs of attributes, etc. In a multivariate situation methods are available to test hypotheses about mean vectors, variance-covariance matrices, correlation matrices, factor structures, etc.

There are two points of view involved in studying the nature of differences between groups. One point of view is descriptive, and has traditionally been treated under the topic of estimation in statistics. The other usually involves a question as to whether it is reasonable to assume that some hypothesized model about the nature of differences between populations is in fact true, and has usually been treated under the ~pic of tests of hypotheses. The descriptive and inferential points of view must of necessity often overlap.
Nonlinear Factors in Two Dimensions
Authors: Gibson W. A.
Published: January 2006

Intercorrelations among tests nonlinearly related to underlying dimensions require more linear factors than content would demand. For the case of two independent underlying content dimensions, a fictitious example is constructed and made to yield a transformation useful for the nonlinear analysis of certain empirical data. That transformation, when applied to a standard factorization (centroid or principal components if certain symmetries obtain) of the appropriate empirical correlations, yields parameters descriptive of plausible nonplanar regression surfaces for tests on the two underlying dimensions. An empirical example is presented and discussed.
A Statistical Test for the Significance of a Coefficient of Reproducibility
Authors: Sagi Philip C.
Published: January 2006

Under the assumption that responses to different dichotomous items are statistically independent, exact distributions for coefficients of reproducibility, CR, are derived. These distributions are useful in testing whether an observed coefficient of reproducibility differs significantly from chance expectations and whether further scaling manipulations are warranted. The effects of purification on sampling distributions of errors are calculated to demonstrate a relationship between scaling operations and expected chance values of the CR.
A Note on the Standard Length of a Test
Authors: Myers Charles T.
Published: January 2006

This paper describes a relationship between the variance-covariance matrix of test items and Woodbury's concept of the standard length of a test. An index of item-test relationship is described in standard length terms. The sum of these indices for the items in a test is equal to the square of Jackson's coefficient of sensitivity.
A Cosine Approximation to the Normal Distribution
Authors: Raab David H. , Green Edward H.
Published: January 2006

A cosine function is suggested to approximate the normal distribution as a device for simplifying algebraic manipulations of the latter. Numerical evaluations remain straightforward and employ only the commonly available trigonometric tables. A method of visual curve fitting requiring only an oscilloscope is also described.
To What Extent can Communalities Reduce Rank?
Authors: Guttman Louis
Published: January 2006

The question is raised as to whether the null hypothesis concerning the number of common factors underlying a given set of correlations should be that this number is small. Psychological and algebraic evidence indicate that a more appropriate null hypothesis is that the number is relatively large, and that smallness should be but an alternative hypothesis. The question is also raised as to why approximation procedures should be aimed primarily at the observed correlation matrix R and not at, say, R−1. What may be best for R may be worst for R−1, and conversely, yet R−1 is directly involved in problems of multiple and partial regressions. It is shown that a widely accepted inequality for the possible rank to which R can be reduced, when modified by communalities, is indeed false.
An Axiomatic Formulation and Generalization of Successive Intervals Scaling
Authors: Adams Ernest , Messick Samuel
Published: January 2006

A formal set of axioms is presented for the method of successive intervals, and directly testable consequences of the scaling assumptions are derived. Then by a systematic modification of basic axioms the scaling model is generalized to non-normal stimulus distributions of both specified and unspecified form.
Interpretation of Second-Order Factors
Authors: Holzinger Karl J.
Published: January 2006

It is shown that a “second-order” factor pattern is equivalent to the transformation employed in rotating an orthogonal factor pattern to an oblique form. The correlation among the second-order factors may then be interpreted as due to the original first-order factors.
Group Differences in Size Estimation
Authors: Ansbacher H. L. , Mather K.
Published: January 2006

Fifty-two subjects differing in sex, age, education and domicile (rural or urban) were given the problem of judging the height of an upright board in a natural setting. A preliminary analysis was made on the basis of the simple initial ratio method, both for the original data in feet and for original data converted to log units. Because the effects of interaction of the several variables made the results of this method inconclusive, the analysis of variance technique, as described by Yates (11) for data where the classes are not equally represented, was applied. This technique showed that, while together the four factors markedly affected judgment, sex had no significant individual effect, age had the biggest individual effect but possibly a spurious one, education and domicile had suspiciously large individual effects, and the effect of the four factors may be regarded as simply additive. The relation of the findings to those of previous investigators is discussed. The authors regard as an important result of the analysis the guidance it offers in the design of further experiments, since it demonstrates the value of equal representation for all classes into which data are to be segregated.
An I.B.M. Technique for the Computation of ΣX2 and ΣXY
Authors: Benjamin Kurt
Published: January 2006

Given I.B.M. cards punched with scores (or any numbers)—but not their squares—a method is presented of tabulating them (on the No. 405 alphameric I.B.M. tabulator) so as to obtain the sum of squares. The technique is also adaptable to summation of cross-products. The principle is an extension of the Mendenhall-Warren-Hollerith technique of vertical progressive digiting, without the necessity of manual addition or summary-punching, and is designed for machines not equipped with the “card cycle total transfer” device or “progressive total” device. Use is made of “counter rolling.” Efficient use of machine capacity is made only when intercorrelations between no more than two variables are required in addition to sums of squares. A resumé of some techniques now commonly employed is included.
A Generalization of Stimulus Sampling Theory
Authors: Atkinson Richard C.
Published: January 2006

A modification of stimulus sampling theory is presented. The restriction that each stimulus element is conditioned to one and only one response is replaced with the notion of a scale of conditioning for each element. This variation provides a context in which such variables as reward magnitude and motivation can be viewed as determiners of behavior. Some experimental results on multiple response problems also have a natural interpretation in terms of these ideas.
The Rationale for an “Oblimax” Method of Transformation in Factor Analysis
Authors: Saunders D. R.
Published: January 2006

Factorial transformation is viewed as an estimation problem in which the usual assumption of homogeneously distributed error cannot be applied, but may be replaced by a principle of maximum kurtosis. This leads to quartimax in the orthogonal case, and to “oblimax” in the oblique case. Oblimax is readily programmable, and typically provides results similar to those of subjective rotation. However, oblimax may encounter special difficulty in data which do not determine a simple structure, or which have been imprecisely factored.
Multidimensional Unfolding: Some Geometrical Solutions
Authors: McElwain D. W. , Keats J. A.
Published: January 2006

A method is proposed whereby the distribution of stimuli and subjects can be derived directly from the subjects' rankings of the stimuli. The solution for four stimuli is presented with examples and suggestions for the solution of problems involving more stimuli. The model is intuitively attractive and is likely to prove useful when direct solutions for larger number of stimuli are available.