bluuebunny/crossref_metadata_2025 huggingface dataset:
Estimation and Tests of Significance in Factor Analysis
Authors: Rao C. Radhakrishna
Published: January 2006

A distinction is drawn between the method of principal components developed by Hotelling and the common factor analysis discussed in psychological literature both from the point of view of stochastic models involved and problems of statistical inference. The appropriate statistical techniques are briefly reviewed in the first case and detailed in the second. A new method of analysis called the canonical factor analysis, explaining the correlations between rather than the variances of the measurements, is developed. This analysis furnishes one out of a number of possible solutions to the maximum likelihood equations of Lawley. It admits an iterative procedure for estimating the factor loadings and also for constructing the likelihood criterion useful in testing a specified hypothesis on the number of factors and in determining a lower confidence limit to the number of factors.
On the Design of Automata and the Interpretation of Cerebral Behavior
Authors: Frankel Stanley
Published: January 2006

In principle it is possible to design automata to display any explicitly described behavior. The McCulloch-Pitts “neuron” is a convenient elementary component for the control mechanisms of automata. Previously described techniques permit the design of an automaton which would arbitrarily well simulate human behavior. The difficulty of producing such a design lies primarily in formulating an explicit description of the required behavior. The control mechanism of such an automaton would be of very great logical complexity. Its mode of operation probably would not resemble that of a human brain. The brain is more plausibly represented by stochastic models as proposed by Hebb. Such models can more easily be designed or understood by reason of lesser logical complexity. A method of computational investigation of the functioning of such stochastic models is described. Several extremely simple models have been investigated. One is shown to have properties suggestive of learning ability.
Note on the Selection of a Panel of Judges so as to Maximize Panel Efficiency
Authors: Harrison Stephen , Ishler Norman H. , Laue Elsie M.
Published: January 2006

Attempts to develop improved methods of selecting a panel of judges for psychometric work are presented. The applications reported are in the sensory field and are limited to the assumption of a unidimensional ability underlying the judgments in question. Some aspects of cost efficiency are also considered.
A Simple Procedure for Rearranging Matrices
Authors: Gibson W. A.
Published: January 2006

Guttman's scalogram board technique for reordering the columns and rows of a matrix is described and its disadvantages are pointed out. A simple and inexpensive procedure for doing the same job without these disadvantages is outlined.
A Distinction Between Exact and Approximate Nonparametric Methods
Authors: Sawrey William L.
Published: January 2006

Nonparametric tests are discussed in relation to parametric tests. A distinction is made between two types of nonparametric tests. One type leads to an exact significance level, the other to an approximate significance level. The failure to distinguish between these two types has led to confusion and error. Examples are cited.
Psychometric Theory: General and Specific
Authors: Tucker Ledyard R
Published: January 2006

Fellow members of the Psychometric Society, and our colleagues, members of Division 5 of the American Psychological Association, I understand my mission tonight is to provide you with both humor and a mild message. Precedent has established an eminently high standard. Maybe I can explain the humbleness with which I approach this task by relating the account of an episode. This occurrence, like much illustrative data in Psychometrika, is fictitious, of course.

During my trip from the splendorous East Coast to the beauteous West Coast, I took vacation time to tour part of the magnificent country in between, as many of you, undoubtedly, did also. 0he afternoon I came upon a small tent village in a fairly remote mountain section. Not that such camps were so uncommon as to be remarkable in themselves; something about this particular camp caught my eye. In the center of this camp was a rustic conference table flanked on one side by a large blackboard mounted on cedar posts.
F-Test Bias for Experimental Designs of the Latin Square Type
Authors: Gourlay Neil
Published: January 2006

In an earlier paper, a method of analysis, due to Neyman and now known generally as variance component analysis, was used to examine F-test bias for experimental designs in education of the randomized block type. The same method is now applied to study F-test bias for designs of the Latin square type. The results, in general, disprove the view that, for a valid application of Latin square techniques, it is necessary that all interactions are zero.
A Statistical Model for Relational Analysis
Authors: Luce R. Duncan , Macy Josiah , Tagiuri Renato
Published: January 2006

The diadic relationships existing in a group can be defined in terms of the members' choices, rejections, and their perceptions of being chosen and rejected. The number of possible distinct diads is 45. Formulas are given for computing the expected frequency and variance of the different diadic forms expected, when certain random factors are taken into account. These values must be known if the operation of factors other than the specified random ones is to be studied. Values obtained from two models with different assumptions are compared with empirical values. A simplified treatment is possible for groups with ten or more members.
Changes in Common-Factor Loadings as Tests are Altered Homogeneously in Length
Authors: Guilford J. P. , Michael William B.
Published: January 2006

Formulas are derived by which, given the factor loadings and the internal reliability of a test of unit length, the following estimates can be made: (1) the common-factor loadings for a similar (homogeneous) test of length n; (2) the number of times (n) that a test needs to be lengthened homogeneously to achieve a factor loading of a desired magnitude; and (3) the correlation between two tests, either or both of which have been altered in length, as a function of (a) the new factor loadings in the altered tests or (b) the original loadings in the unit-length tests. The appropriate use of the derived formulas depends upon the fulfillment of four assumptions enumerated.
A Test of the Equality of Standard Errors of Measurement
Authors: Green Bert F.
Published: January 2006

A procedure is proposed for testing the significance of group differences in the standard error of measurement of a psychological test. Wilks' criterion is used to assure that the tests used in ascertaining reliability and hence variance of errors of measurement may be assumed parallel for each group. Votaw's criterion may be used to check whether the test scores of all the groups have the same mean, variance, and covariance. It is possible, however, for the variance and reliability of the test to differ widely from group to group, so that Votaw's criterion is not satisfied even though the variance of errors of measurement stays relatively constant. For this case a modification of Neyman and Pearson's criterion is developed to test agreement among standard errors of measurement despite group differences in mean, variance, and reliability of the test.
Theory of Learning with Constant, Variable, or Contingent Probabilities of Reinforcement
Authors: Estes W. K.
Published: January 2006

The methods used in recent probabilistic learning models to generate mean curves of learning under random reinforcement are extended to the general case in which probability of reinforcement may vary in any specified manner as a function of trials and to cases in which probability of reinforcement on a given trial is contingent upon responses or outcomes of preceding trials.
Simple Proofs of Relations Between the Communality Problem and Multiple Correlation
Authors: Guttman Louis
Published: January 2006

Solutions of the communality problem and of the problem of meaning of common and unique factors have been shown previously to depend intimately on certain relations with ordinary multiple correlation. To make these basic propositions more accessible, simple proofs of some of them are provided here, avoiding any matrix algebra. New results are also obtained, with no extra work, that extend the previously known propositions to a more general class of coefficients than that of communalities.
Application of a Large Sampling Criterion to Some Sampling Problems in Factor Analysis
Authors: Rippe Dayle D.
Published: January 2006

A technique is presented to test the completeness of factor solutions and also to test the significance of common-component loadings. The chisquare test involved is based upon the asymptotic normal properties of the residuals.
A Note on the Neyman-Johnson Technique
Authors: Abelson Robert P.
Published: January 2006

A statistical problem which frequently arises in educational and psychological experimentation is that of testing the significance of the difference of the mean scores of two groups on some criterion variable, where the differential effects of one or more variables which are correlated with the criterion must be statistically eliminated. The usual analytical technique for this type of problem is the analysis of covariance (9). The Neyman-Johnson technique (7) provides another, and substantially different, approach. A computational procedure is suggested here which utilizes the advantages of both techniques without an undue increase in computational labor. In addition, the Neyman-Johnson technique is generalized to the case of n predictor variables. Its application has heretofore been limited to a maximum of three predictor variables.
Note on Miller's “Finite Markov Processes in Psychology”
Authors: Kao Richard C. W.
Published: January 2006

In his article “Finite Markov Processes in Psychology,” G. A. Miller derived a least-squares “estimate” for a matrix of transitional probabilities. However, the mathematical proof is found to be invalid.

On page 158, Miller defined by the equation

= N + C,

“where the elements of the matrix C are the corrections that must be added to the observed values in N to give the best estimate ”.
A Proposed Index of the Conformity of One Sociometric Measurement to Another
Authors: Katz Leo , Powell James H.
Published: January 2006

An index is proposed to measure the extent of agreement of the data of a sociometric test with another test made at an earlier time or on another test criterion. The index is used to define an index of concordance between the two tests. It is shown how the index may be used for either individuals or groups. Tests of the hypothesis that agreement is random are given for all cases and applied to an example.
Differences in Factor Content of Rights and Wrongs Scores
Authors: Fruchter Benjamin
Published: January 2006

The right-response scores and wrong-response scores of speeded aptitude tests were factor analyzed to determine whether they differ in factorial content. The information thus obtained was used to derive scoring formulas that yield purer measures of a factor than do scoring formulas derived in other ways.
A Note on the Effects of Selection in Factor Analysis
Authors: Degan James W.
Published: January 2006

Professor Godfrey Thomson, in a communication to this laboratory, has drawn our attention to certain computational and editorial errors in a recent publication on the effects of selection in factor analysis. The purpose of this note is to rectify these errors. In so doing, we wish to express our gratitude to Professor Thomson for preventing their prepetuation.

Since the particular tables under consideration appear also in Chapter XIX, “The Effects of Selection,” of and are identical with those of, the material presented in this note is equally applicable to both publications. These tables were numbered identically in both and may be referred to non-differentially. In order to facilitate the exposition in this note, the numbers assigned to each of the corrected tables and figure correspond to the analogous tables and figure of the original publications.
A Study of Speed Factors in Tests and Academic Grades
Authors: Lord Frederic M.
Published: January 2006

Speeded and unspeeded tests of vocabulary, spatial relations, and arithmetic reasoning were factorially analyzed, together with certain reference tests and academic grades. Lawley's maximum likelihood method was used, the computations being carried out on the Whirlwind electronic computer. Four different speed factors were isolated, together with a second-order general speed factor. Consistent small positive correlations between the academic grades and the speed factors were found.
Note on Carroll's Analytic Simple Structure
Authors: Kaiser Henry F.
Published: January 2006

A method for computing the transformation matrix for Carroll's analytic simple structure (1) is presented. The procedure involves successively finding the smallest latent root and associated vector of symmetric matrices.
A Least Squares Solution for Paired Comparisons with Incomplete Data
Authors: Gulliksen Harold
Published: January 2006

A precise and rapid procedure has been devised for dealing with a matrix of incomplete data in paired comparisons. This method should increase the general applicability of paired comparisons since experiments involving large numbers of stimuli may now be shortened to feasible experimental proportions. Also, we may now use sets of stimuli which cover a wide range, resulting in a considerable number of 100 per cent vs. 0 per cent judgments, and still give a precise solution depending equally on each of the observations.
A Non-Parametric Test of Correlation using Rank Orders within Subgroups
Authors: Torgerson Warren S.
Published: January 2006

Kendall's rank order test for association between two variables is generalized to the case where the total sample is made up of several subgroups and the data on one or both variables consist of the rank order within each subgroup. The test involves no assumptions concerning scales of measurement, shapes of distributions, or relative level of excellence or amount of variability of the different subgroups. Two empirical examples indicate that the normal approximation to the exact test of significance can be considered adequate for most practical situations. Special consideration is given to the case of tied ranks. If ties occur in but one variable within any given subgroup, only a slight modification in procedure is needed. Extensive ties in both variables within subgroups lead to difficulties in determining the appropriate correction for continuity.
The Validity of the Successive Intervals Method of Psychometric Scaling
Authors: Rozeboom William W. , Jones Lyle V.
Published: January 2006

The degree to which scale values computed by the method of successive intervals diverge from theoretically “true” values is seen to be due to three types of error: error due to inequalities in variances of the distributions from which the scale values are computed, error due to non-normality of the distributions, and sampling error. The contribution of each type of error to the total error is evaluated; the latter is seen to be surprisingly small under appropriate conditions. Certain aspects of the formal methodology underlying scaling procedures are also briefly considered.
A General Solution for the Latent Class Model of Latent Structure Analysis
Authors: Green Bert F.
Published: January 2006

For the point distribution model of Lazarsfeld's latent structure analysis, the general matrix equation is stated which relates the manifest data in the form of joint occurrence matrices to the latent parameters. The relationship of the item responses and these joint occurrence matrices is also indicated in matrix form. A general solution for the latent parameters is then presented, which is based on the notion of factoring two joint occurrence matrices. The solution is valid under certain conditions which will usually be fulfilled. The solution assumes that estimates are available for the elements in the joint occurrence matrices with recurring subscripts, analogous to item communality or reliability. Some alternative methods of obtaining these estimates are discussed. Finally a fictitious 3-class, 8-item example is presented in detail.
Optimal Test Length for Maximum Battery Validity
Authors: Horst Paul
Published: January 2006

Having given a fixed amount of total testing time it is important to know how long each test in the battery should be so that the correlation of the battery with the criterion will be a maximum. The precise solution for the test lengths will depend on a particular set of conditions which may be specified. The writer has previously presented solutions for two sets of conditions. This article presents the solution for a third set of conditions. These are: (1) The total number of items or testing time is fixed. (2) The score is the total number of items correctly answered. (3) The test lengths are determined in such a way that the correlation of total score with the criterion is a maximum. The solutions for the two previous sets of conditions, together with the current set, are summarized. A set of experimental data is submitted to each solution and the three sets of results are compared.
A Mechanical Model Illustrating the Scatter Diagram with Oblique Test Vectors
Authors: Gulliksen Harold , Tucker Ledyard R
Published: January 2006

A mechanical model is described for illustrating changes in the configuration of points when the reference axes are rotated obliquely and the values of the orthogonal projections of the points on the reference axes are maintained constant. This type of transformation is important in factor analysis.
A Graphical Method for the Rapid Calculation of Biserial and Point Biserial Correlation in Test Research
Authors: Goheen Howard W. , Davidoff Melvin D.
Published: January 2006

A description is given of a diagram (available separately) for computing biserial or point biserial correlation coefficients. The diagram is maximally useful where large numbers of coefficients are to be calculated in test item analysis. The diagram is entered with the mean criterion score of the group passing the item and the proportion of correct answers to the item.
Note on the Least Squares Solution for the Method of Successive Categories
Authors: Bock R. Darrell
Published: January 2006

The problem of estimation in the method of successive categories is reconsidered and a new least squares solution is obtained. An empirical comparison of this solution with Gulliksen's solution is presented.
Communality of a Variable: Formulation by Cluster Analysis
Authors: Tryon Robert C.
Published: January 2006

The communality of a variable represents the degree of its generality across n − 1 behaviors. Domain-sampling principles provide a fundamental conception and definition of the communality. This definition may be alternatively stated in eight different ways. Three definitions lead to precise formulas that determine the true value of the communality: (i) from the k necessary and sufficient dimensions derived by iterated factoring, (ii) from the n − 1 remaining variable-domains, and (iii) from k′ multiple clusters of the n variables. Seven definitions provide approximation formulas: (i) one from the k dimensions as initially factored, (ii) one from the n − 1 remaining variables, and (iii) five from a single cluster. Rank of the matrix is not a desiratum in some definitions. Using an example designed by Guilford to illustrate multiple-factor analysis, applications of the formulas based on the three precise definitions recover the true communalities, and five approximation formulas each gives values closer than the ad hoc estimates usually employed in factor analysis.
Measurement of Subjective Values
Authors: Gulliksen Harold
Published: January 2006

Four different value laws are developed and tested by using them to predict the scale values of composite stimuli from the scale values of their components. These four laws are: an additive law, a square-root law, a logarithmic, and a negative exponential law. They are tried out on a set of food preferences by means of Pearson's Method of False Position. The negative exponential law of diminishing returns gave the best fit to the data but was not markedly better than any of the other laws.
Maximizing Test Battery Prediction when the Weights are Required to be Non-Negative
Authors: Lev Joseph
Published: January 2006

A procedure is developed for computing optimum regression weights under the restriction that they be non-negative. The weights maximize, subject to the restrictions, the multiple correlation between several predictors and a criterion. A numerical example is provided.
A New Coefficient: Application to Biserial Correlation and to Estimation of Selective Efficiency
Authors: Brogden Hubert E.
Published: January 2006

A coefficient of selective efficiency is proposed which can be usefully applied to selection problems involving the evaluation of the validity of (1) dichotomous predictors and (2) continuous predictors at a particular or at successive points of cut. Previously the author has shown that the product-moment correlation can be interpreted as a direct index of selective efficiency if the distribution forms of the criterion and the predictor are similar and the regression of the criterion on the predictor is linear. The coefficient proposed in the present article may be employed to evaluate selective efficiency of a continuous predictor at particular points of cut even when these assumptions are not tenable or are not applicable. It also is demonstrated that the proposed coefficient of selective efficiency may—with somewhat simpler and more generally applicable assumptions than those required in deriving the conventional formula—be employed as a substitute for the biserial correlation coefficient.
Multivariate Information Transmission
Authors: McGill William J.
Published: January 2006

A multivariate analysis based on transmitted information is presented. It is shown that sample transmitted information provides a simple method for measuring and testing association in multi-dimensional contingency tables. Relations with analysis of variance are pointed out, and statistical tests are described.
A Note on the Calculation of Weights for Maximum Battery Reliability
Authors: Green Bert F.
Published: January 2006

Weights may be determined for combining tests so that the composite has maximum reliability, but the calculation of these weights by means of the original equations is cumbersome. It is shown that the desired weighted composite is the first principal axis of a matrix closely related to the intercorrelation matrix. Thus, simple and straightforward procedures are available for calculating the weights.
Osgood and Suci's Measure of Pattern Similarity and Q-Technique Factor Analysis
Authors: Sakoda James M.
Published: January 2006

The purpose of this article is to show that a relationship can be established between Osgood and Suci's D based on raw scores and scores obtained from factor analysis data without equalizing the means and variances of each individual's set of scores.
Matrix Representation of Models for the Analysis of Variance and Covariance
Authors: Rulon Phillip Justin
Published: January 2006

Beginning students of analysis of variance frequently find that the explanations concerning numbers of degrees of freedom are rather more mystical than explanatory, and that the dependencies and independencies among parameters and linear restraints are not systematically covered or explicitly presented. It is the purpose of this paper to set forth the simple matrix representation of these models in a way which has been found useful for teaching purposes, and may be found of some value in the setting up of mathematical models for experimental designs calling for the analysis of variance or the analysis of covariance.

The system I shall portray is a more or less natural outgrowth of suggestions made by Dr. R. C. Bose, with whom I have discussed some of the features very slightly. I am also indebted to Professor Frederick Mosteller for assistance with the mechanics of some of the models. Any deficiencies which the system may have are not to be laid to the doors of these gentlemen, however, as they have not had any opportunity to go over the material at any length.
Regression Tests for Several Samples
Authors: Gulliksen Harold , Wilks S. S.
Published: January 2006

In many situations it is desirable or necessary to administer a set of tests to several different groups, and to ask if the results obtained in the different groups may be regarded as being essentially the same in some sense. In the case of two variables (one dependent and one independent) one may, for instance, ask if the errors of estimate and the regression lines may be regarded as being the same for the populations from which the different groups are drawn. For this case, the present article considers tests for three hypotheses regarding the populations from which the different groups are drawn: (a) HA, the hypothesis that all standard errors of estimate are equal; (b) HB, the hypothesis that all regression lines are parallel, (assuming HA); and (c) HC, the hypothesis that the regression lines are identical, (assuming HB). Test criteria for these three hypotheses and their sampling theory for large samples are presented. The results are extended to the case of several independent variables. An illustrative problem is presented for two groups, two independent and one dependent variable.
The Expected Variance of the Sampling Errors for a Set of Item-Criterion Correlations
Authors: Brogden Hubert E.
Published: January 2006

An expression for the expected variance of the sampling errors for the validities of a set of correlated items that is computationally feasible when the number of items is large is developed. Since the item difficulties are assumed to be constant, the estimate must be applied to pools or sub-pools of items reasonably homogeneous with respect to difficulty.
A Stochastic Model for Rote Serial Learning
Authors: Atkinson Richard C.
Published: January 2006

A model for the acquisition of responses in an anticipatory rote serial learning situation is presented. The model is developed in detail for the case of a long intertrial interval and employed to fit data where the list length is varied from 8 to 18 words. Application of the model to the case of a short intertrial interval is considered; some predictions are derived and checked against experimental data.
The Role of Correlation in Analysis of Variance
Authors: Coombs Clyde H.
Published: January 2006

A test of the significance of a row or column agent in an analysis of variance may be expressed in the form of correlation between the agent and the variate. A test of the significance of interaction variance may be expressed in the form of correlation between the agents. These expressions are principally of theoretical interest in that the degree of significance in an F test or the value of a correlation coefficient may be controlled at will, or inadvertently, within certain limits.
A Note on the Computation of a Table of Intercorrelations
Authors: Tucker Ledyard R
Published: January 2006

Outlined is the method used at present by the Educational Testing Service for computing intercorrelations from basic summations. This procedure is adapted to the use of high speed calculators in performing the calculations, and much of its value lies in the complete system of checks that is a part of the method. Besides the correlations that are the object of the procedure, covariances, means, standard deviations, and the number of cases are also recorded on the completed form to be available for further statistical steps.
A Worksheet for Tetrachoric r and Standard Error of Tetrachoric r using Hayes Diagrams and Tables
Authors: Goheen Howard W. , Kavruck Samuel
Published: January 2006

A worksheet simplifying the calculation of tetrachoric correlation coefficients and their standard errors is presented for use with Hayes' percentage difference method.
The Concept of Parsimony in Factor Analysis
Authors: Ferguson George A.
Published: January 2006

The concept of parsimony in factor analysis is discussed. Arguments are advanced to show that this concept bears an analogic relationship to entropy in statistical mechanics and information in communication theory. A formal explication of the term parsimony is proposed which suggests approaches to the final resolution of the rotational problem. This paper provides the rationale underlying Carroll's (2) analytical solution for approximating simple structure, and the solutions of Saunders (7) and Neuhaus and Wrigley (5).
A Factor-Analytic Study of Creative-Thinking Abilities
Authors: Wilson Robert C. , Guilford J. P. , Christensen Paul R. , Lewis Donald J.
Published: January 2006

Fifty-three tests designed to measure aspects of creative thinking were administered to 410 air cadets and student officers. The scores were intercorrelated and 16 factors were extracted. Orthogonal rotations resulted in 14 identifiable factors, a doublet, and a residual. Nine previously identified factors were: verbal comprehension, numerical facility, perceptual speed, visualization, general reasoning, word fluency, associational fluency, ideational fluency, and a factor combining Thurstone's closure I and II. Five new factors were identified as originality, redefinition, adaptive flexibility, spontaneous flexibility, and sensitivity to problems.
Analysis of Variance for Correlated Observations
Authors: Collier Raymond O.
Published: January 2006

Two different linear models are presented for the four-dimensional classification system in which correlations exist between certain pairs of observations. Except for the assumption of correlated observations, classical assumptions associated with classification systems are made. The models considered are modifications of those which underlie the split-plot design and the split-split-plot design. In the first model the correlations between observations of the levels of one dimension are all set equal to ρ. In the second model the observations of the levels of one dimension are assumed correlated to degree ρ1, whereas the observations of a second dimension are correlated to degree ρ2. Analyses for the two models and tests of hypotheses for various parameters are indicated.
The Kuder-Richardson formula (21) as a Split-Half Coefficient, and Some Remarks on its Basic Assumption
Authors: Lyerly Samuel B.
Published: January 2006

Case IV of the Kuder-Richardson series, their formula (21), is derived as a generalized split-half Spearman-Brown coefficient. The basic assumption employed is shown to be sufficient to justify the various assumptions used in derivations by other authors. Some of the implications of this assumption are discussed.
The Average Spearman Rank Criterion Correlation when Ties are Present
Authors: Cureton Edward E.
Published: January 2006

This note presents the average Spearman rank correlation between m independent rankings and an untied criterion ranking, corrected for ties in any or all of the independent rankings.
A Simplified Method for Approximating Multiple Regression Coefficients
Authors: Gengerelli J. A.
Published: January 2006

A method of exhaustion has been described for calculating regression coefficients. This method dispenses with the solution of simultaneous equations but utilizes a process of successive extraction in obtaining β's, where each successive β is maximized. This procedure permits the worker to discard as he goes along those weights which are deemed unsatisfactory for purposes of prediction. The β coefficients and the R in a problem involving a criterion and six independent variables were calculated in sixty minutes. The R's obtained by this method are smaller than those yielded by the Doolittle technique, but in problems which have been considered this discrepancy has not exceeded .05.
Note on the “Correction for Continuity” in Testing the Significance of the Difference between Correlated Proportions
Authors: Edwards Allen L.
Published: January 2006

Methods of correcting for continuity in tests of significance of the difference between correlated proportions are presented. These corrections should increase the range of usefulness of the formulas developed by McNemar (1).
Image Theory for the Structure of Quantitative Variates
Authors: Guttman Louis
Published: January 2006

A universe of infinitely many quantitative variables is considered, from which a sample of n variables is arbitrarily selected. Only linear least-squares regressions are considered, based on an infinitely large population of individuals or respondents. In the sample of variables, the predicted value of a variable x from the remaining n − 1 variables is called the partial image of x, and the error of prediction is called the partial anti-image of x. The predicted value of x from the entire universe, or the limit of its partial images as n → ∞, is called the total image of x, and the corresponding error is called the total anti-image. Images and anti-images can be used to explain “why” any two variables xj and xk are correlated with each other, or to reveal the structure of the intercorrelations of the sample and of the universe. It is demonstrated that image theory is related to common-factor theory but has greater generality than common-factor theory, being able to deal with structures other than those describable in a Spearman-Thurstone factor space. A universal computing procedure is suggested, based upon the inverse of the correlation matrix.
A Factorial Study of Number Ability
Authors: Coombs Clyde H.
Published: January 2006

In order to investigate certain hypotheses concerning the nature of number ability, and, secondarily, the nature of perceptual speed, a battery of thirty-four tests was given to 223 Chicago high school seniors and the data were factored by the centroid method. Seven primary factors were identifiable upon rotation. Several deductions are made relative to the interpretation of the factors and relative to the consistency of the data with the hypotheses which were to be tested.
A Note on the Discovery of a g Factor by Means of Thurstone's Centroid Method of Analysis
Authors: Guilford J. P.
Published: January 2006

A fictitious factor matrix including 16 tests and 3 factors, one of which was a g factor, was prescribed. From it two typical factor problems, including errors of sampling, were derived. Students in training, without awareness of the factor patterns, arrived at essentially correct solutions by the use of Thurstone's centroid method with rotation of axes. Errors in the calculated factor matrix were very close in size to the sampling errors in the correlation coefficients. It is concluded that a g factor need not escape detection by Thurstone's procedures if the criteria of complete simple structure are not demanded.
The Use of Psychological Techniques in Measuring and Critically Analyzing Navigators' Flight Performance
Authors: Carter Launor F. , Dudek Frank J.
Published: January 2006

Under controlled flight conditions, the distance between a navigator's report of position and his actual position is a criterion of success in dead reckoning navigation. Students' logs were evaluated for five separate missions by comparing the students' entries with standards determined by experts. The reliability of this technique is indicated by the fact that mission to mission intercorrelations of error scores were low, while the intercorrelations between legs of the same mission were moderately high. The intercorrelations between the error scores for the different navigation variables were computed and analyzed by using both factor analysis and multiple regression techniques. Both analyses indicated that a major portion of all dead reckoning error could be attributed to errors made in determining magnetic deviation. As a result of these analyses, recommendations were made for changing the instruction in dead reckoning and alterations in the equipment used were suggested.
Analysis in Terms of Frequencies of Differences
Authors: Voss Harold A.
Published: January 2006

A technique of analysis utilizing frequencies of differences is described and applied to a hypothetical experiment involving two methods of instruction. A nomograph is provided for computing the chi-square values applicable to the method.
An Index of Item Validity Providing a Correction for Chance Success
Authors: Johnson A. P.
Published: January 2006

The KG Index described below is proposed for evaluation as one approach to the problem of providing an index giving comparable values for items (1) of equal discriminative power at all levels of difficulty and (2) of different numbers of alternative responses.
An Approach to the Problem of Differential Prediction
Authors: Brogden Hubert E.
Published: January 2006

A procedure for maximizing selective efficiency is developed for application to situations in which it is desired to select from a single group of applicants for several possible assignments. The problem of comparable units for the several criteria whose values must be compared to each other for differential assignment purposes is discussed. It is demonstrated that, assuming linear regressions, maximal selection is obtained if individuals in any given assignment are differentiated from those rejected according to critical rejection scores on the multiple weighted sum of the predictors and from another possible assignment by critical difference scores which are merely the differences between the two critical rejection scores. Since the relationships just indicated give no way of determining the magnitude of the critical scores required to select the required number of persons for each assignment, a successive approximation procedure for accomplishing this purpose has been devised and a computational example is worked out.
Note on a Reanalysis of Davis' Reading Tests
Authors: Thurstone L. L.
Published: January 2006

Correlation data on nine reading tests originally analyzed by Frederick B. Davis by the principal axes method are reanalyzed by Spearman's uni-dimensional method. It is concluded that a single common factor (reading ability) accounts for the correlations among the tests with residuals remarkably small in view of the fact that the tests were designed to test nine supposedly different skills. Three of the tests showed additional specific variance not attributable to the common factor.
Excitation of a Chain of Neurones
Authors: Householder A. S.
Published: January 2006

When the first of a uniform chain of neurones is excited with a stimulus intensity S1, it is found that, according to the nature of the chain, either the excitation is always transmitted with decreasing intensity, or else the intensity for succeeding neurones of the chain approaches a fixed finite value, characteristic of the chain and independent of S1, whenever S1 exceeds a certain “threshold” value.
A Comparison of Factor Analytic Techniques
Authors: Browne Michael W.
Published: January 2006

Statistical properties of several methods for obtaining estimates of factor loadings and procedures for estimating the number of factors are compared by means of random sampling experiments. The effect of increasing the ratio of the number of observed variables to the number of factors, and of increasing sample size, is examined. A description is given of a procedure which makes use of the Bartlett decomposition of a Wishart matrix to generate random correlation matrices.
Alpha-Maximized Factor Analysis (Alphamax): Its Relation to Alpha and Canonical Factor Analysis
Authors: Bentler P. M.
Published: January 2006

An alpha-O coefficient of internal consistency is defined for an observed score composite. Maximizing alpha-O leads to a system of psychometric (vs. statistical) factor analysis in which successive factors describe dimensions of successively less internal-consistency. Factoring stops when alpha-O is zero or less. In contrast to Kaiser-Caffrey's alpha-C analysis, when the factored matrix is rank 1, alpha-O does not reach unity; it can approach unity only as the number of variables reach infinity. The relative usefulness and domains of generalization of alpha-C and alpha-O are compared. Basically, alpha-C analysis is concerned with the representativeness of factors while alpha-O analysis is concerned with the assessibility of factors. Consequently, either system of factoring can and should be summarized by both the alpha-C and alpha-O coefficients. Not surprisingly, alpha-O analysis is computationally analogous to Rao's canonical factor analysis.
The Asymptotic Values of Response Probabilities in the Audley-Jonckheere Learning Model
Authors: Wolter David G. , Earl Robert W.
Published: January 2006

The asymptotic values of response probabilities in the Audley-Jonckheere learning model, as applied to the two-choice learning situation, are derived for (1) the experimenter-controlled events model, (2) the subject-controlled events model, and (3) the experimenter-subject-controlled events model.
More on Least Squares Estimation of the Transition Matrix in a Stationary First-Order Markov Process from Sample Proportions Data
Authors: McGuire Timothy W.
Published: January 2006

Miller suggested ordinary least squares estimation of a constant transition matrix; Madansky proposed a relatively more efficient weighted least squares estimator which corrects for heteroscedasticity. In this paper an efficient generalized least squares estimator is derived which utilizes the entire covariance matrix of the distrubances. This estimator satisfies the condition that each row of the transition matrix must sum to unity. Madansky noted that estimates of the variances could be negative; a method for obtaining consistent non-negative estimates of the variances is suggested in this paper. The technique is applied to the hypothetical sample data used by Miller and Madansky.
Coefficient Alpha and the Reliability of Composite Measurements
Authors: Novick Melvin R. , Lewis Charles
Published: January 2006

Following a general approach due to Guttman, coefficientα is rederived as a lower bound on the reliability of a test. A necessary and sufficient condition under which equality is attained in this inequality and hence that α is equal to the reliability of the test is derived and shown to be closely related to the recent redefinition of the concept of parallel measurements due to Novick. This condition is then also shown to be closely related to the unit rank assumption originally adopted by Kuder and Richardson in the derivation of their formula 20. The assumption later adopted by Jackson and Ferguson and the one adopted by Gulliksen are shown to be related to the necessary and sufficient condition derived here. It is then pointed out that the statement that “coefficient α is equal to the mean of the split-half reliabilities” is true only under the restricted condition assumed by Cronbach in the body of his derivation of this result. Finally some limitations on the uses of any function of α as a measure of internal consistency are noted.
Tests of Hypothesis in a Repeated Measures Design from a Permutation Viewpoint
Authors: Collier Raymond O. , Baker Frank B. , Mandeville Garrett K.
Published: January 2006

Repeated measures designs have been widely employed in psychological experimentation, however, such designs have rarely been analyzed by means of permutation procedures. In the present paper certain aspects of hypothesis tests in a particular repeated measures design (one non-repeated factor (A) and one repeated factor (B) with K subjects per level of A) were investigated by means of permutation rather than sampling processes. The empirical size and power of certain normal theory F-tests obtained under permutation were compared to their nominal normal theory values. Data sets were established in which various combinations of kurtosis of subject means and intra-subject variance heterogeneity existed in order that their effect upon the agreement of these two models could be ascertained. The results indicated that except in cases of high intra-subject variance heterogeneity, the usual F-tests on B and AB exhibited approximately the same size and power characteristics whether based upon a permutation or normal theory sampling basis.
The Analysis of Variance and Pairwise Scaling
Authors: Bechtel Gordon G.
Published: January 2006

Variance analyses are presented for two data layouts—each corresponding to the class of all ordered pairs from a single finite set. The analysis of the dominance layout is in terms of a fixed effects linear model which includes parameters representing the scale values of the elements of the set, response bias, and pairwise interactions. A parallel parametrization is carried out for the composition layout for which corresponding point estimates and hypothesis tests are given. A joint treatment of concurrently observed dominance and composition layouts is suggested and illustrative data are presented.
The Classification of Individuals into Two Criterion Groups on the Basis of a Discontinuous Payoff Function
Authors: Alf Edward F. , Dorfman Donald D.
Published: January 2006

An analytic method is presented for optimally classifying individuals into two subgroups on the basis of a cutting score on a test or test composite. The development assumes the test and criterion scores to be normally distributed, and the correlation surface to be bivariate normal. It is further assumed that individuals belong to the first or second sub-group depending on whether their criterion score is above or below a specified value. The predictor cutting score is determined so as to maximize the expected value of the decision procedure, taking gains and losses associated with correct and incorrect assignments into account.
Tandem Criteria for Analytic Rotation in Factor Analysis
Authors: Comrey Andrew L.
Published: January 2006

Two related orthogonal analytic rotation criteria for factor analysis are proposed. Criterion I is based upon the principle that variables which appear on the same factor should be correlated. Criterion II is based upon the principle that variables which are uncorrelated should not appear on the same factor. The recommended procedure is to rotate first by criterion I, eliminate the minor factors, and then rerotate the remaining major factors by criterion II. An example is presented in which this procedure produced a rotational solution very close to expectations whereas a varimax solution exhibited certain distortions. A computer program is provided.
F Tests for the Absolute Invariance of Dominance and Composition Scales
Authors: Bechtel Gordon G.
Published: January 2006

Significance tests are developed for evaluating the absolute invariance of the dominance and composition scales presented in a previous paper [Bechtel, 1967]. These tests derive from the multivariate normality of the estimated scale values—this multinormality stemming from that of the observations upon which these estimated scale parameters are based. The scales compared by means of the present techniques will typically be constructed under distinct experimental conditions, which may take the concrete form of treatments, occasions, individuals, or groups. Thus the present tests possess a wide range of applicability including various experimental designs in which scale configuration is the dependent variable. Illustrative data are used in statistically comparing the scale structures of two different individuals.
Latent Partition Analysis
Authors: Wiley David E.
Published: January 2006

Latent partition analysis has been formulated to study the relationships between two or more partitions of the same set of items. The major structural hypothesis is that a latent partition underlies the manifest partitions; that is, it is assumed that each item belongs to a latent category and that the manifest categories are derived by dividing and combining the latent categories. We have found that by examining manifest categories it is possible to reconstruct information about the latent partition and about its relation to the manifest partitions.