bluuebunny/crossref_metadata_2025 huggingface dataset:
An Empirical Study of the Normality and Independence of Errors of Measurement in Test Scores
Authors: Lord Frederic M.
Published: January 2006

An empirical study of test scores shows the variance of the errors of measurement to be significantly associated with true score in each of four groups studied; it also shows the distribution of the errors of measurement to be significantly skewed in three of these four groups. The mathematical rationale underlying the statistical treatment is presented. Standard error formulas are given for making the necessary significance tests.
P-Technique Demonstrated in Determining Psychophysiological Source Traits in a Normal Individual
Authors: Cattell R. B. , Cattell A. K. S. , Rhymer R. M.
Published: January 2006

P-technique, a method employing intra-individual correlation, is tried out for the first time. As part of the general design it uses some variables the same as those in a coordinated R-technique study and a second, parallel P-technique study with a clinical case. Definite factors are obtained among the psychological and physiological variables, which can be mutually matched. One is a fatigue factor, but the rest are general personality factors readily identifiable with those obtained in past R-technique researches.
Sampling Fluctuations Resulting from the Sampling of Test Items
Authors: Lord Frederic M.
Published: January 2006

Sampling fluctuations resulting from the sampling of test items rather than of examinees are discussed. It is shown that the Kuder-Richardson reliability coefficients actually are measures of this type of sampling fluctuation. Formulas for certain standard errors are derived; in particular, a simple formula is given for the standard error of measurement of an individual examinee's score. A common misapplication of the Wilks-Votaw criterion for parallel tests is pointed out. It is shown that the Kuder-Richardson formula-21 reliability coefficient should be used instead of the formula-20 coefficient in certain common practical situations.
The Choice of an Error Term in Analysis of Variance Designs
Authors: Binder Arnold
Published: January 2006

This article presents a survey of the assumptions which may be made in variance designs, a description of the mathematical models which reflect these assumptions, and a discussion of the ways in which various experimental conditions affect the choice of an error mean square. Particular emphasis is laid upon the principles, purposes, and dangers of pooling error mean squares in order to raise the power of a test. Specific recommendations are made for the rules of procedure for pooling (under various conditions) which produce tests with optimum power and error characteristics.
A Measure of Interrelationship for Overlapping Groups
Authors: Winer Ben J.
Published: January 2006

A coefficient of interrelationship between overlapping groups that avoids indeterminacies inherent in the construction of fourfold tables for such purposes and, at the same time, is relatively insensitive to the absolute magnitude of marginal totals of fourfold tables, is developed. Under assumptions that are consistent with the objectives of organizational analysis, this coefficient is shown to be equivalent to a product-moment correlation coefficient. The advantages and limitations of this coefficient are pointed out. A numerical example giving computational procedures is presented.
A Factor Analysis of Mental Abilities and Personality Traits
Authors: Denton J. C. , Taylor Calvin W.
Published: January 2006

The relationship between measures of verbal fluency and certain personality traits is examined by factor techniques. From a matrix of eight factor scores derived from mental tests plus five personality scores, six factors were obtained. An oblique solution lends limited support to the hypothesized relationship between the two domains.
A Tabular Method of Obtaining Tetrachoric r with Median-Cut Variables
Authors: Welsh George Schlager
Published: January 2006

A method is presented that enables the immediate determination of tetrachoric r from a table if the proportion in the plus-plus cell for median-cut variables is known.
General Resolution of Correlation Matrices into Components and its Utilization in Multiple and Partial Regression
Authors: Creager John A.
Published: January 2006

The derivation of multiple and partial regression statistics from uniqueness-augmented factor loadings, presented in the literature for orthogonal factor solutions, is generalized to oblique solutions. A mathematical rationale for the general case, without restriction to uncorrelated factors, is presented. Use of the general formulation is illustrated with a two-factor, seven-variable example.
Error of Measurement and the Sensitivity of a Test of Significance
Authors: Sutcliffe J. P.
Published: January 2006

Implications of random error of measurement for the sensitivity of the F test of differences between means are elaborated. By considering the mathematical models appropriate to design situations involving true and fallible measures, it is shown how measurement error decreases the sensitivity of a test of significance. A method of reducing such loss of sensitivity is described and recommended for general practice.
Properties of the Item Score Matrix
Authors: MacLean Angus G.
Published: January 2006

A method of deriving from the item score matrix all the usual statistics describing the performance on a test of a group of examinees is given. Since this matrix usually is not actually written out, but is implicit in a set of punched cards, a method of working from a more compact matrix F is described. A numerical example is presented. Applications and advantages of the method are cited, as compared with that of recording only the examinees' test scores and the item difficulties.
A Retest Method of Studying Partial Knowledge and other Factors Influencing Item Response
Authors: Brownless Vera T. , Keats John A.
Published: January 2006

A method of studying the problem of correction for guessing and other problems associated with behavior in the test situation is described and an illustrative example presented. As far as the writers are aware this method of approach is novel but, at the same time, it covers many of the practical and theoretical points raised by other writers as reviewed in the introduction.
Reliability Formulas for Noncompleted or Speeded Tests
Authors: Guttman Louis
Published: January 2006

New formulas are developed to give lower bounds to the reliability of a test, whether or not all respondents attempt all items. The formulas apply in particular, then, to completed tests, pure speed tests, pure power tests, and any mixture of speed and power. For the case of completed tests, the formulas give the same answer as certain standard ones; for noncompleted tests the formulas give a correct answer where previous standard formulas are inappropriate. The formulas hold both in the sense of retest reliability and of parallel tests.
Two Models of Group Behavior in the Solution of Eureka-Type Problems
Authors: Lorge Irving , Solomon Herbert
Published: January 2006

A study by Shaw (7) some twenty years ago is frequently cited by social scientists to support the generalization that groups are superior to individuals in problem-solving. Shaw suggests that personal interaction within the group is responsible for the superior performance of groups. This article re-examines her data in the light of two models which propose that the difference in quality of solution between group and individual performance is solely a matter of ability. It is shown that Shaw's data may be considered to have been an outcome of behavior postulated by the models. Since Shaw's observations relate to a special population and to special kinds of problems, the proposed models may not be appropriate under differing experimental conditions. In fact, Lorge et al. (4) have indicated that experimental demonstration of the superiority of groups over individuals in problem-solving depends not only on the kind of group but also on the kind of problem to be solved. In addition, the diversity of transfer of training for groups and for individuals is considered.
The Mathematical Theory of Factorial Invariance Under Selection
Authors: Ahmavaara Yrjö
Published: January 2006

It is first demonstrated that Aitken's selection formulas are equivalent to a linear transformation in the factor space. On this basis the Thomson-Ledermann theorem concerning the invariance of the number of common factors under selection, and a theorem concerning the invariance of factor loadings under selection are derived. A mathematical proof of the results of Thurstone, which are concerned with the invariance of simple structure under selection, is given. The paper provides a conclusive answer to the question, considered by Thurstone and Thomson, whether a multivariate selection is always reducible to successive univariate selections.
The Square Root Method and Multiple Group Methods of Factor Analysis
Authors: Harman Harry H.
Published: January 2006

The square root method for the solution of a set of simultaneous linear equations or the reduction of a matrix has been known for some time under a variety of names. Because of its usefulness in statistical work, especially in factor analysis, the square root method is presented in general terms and an example given. Several independently developed “multiple group methods” for factor analysis are compared and synthesized. Their fundamental concepts are set forth and an appropriate system of notation developed. Detailed computational procedures are outlined, and the square root method is emphasized as a computing aid in multiple group analysis.
A Solution for Case III of the Law of Comparative Judgment
Authors: Burros Raymond H. , Gibson W. A.
Published: January 2006

A solution for Case III of the Law of Comparative Judgment, modeled after Thurstone's solution for Case IV but eliminating the restrictive assumption of relatively equal discriminal dispersions, is developed.
A Table for the Rapid Determination of the Tetrachoric Correlation Coefficient
Authors: Davidoff Melvin D. , Goheen Howard W.
Published: January 2006

A table is developed and presented to facilitate the computation of the Pearson Q3 (“cosine method”) estimate of the tetrachoric correlation coefficient. Data are presented concerning the accuracy of Q3 as an estimate of the tetrachoric correlation coefficient, and it is compared with the results obtainable from the Chesire, Saffir, and Thurstone tables for the same four-fold frequency tables.
A Method for Factoring Large Numbers of Items
Authors: Wherry Robert J. , Winer Ben J.
Published: January 2006

The computation of intercorrelation matrices involving large numbers of variables and the subsequent factoring of these matrices present a formidable task. A method for estimating factor loadings without computing the intercorrelation matrix is developed. The estimation procedure is derived from a theoretical model which is shown to be a special case of the multiple-group centroid method of factoring. Empirical checks have indicated that the model, even though it makes some stringent assumptions, can be applied to a variety of variables found in psychological factoring problems. It has been found to be particularly useful in factoring test items.
Reliability for the Law of Comparative Judgment
Authors: Gulliksen Harold , Tukey John W.
Published: January 2006

A variance-components analysis is presented for paired comparisons in terms of three components: s, the scale value of the stimuli; d, a deviation from the linear model specified by the law of comparative judgment; and b, a binomial error component. Estimates are given for each of the three variances, σs2, σd2, and σb2. Several coefficients, analogous to reliability coefficients, based on these three variances are indicated. The techniques are illustrated in a replicated comparison of handwriting specimens.
An Inter-Battery Method of Factor Analysis
Authors: Tucker Ledyard R
Published: January 2006

The inter-battery method of factor analysis was devised to provide information relevant to the stability of factors over different selections of tests. Two batteries of tests, postulated to depend on the same common factors, but not parallel tests, are given to one sample of individuals. Factors are determined from the correlation of the tests in one battery with the tests in the other battery. These factors are only those that are common to the two batteries. No communality estimates are required. A statistical test is provided for judging the minimum number of factors involved. Rotation of axes is carried out independently for the two batteries. A final step provides the correlation between factors determined by scores on the tests in the two batteries. The correlations between corresponding factors are taken as factor reliability coefficients.
Comparatal Dispersion, a Measure of Accuracy of Judgment
Authors: Gulliksen Harold
Published: January 2006

It is suggested that the ambiguity of a set of paired comparison judgments may be measured by the quantity √σi2 + σj2 − 2rijσiσi, This quantity is termed the comparatal dispersion. A simultaneous solution for scale values and ratios of comparatal dispersions has been presented and applied to some data on food preferences.
A Generalized Simplex for Factor Analysis
Authors: Guttman Louis
Published: January 2006

By a simplex is meant a set of statistical variables whose interrleations reveal a simple order pattern. For the case of quantitative variables, an order model was analyzed previously which allowed only for positive correlations among the variables and a limited type of gradient among the correlation coefficients. The present paper analyzes a more general model and shows how it is more appropriate to empirical data. Among the novel features emerging from the analysis are: (a) the “factoring” implied of the correlation matrix; (b) the use of a non-Euclidean distance function; and (c) the possible underlying psychological theories.
Equating Test Scores—A Maximum Likelihood Solution
Authors: Lord Frederic M.
Published: January 2006

Certain problems of equating are discussed. The maximum likelihood solution is presented for the following special equating problem: Two tests, U and V, are to be equated, making use of a third “anchor” test, W. The examinees are divided into two random halves. Tests U and W are administered to one half; tests V and W are administered to the other half. It is assumed that any practice effect or other effect, exerted by U and V on W, is the same for U and for V.
Least Squares Estimates and Optimal Classification
Authors: Brogden Hubert E.
Published: January 2006

A simple algebraic development is given showing that criterion estimates derived by usual multiple regression procedures are optimal for personnel classification. It is also shown that, for any assignment of men to jobs, the sum of the multiple regression criterion estimates will equal the sum of the actual criterion scores.
An Improved Method for Tetrachoric r
Authors: Jenkins W. L.
Published: January 2006

From the ratio of the cross-products of a fourfold table, with the application of two tabled corrections, tetrachoric r's can be estimated with a mean discrepancy of less than .005 even when splits vary greatly from the medians. The necessary calculations can be handled by slide rule and the correction tables used without interpolation.
A Least-Squares Solution for Case IV of the Law of Comparative Judgment
Authors: Gibson W. A.
Published: January 2006

Case IV of Thurstone's Law of Comparative Judgment is displayed as a system of homogeneous linear equations for which a least-squares solution is presented, using various conditional equations which fix the origin and the unit of measurement. The computational load is, however, quite heavy.
A New Status Index Derived from Sociometric Analysis
Authors: Katz Leo
Published: January 2006

For the purpose of evaluating status in a manner free from the deficiencies of popularity contest procedures, this paper presents a new method of computation which takes into account who chooses as well as how many choose. It is necessary to introduce, in this connection, the concept of attenuation in influence transmitted through intermediaries.
An Application of Confidence Intervals and of Maximum Likelihood to the Estimation of an Examinee's Ability
Authors: Lord Frederic M.
Published: January 2006

A mathematical definition of the theoretical relation between the examinee's actual responses to the test items and his “true ability” is selected. A maximum-likelihood solution is obtained for estimating the examinee's “true ability” from his responses to the items. The standard error of the maximum-likelihood estimate is obtained, its relation to the discriminating power of the test is pointed out, and some generalizations are drawn as to the optimum level of item difficulty. The Neyman-Pearson power function is applied to determine which of two psychological tests is the most powerful for the selection of “successful” examinees.
Characteristics of Two Measures of Profile Similarity
Authors: Harris Chester W.
Published: January 2006

Analogs of Pearson's coefficient of racial likeness and of Mahalanobis' distance measure have been proposed as descriptive statistics for comparing two individuals. This paper shows that two different definitions of “uncorrelated” variables—one associated with an inverse transformation and the other with a principal-axis transformation—give rise to these two descriptive statistics. The effects of putting the data into certain forms, such as equalizing the variances of the variables or equalizing the means of the persons, prior to using either of the two transformations, are discussed.
The Problem of Classification of Personnel
Authors: Thorndike Robert L.
Published: January 2006

The personnel classification problem arises in its pure form when all job applicants must be used, being divided among a number of job categories. The use of tests for classification involves problems of two types: (1) problems concerning the design, choice, and weighting of tests into a battery, and (2) problems of establishing the optimum administrative procedure of using test results for assignment. A consideration of the first problem emphasizes the desirability of using simple, factorially pure tests which may be expected to have a wide range of validities for different job categories. In the use of test results for assignment, an initial problem is that of expressing predictions of success in different jobs in comparable score units. These units should take account of predictor validity and of job importance. Procedures are described for handling assignment either in terms of daily quotas or in terms of a stable predicted yield.
The Reliability of Speeded Tests
Authors: Gulliksen Harold
Published: January 2006

Some methods are presented for estimating the reliability of a partially speeded test without the use of a parallel form. The effect of these formulas on some test data is illustrated. Whenever an odd-even reliability is computed it is probably desirable to use one of the formulas noted in Section 2 of this paper in addition to the usual Spearman-Brown correction. Since the formulas given here involve the mean and the standard deviation of the “number unattempted score,” a method is given in Section 4 for computing this mean and standard deviation from item analysis data. If the item analysis data are available, this method will save considerable time as compared with rescoring answer sheets.
An Experimental Study of the Effects on Item-Analysis Data of Changing Item Placement and Test Time Limit
Authors: Mollenkopf William G.
Published: January 2006

Item-analysis data are usually obtained from a single test administration, with a given item sequence and time limit. Questions can be raised as to the effects upon item data resulting from changes in item-position and test-timing. In this study, two forms of a verbal test and two forms of a mathematics test were used. In each case, both forms of each test contained the same items, but items coming early in one form were placed late in the other. Each of these forms was administered once with a short time limit and once with generous timing to comparable groups of high school students. The relationships of various speed and power scores were determined, and the changes which occurred during the added time were studied. Values of the item indices p (proportion right), Δ† (another difficulty index), and the item-test biserial correlation coefficient were obtained for both the speed and the power conditions and were systematically compared. The proportion right of those attempting the item, the Δ index, and the biserial r were all found to have undesirable characteristics for items appearing late in a speeded test.
A Proposed Method for Absolute Ratio Scaling
Authors: Comrey Andrew L.
Published: January 2006

A method of ratio scaling is described for treating comparative judgments of paired stimuli. A method of comparative judgment developed by Metfessel is employed. Formulas for scale values and the solution of a sample problem are provided. The method is designed to provide internal-consistency checks on the scale values. Experimental interpretations of equal-unit and ratio properties of measurement scales are inherent in the procedure.
On the Applications of the Method of Absolute Scaling
Authors: Fan Chung-Teh
Published: January 2006

Empirical and fictitious examples are described for investigating the applications of the absolute scaling method for item scaling and score scaling. A discrepancy between the correct values and the values estimated through the absolute scaling method is demonstrated. It is concluded that when the groups are different the assumption of an identity between test score conversion and item difficulty conversion is not met.
A Method of Score Conversion Through Item Statistics
Authors: Swineford Frances , Fan Chung-Teh
Published: January 2006

A method is presented for converting the scores on one form of a test to those on another form of the same test. The method is particularly applicable to the case where each form has been administered to a different group and the only link between the two forms is a subset of items common to both. The proposed method, called the item method of conversion, has been applied to several tests for which other methods of conversion are available for comparison. The necessary data are limited to tests for which the total score is the criterion for item analyses. The method gives highly satisfactory results for all the tests to which it has been applied, particularly when the two groups are rather different, in which case the delta method (a different item method) is inappropriate.
A Fast Approximate Algebraic Factor Rotation Method to Maximize Agreement Between Loadings and Predetermined Weights
Authors: Rodgers David A.
Published: January 2006

A method of rotating a set of orthogonal axes into a reference frame on which loadings are as nearly proportional to a predetermined set of weights as possible is presented. The method, an approximate algebraic solution, often requires some additional graphical refinement but eliminates most of the rotations involved in usual graphical solutions. Its primary value is speed and ease of calculation, involving only one matrix multiplication and solution of a simple formula to determine the rotation cosines.
The Stability of the Factorial Pattern of Aircrew Classification Tests in Four Analyses
Authors: Zachert Virginia , Friedman Gabriel
Published: January 2006

This study consists of four factor analyses of the Army Air Forces Aircrew Classification Batteries. The first was an analysis of the 1945 wartime battery, while the other three were analyses of the 1947 postwar battery, consisting of essentially the same variables, but using different samples. Eleven factors were found which had been identified and reported in previous analyses. An additional factor, possibly an artifact, was identified as an age-education doublet. The only factor which differed significantly in the analyses was pilot or flying interest. These factor analyses show that the factorial content of the tests remains quite similar in both wartime and postwar populations.
A Further Note on “Finite Markov Processes in Psychology”
Authors: Goodman Leo A.
Published: January 2006

In his interesting article “Finite Markov Processes in Psychology,” G. A. Miller derived a “least-squares estimate” for a matrix of transitional probabilities (I). However, the mathematical proof seems to be unclear. Since this proof is considered invalid (2), we shall present a somewhat clearer version of the proof of this result. We shall also examine the general problem in some detail.

In the proof we shall assume that the reader is familiar with matrix notation, which enables a considerably shorter presentation. We shall follow the matrix conventions and the terminology adopted by Miller (I).
A Binomial Method for Analyzing Psychological Functions
Authors: Gengerelli J. A.
Published: January 2006

On the basis of the assumption that distributions of scores on psychological functions are generated by a finite number of equally probable factors, a method is presented which yields the number of factors and their probability p. The statistics β1 and β2 are used for this purpose. An experiment utilizing a code-transcription test is described in which the method was employed to analyze performance at several stages in the learning process. n was found to be 10 for the first 2 minutes of practice and 19 for the second 2 minutes. For the third, fourth, and fifth 2-minute periods, no value could be obtained owing to the pronounced leptokurtosis of the distributions. The first 3 periods of practice, when lumped together, gave an n of 33. It is suggested that the method offers a means of comparing the variability and “complexity” of otherwise non-comparable psychological functions. The use of the method as an instrument of investigation in the field of factor analysis is described.
An Abac for the Sample Range
Authors: Schützenberger Marco P.
Published: January 2006

An abac is computed which gives the probability that at least q% of the whole population will be included in the range of a random sample of given size. Applications are suggested for testing homogeneity of a sampling from a given population.
Markov Processes in Learning Theory
Authors: Kemeny John G. , Snell J. Laurie
Published: January 2006

Consideration is given mathematical problems arising in two learning theories—one developed by Bush and Mosteller, the other developed by Estes. The theory of Bush and Mosteller leads to a class of Markov processes which have been studied in considerable detail (see [1] and [7]). The Estes model can be treated as a Markov chain, i.e., a Markov process with a finite number of states. For an important class of special cases, it is shown that the Bush-Mosteller model is, in a sense, a limiting form of the Estes model. The limiting probability distributions are derived for the cases treated in both models.
Amounts of Fixation and Discovery in Maze Learning Behavior
Authors: Simon Herbert A.
Published: January 2006

The proposed quantitative description of maze learning rests on the assumption that two independent processes are involved: (i) a discovery process based on trial-and-error search for the correct response, (ii) a fixation process equivalent to that observed in serial learning. The model leads to predictions that are consistent with the available experimental data. In particular, the number of trials required for fixation is independent of the number of alternatives at each choice point (and hence independent of the number of bits of information contained in each correct response).
A Measure of Coherence for Human Information Filters
Authors: Wilcox Richard H.
Published: January 2006

When an information processing system is faced with an excess of input information the task of selecting the items which are to get immediate processing is frequently assigned to a human being. A quantitative measure of the extent to which a man avoids random activity during such filtering operations is derived in terms of two parameters (normalized overload and correct proportion of selections) which are determined from experimentally available quantities. This coherence measure may be used for studies of random behavior, comparison of rules for selecting items, and perhaps prediction of human performance at filtering tasks.
A Measure of the Gambling Response-Set in Objective Tests
Authors: Ziller Robert C.
Published: January 2006

A formula is developed for measuring the gambling response-set or utility for risk in objective tests in which the testees are apprised of the application of a correction for guessing. Some implications of this measure for test theory and construction are discussed briefly.
The Relation between Information and Variance Analyses
Authors: Garner W. R. , McGill William J.
Published: January 2006

Analysis of variance and uncertainty analysis are analogous techniques for partitioning variability. In both analyses negative interaction terms due to negative covariance terms that appear when non-orthogonal predictor variables are allowed may occur. Uncertainties can be estimated directly from variances if the form of distribution is assumed. The decision as to which of the techniques to use depends partly on the properties of the criterion variable. Only uncertainty analysis may be used with a non-metric criterion. Since uncertainties are dimensionless (using no metric), however, uncertainty analysis has a generality which may make it useful even when variances can be computed.
Rank-Biserial Correlation
Authors: Cureton Edward E.
Published: January 2006

A formula is developed for the correlation between a ranking (possibly including ties) and a dichotomy, with limits which are always ±1. This formula is shown to be equivalent both to Kendall's τ and Spearman's ρ.
A Note on the Estimation of Nonspurious Correlations
Authors: Angoff William H.
Published: January 2006

A method is provided for estimating the nonspurious correlation of a part of a test with the total test. Two cases are considered: one in which the actual subtest is parallel to the total test, the other in which the actual subtest is not parallel to the total test.
A Note on the Estimation of Test Reliability by the Kuder-Richardson Formula (20)
Authors: Tucker Ledyard R
Published: January 2006

The Kuder-Richardson formula (20) is rewritten to be identical with the simplest formula, (21), except for the addition of a term involving the standard deviation, σ
p
, of the item p's. If σ
p
can be estimated, a rapid and superior estimate of test reliability is possible in contrast to the simpler formula (21) used when the number of items and mean and standard deviation of test scores are known.
Variation of the Standard Error of Measurement
Authors: Mollenkopf William G.
Published: January 2006

As usually interpreted, the standard error of measurement is assumed to be constant throughout the test-score range. In this investigation the standard error of measurement was assumed to be not higher than a second-degree function of the test score. By conceiving a test score to be made up of the scores on two parallel tests, an equation was derived for predicting the standard error of measurement from the test score. In the derivation the corresponding first four moments of the score distributions for the parallel tests were assumed to be identical, and certain errors of estimate involved in predicting the second test score from the first were assumed to be uncorrelated with powers of the score on the first test. An empirical verification was carried out, using nine synthetic tests and a 1000-case sample, and showed good agreement between predicted and observed results. The findings indicated that the standard error of measurement was constant only for a symmetrical, mesokurtic distribution of scores.
A Rationale for Minimizing Distortion in Personality Questionnaire Keys
Authors: Brogden Hubert E.
Published: January 2006

A rationale and a procedure for constructing questionnaire keys so as to minimize the effect of distortion or faking by the respondents is developed. This rationale is based on the supposition that suppressor items can be identified to reduce distortion in, and thus add to, the validity of questionnaire keys. The procedure is designed primarily for application to the construction of forced choice items.

The results of an empirical test of the efficicacy of the forced choice pairing procedure developed as a consequence of this rationale are presented. A key based on forced choice pairs developed by this procedure gave a validity of .33; a second key based on forced choice pairs developed by more conventional procedures gave a validity of .23.
Some Necessary Conditions for Common-Factor Analysis
Authors: Guttman Louis
Published: January 2006

Let R be any correlation matrix of order n, with unity as each main diagonal element. Common-factor analysis, in the Spearman-Thurstone sense, seeks a diagonal matrix U2 such that G = R − U2 is Gramian and of minimum rank r. Let s1 be the number of latent roots of R which are greater than or equal to unity. Then it is proved here that r ≥ s1. Two further lower bounds to r are also established that are better than s1. Simple computing procedures are shown for all three lower bounds that avoid any calculations of latent roots. It is proved further that there are many cases where the rank of all diagonal-free submatrices in R is small, but the minimum rank r for a Gramian G is nevertheless very large compared with n. Heuristic criteria are given for testing the hypothesis that a finite r exists for the infinite universe of content from which the sample of n observed variables is selected; in many cases, the Spearman-Thurstone type of multiple common-factor structure cannot hold.
Note on “A Table for the Rapid Determination of the Tetrachoric Correlation Coefficient”
Authors: Davidoff Melvin D.
Published: January 2006

This note revises the figures in the original article concerning the accuracy of the tetrachoric estimates involved. These estimates are better than previously noted and are very satisfactory. Some minor known errors in the original article are also noted.
The Calculation of Sums of Squares for Interactions in the Analysis of Variance
Authors: Edwards Allen L. , Horst Paul
Published: January 2006

A method is described for the calculation of the sum of squares for a second-order interaction. It is then shown that the method is general and can be used for the calculation of the sum of squares for any higher-order interaction.
A Factorial Study of the Multiphasic, Strong, Kuder, and Bell Inventories using a Population of Adult Males
Authors: Cottle Wm. C.
Published: January 2006

In a centroid factor analysis of the Multiphasic, Strong, Kuder, and Bell inventories using a population of 400 adult males, eight common factors dealing with aspects of personality as measured by these instruments were isolated. Seven of the factors were meaningful and one was a residual. This study indicates little overlap between the two personality and the two interest inventories. It would appear that factors found in these instruments measuring aspects of personality are dichotomous in nature and are not common to the two types of instruments included in this study. That is, two of the factors were common to the two personality inventories, and five of the factors were common to the two interest inventories.
A Note on the Measurement of Reversals of Perspective
Authors: Bruner J. S. , Postman L. , Mosteller F.
Published: January 2006

The contradictory findings in the classical literature on the rate of reversal of perspective illusions stem, at least partly, from a failure to isolate three major sources of variance: set, subjects, and sequence. This paper provides a model for the statistical isolation of these variables. It consists of the square-root transformation of reversible data which appear to constitute a Poisson distribution. Such a transformation permits the full utilization of the analysis of variance.
Two Kinds of Factor Analysis?
Authors: Hartley Raymond E.
Published: January 2006

In descriptive factor analysis, the factor matrix is merely an alternate mode of expression of the meaning expressed by the correlation matrix. In inferential factor analysis, the factor matrix expresses material inferred from the correlation matrix but not contained in the correlation matrix. A major problem has been whether or not the latter type is possible. Granit's color cone study is interpreted as a factor study in the hope of showing that inferential factor analysis actually exists. It is argued that proof of these and other points in factor theory can be accomplished only by logical analysis.
A Simple Proof of a Personnel Classification Theorem
Authors: Brogden Hubert E.
Published: January 2006

A simple algebraic proof of a theorem defining the optimal solution to the personnel classification problem is given. If a set of constants, one for each job, are known, the theorem indicates that each individual should be classified by adding the constants to the estimates of the individual's productivity in the several jobs and selecting the job for which the resulting sum is highest.
Note on Construction of an Item Analysis Table for the High-Low-27-Per-Cent Group Method
Authors: Fan C. T.
Published: January 2006

This paper describes the construction of a new item analysis table for the high-low-27-per-cent group method. The table provides a ready means of translating the observed proportions of success in the two extreme groups (pH, pL) into measures of item difficulty and item discrimination (p, Δ, and r). The tabled values of both the difficulty index, p, and the discrimination index, r, have been derived from Karl Pearson's tables of the normal bivariate surface.
Changes in Factor Structure of a Complex Psychomotor Test as a Function of Practice
Authors: Fleishman Edwin A. , Hempel Walter E.
Published: January 2006

Scores obtained at eight different stages of practice on the Complex Coordination Test together with scores on 18 reference tests were subjected to a Thurstone Centroid Factor Analysis. Nine meaningful factors were identified in the experimental battery. The results indicated considerable, but systematic, changes in the factor structure of the Complex Coordination Test as practice on the task was continued. The test became less complex (factorially) as practice was continued. Moreover, there was a change in the nature of the factors contributing variance at early and later stages of practice. Implications of the findings are related to certain problems of learning theory, psychomotor test development, and criterion analysis.
A Note on Item Analysis with an Electronic Computer
Authors: Ziegler James
Published: January 2006

An electronic computer with large capacity memory, and employing binary numbers, is ideally suited for large-scale item analysis. The adaptation and use of one computer, SWAC, is described.
A Factor Analysis of the Stanford-Binet at Four Age Levels
Authors: Jones Lyle V.
Published: January 2006

Standardization scores on the 1937 Revision of the Stanford-Binet are analyzed by the Thurstone centroid factor technique. Correlation matrices at age levels seven, nine, eleven, and thirteen, each based on two hundred subjects, are analyzed. The factors after rotation are interpreted in terms of the items exhibiting high factor saturations. In contrast to the findings of McNemar (1942) no evidence for a general factor in the Stanford-Binet battery is found in the present study. Rather, I.Q. variance can be explained in terms of psychologically meaningful group factors at the various age levels. The results indicate a need for cautious interpretation and use of single score indices of intelligence such as the Stanford-Binet I.Q.
Bias and Error in Multiple-Choice Tests
Authors: Hamilton C. Horace
Published: January 2006

A formula for estimating real scores on a multiple-choice test from a knowledge of raw scores is derived. This formula does not involve the assumption of a binomial distribution of real scores as does the Calandra formula. Other important formulas derived show: the variance of real scores in terms of the variance of raw scores and the correlation between real scores and raw scores. If the variance of real scores (or of raw scores also) is binomial, the regression of real scores on raw scores is linear; but, otherwise the regression is curvilinear. Yet the linear estimating formula is a close approximation to the curvilinear relationship. Factors affecting the regression of real scores on raw scores and the correlation coefficient are: (1) the number of choices per question; (2) the number of questions answered; (3) the ratio of the average group raw score to the variance of raw scores.
New Analysis of Variance Formulas for Treating Data from Mutually Paired Subjects
Authors: Lev Joseph , Kinder Elaine F.
Published: January 2006

The experimental design considered in this paper is one in which each of a group of several subjects is observed in the presence of each of the other subjects of the group, the entire set of possible pairings being repeated or replicated on several occasions. Analysis of variance formulas are described for this somewhat unusual design. Both the model of constants and mixed model are considered. Reliability formulas growing out of the analysis of variance calculations are developed.
Estimation of Error Variances of Test Scores
Authors: Keats John A.
Published: January 2006

The representation of test scores as n-dimensional points leads directly to an estimate of error variance at a particular score level in the case of equivalent items. Approximations are suggested for the case of non-equivalent items. These approximations are compared, with satisfactory results, with empirical data prepared by Dr. Mollenkopf.
The Development of Hierarchical Factor Solutions
Authors: Schmid John , Leiman John M.
Published: January 2006

Although simple structure has proved to be a valuable principle for rotation of axes in factor analysis, an oblique factor solution often tends to confound the resulting interpretation. A model is presented here which transforms the oblique factor solution so as to preserve simple structure and, in addition, to provide orthogonal reference axes. Furthermore, this model makes explicit the hierarchical ordering of factors above the first-order domain.
A Computational Procedure for Tau Correlation
Authors: Cartwright Desmond S.
Published: January 2006

The tau coefficient is defined, and a computational procedure for tied ranks is described. The procedure maintains continuous computational checks, saves labor, and particularly facilitates the use of tau with large samples. It is also shown how tau correlation may be applied to Q-sorts with any shape of forced distribution or with unforced distributions.
War-Moods: II
Authors: Richardson Lewis F.
Published: January 2006

This is a continuation of a paper in the previous issue of Psychometrika (Sept., 1948, pp. 147-174) in which some historical facts about the First World War were expressed in mathematical form. The present introduction is intended to make the sequel readable by a person who has never seen Part I. This can perhaps just be done; although for ease, clarity, and conviction a prior study of Part I is strongly to be recommended. The independent variable is t, the time.
Nomogram for the Tetrachoric Correlation Coefficient
Authors: Hamilton Max
Published: January 2006

This article offers a new nomogram for the tetrachoric correlation coefficient, together with a correcting table. The development of the nomogram is described and directions for its use are included.
The Validity of a Persistence Test
Authors: French John W.
Published: January 2006

In order to raise the predictive efficiency of its college entrance test battery, the Educational Testing Service is working on the development of non-academic measures to supplement the standard aptitude and achievement examinations. A test of difficult number series problems was set up to measure persistence by tempting the students to give up early; the students were informed that some of the problems had no solution, and that full credit would be received by so marking them. This test was tried out and found to have some correlation with grades, while having no correlation with the other tests. Adding this test to the battery showed an appreciable rise in the battery's multiple correlation with grades.
Thurstone's Analytical Method for Simple Structure and a Mass Modification Thereof
Authors: Sokal Robert R.
Published: January 2006

The analytical method for simple structure proposed by Thurstone is applied to four separate cases and found to yield satisfactory results. The simple structure obtained by Thurstone's method is found to match closely that obtained by other methods and corresponds to the true structure of the matrix in those cases where true structure is known. Difficulties about the choice of the correct trial vector led the writer to develop a modification of Thurstone's method, useful where high speed computational facilities are available. Instructions are given for this so-called mass modification, and the procedure is illustrated with a 5-factor, 14-variable example. While the results do not fully correspond to a previous graphical solution, it can be argued that the results obtained by the new method show an improved simple structure. The modified method is applied to three other correlation matrices, yielding in each case a satisfactory simple structure.
Factor Analysis and Physical Types
Authors: Burt Cyril
Published: January 2006

Physical measurements, obtained from several different age-groups and national groups, have been correlated and factorized. The largest of the investigations was based on 2,400 British airmen in the R.A.F., and the most recent included as many as 17 traits. The methods of factorization employed were those worked out in early investigations of mental and scholastic tests, and differed in minor respects from those more recently used by Thurstone in his re-analysis of some of our data. The factor patterns reveal a remarkable constancy from age to age and from one national group to another. The general factor accounts for about the same proportion of the variance as the general factor in cognitive tests. The largest of the bipolar factors classifies traits into longitudinal and transverse, thus in some measure confirming the traditional classification of body-types.
Regression Weights as a Function of Test Length
Authors: Horst Paul
Published: January 2006

A battery of pencil-and-paper tests is commonly used for predicting a single criterion. If the score on each test is the number of correct answers, the composite battery score would normally be the sum of the weighted test scores, where the weights are the raw score regression weights. Knowing the reliability of each test, it is possible to alter the lengths of the tests in a manner such that the weights will all be equal. The composite battery score would then simply be the total number of items answered correctly and scoring would be greatly simplified. Such simplification is particularly desirable where the volume of testing is large. Section I of the article outlines the procedure for altering the lengths of the tests, and Section II gives a proof of the method.
War-Moods: I
Authors: Richardson Lewis F.
Published: January 2006

A person can be openly friendly, or hostile, or war-weary. Depth-psychology has shown that the underlying mood is also important. In the present theory the independent variable is time, and the dependent variables are the numbers of persons in different warmoods in two opposing nations. The rate of conversion of persons from one mood to another is taken to be proportional both to the number of susceptible persons and to the number of influencing persons, as in Kermack and McKendrick's theory of epidemics of cholera (15). This formulation leads to a set of differential equations nearly but not quite like those whereby Volterra (41) described the interaction between predator and prey among fish. Here the constants are fitted to the history of the First World War. The gregarious motive to follow a fashion of either peace or war is formulated as an amendment.