bluuebunny/crossref_metadata_2025 huggingface dataset:
Methods of Solving Some Personnel-Classification Problems
Authors: Votaw D. F.
Published: January 2006

The personnel-classification problems considered in this paper are related to those studied by Brogden (2), Lord (6), and Thorndike (8). Section 1 gives an approach to personnel classification. A basic problem and variations of it are treated in section 2; and the computation of a solution is illustrated in section 3. Two extensions of the basic problem are presented in section 4. Most of the methods indicated for computing solutions are applications of the “simplex” method used in linear programming (see 1, Chs. XXII, XXIII). The capabilities of a high speed computer in regard to the simplex method are discussed briefly (see section 1).
The Factorial Composition and Validity of Differently Speeded Tests
Authors: Myers Charles T.
Published: January 2006

Scores on five differently speeded parts of a nonverbal reasoning test were analyzed to determine the relationship between the abilities measured by the speeded and the unspeeded parts. Two orthogonal factors were found: One is described as the ability to answer the problems correctly; the other is described as the tendency to answer the problems quickly. The first factor was found to be somewhat more valid than the second for predicting grades at the U. S. Naval Academy. The suggestion is made that descriptions of tests are incomplete unless they include some specification describing the speededness of the test.
Finite Markov Processes in Psychology
Authors: Miller George A.
Published: January 2006

Finite Markov processes are reviewed and considered for their usefulness in the description of behavioral data. The various alternative responses in an experimental situation define a vector space, and changes in the probabilities of these alternatives are represented by movements in this space. Methods of fitting the theory to experimental data are considered.

The simplest process, with a constant matrix of transitional probabilities that is applied repeatedly to represent the effect of successive trials, seems inadequate for most learning data. A matrix function that may be useful for learning theory is presented.
On the Determination of Redundancies in Sociometric Chains
Authors: Ross Ian C. , Harary Frank
Published: January 2006

The use of a matrix to represent a relationship between the members of a group is well known in sociometry. If this matrix is raised to a certain power, the elements appearing give the total number of connecting paths between each pair of members. In general, some of these paths will be redundant. Methods of finding the number of such redundant paths have been developed for three- and four-step chains by Luce and Perry (3) and Katz (2), respectively. We have derived formulas for the number of redundant paths of five and six steps; and in addition, an algorithm for determining the number of redundant paths of any given length.
Multiple Group Methods for Common-Factor Analysis: their Basis, Computation, and Interpretation
Authors: Guttman Louis
Published: January 2006

In a previous paper (1) were developed three basic theorems which were shown to provide numerical routines, as well as algebraic proof, for existing common-factor methods. New “multiple” routines were also indicated. The first theorem showed how to extract as many common factors as one wished from the correlation matrix in one operation. The second theorem showed how to do the same from the score matrix. The third proved that factoring the correlation matrix was equivalent to factoring the score matrix. A particular application of these theorems is the multiple group factoring method, which the writer first used in practice on some Army attitude scores during World War II. The present paper explains the basic theorems in more detail with special reference to group factoring. Computations are outlined as consisting of five simple matric operations. The meaning of commonfactor analysis is given in terms of the basic theorems, as well as the relationship to “inverted” factor theory.
The Effect of Difficulty and Chance Success on Item-Test Correlation and on Test Reliability
Authors: Plumlee Lynnette B.
Published: January 2006

An equation is derived for predicting the effect of chance success, relative to item difficulty, on item-test correlation. The values predicted by this equation and by equations derived by Guilford and Carroll for predicting the effect of chance success on item difficulty and test reliability are compared with empirical values in an experiment which used identical test items in multiple-choice and answer-only form.
A Factor Analysis of Women's Measurements taken for Garment and Pattern Construction
Authors: Heath Helen
Published: January 2006

In order to facilitate garment and pattern construction, a research which involved taking a minimum of fifty-five measurements on several thousand women was conducted by the Bureau of Home Economics. Partial correlations with age held constant were computed for a representative group of 4,128 of the women. The correlations among twenty-nine of these variables served as the basis of the present study. By a combination of the multiple-group and the centroid method of factoring, five factors were extracted. After twenty-nine rotations, simple structure was evident, and the factors were interpreted as bone length, size of joints, circumference below the waist, circumference of extremities, and circumference above the waist. The intercorrelations of the primaries were computed, and two second-order factors were extracted. One of these seems to be primarily related to the growth of fatty tissue and the other to the development of the bones.
A Technique for Criterion-Keying and Selecting Test Items
Authors: French John W.
Published: January 2006

For multiple-choice tests where no a priori key exists, the initial selection of a key for maximum validity may be made on the basis of the number of persons choosing each alternative and their mean criterion score. The keying formula is derived. Once the initial keying has been done, further precision in keying and item selection may use, in addition, the mean total test score for persons choosing each alternative. Item-selection formulas suggested by Horst and by Gulliksen for maximizing test validity are both in the form of a ratio, an “item-validity index” divided by an “item-reliability index.” The formula derived here is shown to be equivalent to the numerators of these formulas. The expression in the denominators uses the total test score. Although a radical appears in the denominator of Horst's formula and not in the denominator of Gulliksen's formula, both of them select the same items in practice.
A Square Root Method of Selecting a Minimum Set of Variables in Multiple Regression: II. A Worked Example
Authors: Lubin A. , Summerfield A.
Published: January 2006

The square root method of selection has been explained in a previous article. In the present article a worked example is given which illustrates the compactness of the procedure. The square root method is compared with the Wherry-Doolittle method.
A Superior Rotational Method in Factor Analysis or Psychometricians in Government Service
Authors: Adkins Dorothy C.
Published: January 2006

The topic that I have chosen, “A Superior Rotational Method in Factor Analysis or Psychometricians in Government Service,” may puzzle you at first. But there is an explanation. A study in progress at the University of North Carolina requires the interpretation of 16 factors obtained from a centroid analysis of 66 variables. The task that was approached with greatest apprehension was the location of a meaningful reference frame. With so many vectors protruding into a space of such a large number of dimensions, the problem appeared practically insoluble. Hence we sought a rotational method that would obviate the necessity for the numerous graphs and the matrix multiplication associated with the commonly accepted techniques.

Perhaps some of you have had the experience of solving a difficult mathematical problem in a state of sleep and later being able to transcribe the complete solution immediately. A relatively painless approach to mathematics, it is the one which enabled me to pass a course in Mathematical Probability years ago. I scarcely dared presume that I could evoke it in the present emergency. To my astonishment, however, it worked. One day the project staff had had a particularly trying session during which we tried in vain to stretch the available funds to cover the rotational work. Upon falling asleep in my office chair, I dreamed a solution so simple that an ordinary statistical clerk, upon mere inspection of the score matrix, could visualize the most interpretable reference frame in up to an infinite number of dimensions. This was beyond our most extravagant hopes, for it rendered obsolete both the correlation matrix and the centroid solution.
A Note on Optimal Test Length
Authors: Horst Paul
Published: January 2006

Elsewhere in this issue is an article by Dr. Calvin Taylor entitled “Maximizing Predictive Efficiency for a Fixed Total Testing Time.” The purpose of this note is to point out that the formulation developed by Dr. Taylor is mathematically equivalent to one presented by me in a previous issue of this journal.

We start from Taylor’s equation (36) .
A Comparison of Two Procedures for Calculating Discriminant Function Coefficients
Authors: Schmid John
Published: January 2006

Alternative procedures for calculating discriminant function coefficients have been illustrated in reported research. One method proceeds from data which has been expressed in deviation score units, whereas the other method implies that the data has been expressed in standard units. It is shown algebraically that both procedures yield identical discriminant function coefficients, and therefore, the method involving less mathematical manipulation and computation is preferable.
Machine Short-Cuts in the Computation of Chisquare and the Contingency Coefficient
Authors: Carroll John B. , Bennett C. C.
Published: January 2006

Rapid computational routines are presented for calculating x2 from frequency data in the following cases: (1) test of goodness of fit between an observed and a theoretical distribution; (2) test of independence of distributions displayed in an r ✗ c table; (3) test of independence of distributions displayed in an r ✗ 2 table. A rapid method of computing the contingency coefficient also follows from the procedure used in the second of these cases.
A Note on Reliability
Authors: Kaitz Hyman B.
Published: January 2006

A formula for internal consistency reliability is developed within the framework of the analysis of variance. The test items are assumed to be homogeneous, but may have any weights. Data needed for computation are the student test scores, and the total number of items answered so as to have the same weight. It is shown that this formula reduces to the Kuder-Richardson (21) for item weights of one and zero. Some empirical validation is offered.
The Prediction of Choice
Authors: Thurstone L. L.
Published: January 2006

This paper is concerned with a central concept in social measurement such as opinion polls, the measurement of attitudes, the prediction of political elections, the measurement of moral values, the measurement of consumer preferences, the measurement of utility, and the measurement of aesthetic values. The concept is that of the discriminal dispersion and its interesting effects in the prediction of choice.
A Simple Orthogonal Multiple Factor Approximation Procedure
Authors: Carlson Hilding B.
Published: January 2006

This paper describes a simple orthogonal multiple factor approximation procedure that involves no inversion of the sign of negative residuals, the estimation of only as many communalities as there are factors, and none or only a few minor rotations of the axes in an attempt to obtain a “meaningful” solution. It also suggests a technique for the estimation of those communalities that must be estimated. The factor loadings obtained by means of this procedure, which we shall designate as the pre-selection procedure, are affected by the order in which the factors are obtained, showing a reduction in variance accounted for by each successive factor, as is characteristic of the centroid, bi-factor, and principal factor solutions. The entire procedure takes considerably less time than that involved in the orthodox centroid method alone.
Factor Analysis and Body Types
Authors: Thurstone L. L.
Published: January 2006

A factorial analysis was made of a small battery of twelve anthropometric measurements. The correlations can be accounted for by four factors in a simple structure. This small battery has been used by the author for teaching purposes. Several of these factors seem to be meaningful, but their acceptance must depend on more comprehensive studies of body measurements with a larger number of measurements.
The Average Spearman Rank Correlation Coefficient
Authors: Lyerly Samuel B.
Published: January 2006

A method is derived for finding the average Spearman rank correlation coefficient of N sets of ranks with a single dependent or criterion ranking of n items without computing any of the individual coefficients. Procedures for calculating the exact distribution of ρav for small values of N and n are described for the null case. The first four moments about zero of this distribution are derived, and it is concluded that for samples as small as N = 4 and n = 4 the normal distribution can be used safely in testing the hypothesis ρav = 0.
The Test-Retest Reliability of Qualitative Data
Authors: Guttman Louis
Published: January 2006

The test-retest reliability of qualitative items, such as occur in achievement tests, attitude questionnaires, public opinion surveys, and elsewhere, requires a different technique of analysis from that of quantitative variables. Definitions appropriate to the qualitative case are made both for the reliability coefficient of an individual on an item and for the reliability coefficient of a population on the item. From but a single trial of a large population on the item, it is possible to compute a lower bound to the group reliability coefficient. Two kinds of lower bounds are presented. From two experimentally independent trials of the population on the item, it is possible to compute an upper bound to the group reliability coefficient. Two upper bounds are presented. The computations for the lower and upper bounds are all very simple. Numerical examples are given.
General Solution of the Analysis of Variance and Covariance in the Case of Unequal or Disproportionate Numbers of Observations in the Subclasses
Authors: Tsao Fei
Published: January 2006

In this paper a preview of the problem is given. Then the mathematical solutions of estimating the sums of squares and products of different sources of variation under different assumptions are presented. Two kinds of populations from which our samples are supposed to be drawn are specified. One is defined as possessing approximately the same stratification as our sample; while the other is defined as having equal frequencies in the subclasses. For the first kind of population, we should use the restrictions of “the weighted means.” For the second kind, we should use the restrictions of “the unweighted means.” The assumptions of zero interactions and significant interactions are also considered. After working out the exact method, two approximate methods with appropriate statistical assumptions to be fulfilled are given.
Remarks on Tucker's Inter-Battery Method of Factor Analysis
Authors: Gibson W. A.
Published: January 2006

Tucker's inter-battery method of factor analysis is shown to assume implicitly that, within the factor space of overlap between the vector configurations of the two test batteries involved, the locations of the two sets of principal axes and the sizes of the associated characteristic roots are identical. A suggested modification of the inter-battery method to avoid these restrictions is considered.
Multidimensional Unfolding: Determining the Dimensionality of Ranked Preference Data
Authors: Bennett Joseph F. , Hays William L.
Published: January 2006

A model is proposed which treats rankings given by a group of judges as representing regions in an isotonic space of dimensionality r. Three possible criteria for estimating lower bound dimensionality are discussed: mutual boundary, cardinality, and the occurrence of transposition groups. Problems associated with each criterion are mentioned.
Some Multiple Correlation and Predictor Selection Methods
Authors: Anderson Harry E. , Fruchter Benjamin
Published: January 2006

The Doolittle, Wherry-Doolittle, and Summerfield-Lubin methods of multiple correlation are compared theoretically as well as by an application in which a set of predictors is selected. Wherry's method and the Summerfield-Lubin method are shown to be equivalent; the relationship of these methods to the Doolittle method is indicated. The Summerfield-Lubin method, because of its compactness and ease of computation, and because of the meaningfulness of the interim computational values, is recommended as a convenient least squares method of multiple correlation and predictor selection.
Approaches to Univocal Factor Scores
Authors: Guilford J. P. , Michael William B.
Published: January 2006

Two current methods of deriving common-factor scores from tests are briefly examined and rejected. One of these estimates a score from a multiple-regression equation with as many terms as there are tests in the battery. The other limits the equation to a few tests heavily saturated with the desired factor, with or without tests used to suppress the undesired factors. In the proposed methods, the single best test for each common factor is the starting point. Such a test ordinarily has a very few undesired factors to be suppressed, frequently only one. The suppression test should be univocal, or nearly so. Fortunately, there are relatively univocal tests for factors that commonly require suppression. Equations are offered by which the desired-factor test and a single suppression test can be weighted in order to achieve one or more objectives. Among the objectives are (1) maximizing the desired factor variance, (2) minimizing the undesired factor variance, (3) a compromise, in which the undesired variance is materially reduced without loss in desired variance, and (4) a change to any selected ratio of desired to undesired variance. A more generalized solution is also suggested. The methods can be extended in part to the suppression of more than one factor. Equations are derived for the suppression of two factors.
A Table for Estimating the Significance of the Difference between Correlated Percentages
Authors: Swineford Frances
Published: January 2006

A table to aid in testing the statistical significance of the difference between correlated percentages is presented. Percentage points which range from .10 to .001 are included.
An Extension of Anderson's Solution for the Latent Structure Equations
Authors: Gibson W. A.
Published: January 2006

Anderson's solution for the latent structure equations is summarized and then extended in two ways so as to involve all items simultaneously.
The Relationship between Factorial Composition of Test Items and Measures of Test Reliability
Authors: Cotton John W. , Campbell Donald T. , Malone R. Daniel
Published: January 2006

For continuous distributions associated with dichotomous item scores, the proportion of common-factor variance in the test, H2, may be expressed as a function of intercorrelations among items. H2 is somewhat larger than the coefficient a except when the items have only one common factor and its loadings are restricted in value. The dichotomous item scores themselves are shown not to have a factor structure, precluding direct interpretation of the Kuder-Richardson coefficient, rK-R, in terms of factorial properties. The value of rK-R is equal to that of a coefficient of equivalence, H2Φ, when the mean item variance associated with common factors equals the mean interitem covariance. An empirical study with synthetic test data from populations of varying factorial structure showed that the four parameters mentioned may be adequately estimated from dichotomous data.
The Use of Configural Analysis for the Evaluation of Test Scoring Methods
Authors: Osburn H. G. , Lubin Ardie
Published: January 2006

A method based on configural analysis has been given whereby test scoring techniques can be evaluated to see if they have optimal validity. Configural analysis has also been used to show how three well known item scoring techniques, multiple regression, total score, and multiple cut-off, imply (for optimal validity) certain conditions on the answer pattern means. The method is illustrated by a worked example.
A Model for Response Tendency Combination
Authors: Birch David
Published: January 2006

A model is proposed to predict the performance on a compound stimulus as a function of the performance on the component stimuli in a two-choice situation. Data from a learning task are used to evaluate the model.
Procedures for Obtaining Separate Set and Content Components of a Test Score
Authors: Helmstadter Gerald C.
Published: January 2006

Using two distinct models, several formulas for obtaining separate set and content components of a test score have been derived. Comparisons among the methods are made algebraically and through their application to a set of test data apparently affected by response sets.
Item Selection Methods for Increasing Test Homogeneity
Authors: Webster Harold
Published: January 2006

A number of methods for increasing test homogeneity by item selection are discussed. Exact selection conditions which will maximize obtained homogeneity as measured by KR - 20 and KR - 21 are derived, and an application is given. Since they require only item count data, the selection conditions are economical to apply.
Determination of Parameters of a Functional Relation by Factor Analysis
Authors: Tucker Ledyard R
Published: January 2006

Consideration is given to determination of parameters of a functional relation between two variables by the means of factor analysis techniques. If the function can be separated into a sum of products of functions of the individual parameters and corresponding functions of the independent variable, particular values of the functions of the parameters and of the functions of the independent variables might be found by factor analysis. Otherwise approximate solutions may be determined. These solutions may represent important results from experimental investigations.
The Counseling Assignment Problem
Authors: Ward Joe H.
Published: January 2006

A disposition index, DI, which provides information about each possible placement to be considered in a personnel classification situation is discussed. The index is readily computed by machine methods and can be used by counselors required to make assignments. The use of the disposition index provides an adequate approximation to optimal solutions obtained by other methods.
A Mathematical Model for Conditioning
Authors: Boguslavsky G. W.
Published: January 2006

It is postulated that occurrence of a conditioned response depends on recurrence of one of a finite number of specific vigilance reactions. Number of trial on which a conditioned response occurs is shown to be a sufficient statistic for estimating the number of such vigilance reactions. The hypothesis is tested by noting whether numbers of trials on which conditioned responses occur fall within confidence intervals determined on the basis of a selected sufficient statistic. Applications of the model to psychological research are suggested.
Solution of the Personnel Classification Problem with the Method of Optimal Regions
Authors: Dwyer Paul S.
Published: January 2006

The personnel classification problem is identified mathematically with other problems in the social and biological sciences. This mathematical problem is shown to be a special case of the general mathematical problem of linear programming. It is proposed here that the personnel classification problem may be solved directly by methods particularly appropriate to it as well as by the simplex method, which is a standard method for solving the general linear programming problem. The method of optimal regions is derived and illustrated in this paper.
The Predicted and Observed Effect of Chance Success on Multiple-Choice Test Validity
Authors: Plumlee Lynnette B.
Published: January 2006

Assuming chance to be fully operative, the predicted effect of chance success on test validity when answer options are supplied depends on the number of options, the difficulty of the test and the variance of test scores. Predicted validity values are compared with empirical validity values in an experiment which used the same mathematics test items with and without answer options.
A Second-Order Factor Analysis of Reasoning Abilities
Authors: Matin Leonard , Adkins Dorothy C.
Published: January 2006

This article reports a second-order factor analysis of the 13 interpretable first-order factors of Adkins and Lyerly based on 66 variables for 200 Army men. The approach to simple structure for 6 second-order factors was unusually good. Loadings of the original 66 variables on the second-order factors were also obtained. Five of the factors are tentatively interpreted as Precision in Formation and Use of Verbal Concepts, General Verbal Fluency, Visualizing Spatial Constancy During Movement, Speed in Analysis, and Flexibility in Analysis.
Estimation of the Correlation Coefficient in the Case of a Bivariate Normal Population when One of the Variables is Dichotomized
Authors: Maritz J. S.
Published: January 2006

It is shown that the problem of estimation of the correlation coefficient of a bivariate normal population when one of the variables is dichotomized may be attacked with “probit analysis” methods. This represents an extension of the work of Gillman and Goode (3), as it was possible to find by this approach an approximation to the large-sample variance of the resulting estimate G of ρ. An empirical investigation was undertaken with the object of obtaining some information about the distribution of G for large sample size. Methods for determining the “pass-fail” cut-off are considered.
A Factor-Analytic Study of Reasoning Abilities
Authors: Green Russel F. , Guilford J. P. , Christensen Paul R. , Comrey Andrew L.
Published: January 2006

A battery of 32 tests was administered to a sample including 144 Air Force Officer Candidates and 139 Air Cadets. The factor analysis, using Thurstone's complete centroid method and Zimmerman's graphic method of orthogonal rotations, revealed 12 interpretable factors. The non-reasoning factors were interpreted as verbal comprehension, numerical facility, perceptual speed, visualization, and spatial orientation. The factors derived from reasoning tests were identified as general reasoning, logical reasoning, education of perceptual relations, education of conceptual relations, education of conceptual patterns, education of correlates, and symbol substitution. The logical-reasoning factor corresponds to what has been called deduction, but eduction of correlates is perhaps closer to an ability actually to make deductions. The area called induction appears to resolve into three eduction-of-relations factors. Reasoning factors do not appear always to transcend the type of test material used.
Application of the Quartimax Method of Rotation to Thurstone's Primary Mental Abilities Study
Authors: Wrigley Charles , Saunders David R. , Neuhaus Jack O.
Published: January 2006

This study compares a quartimax rotation of the centroid factor loadings for Thurstone's Primary Mental Abilities Test Battery with factorings of the same correlation matrix by Thurstone (simple structure), Zimmerman (revised simple structure), Holzinger and Harman (bi-factor analysis), and Eysenck (group factor analysis). The quartimax results agree very closely with the solutions of Holzinger and Harman and of Eysenck, and reasonably well with the two simple structure analyses. The principal difference is the general factor provided by the quartimax solution. Reproduction of the factorial structure is sufficiently good to justify its use at least as the first stage of rotation. More extensive trial of the method will be needed with more varied data before it will be possible to decide whether quartimax factors meet psychological requirements sufficiently well without further rotation.
Axioms of a Theory of Discrimination Learning
Authors: Restle Frank
Published: January 2006

Analysis of an empirical theory into a formal system with specified primitive notions and axioms has the advantage of making it clear what deductions from the theory are permissible, and clarifying the internal structure of the theory. An example of such analysis is presented in this paper.
The Objective Definition of Simple Structure in Linear Factor Analysis
Authors: Tucker Ledyard R
Published: January 2006

Requirements for an objective definition of simple structure are investigated and a number of proposed objective criteria are evaluated. A distinction is drawn between exploratory factorial studies and confirmatory factorial studies, with the conclusion drawn that objective definition of simple structure depends on study design as well as on objective criteria. A proposed definition of simple structure is described in terms of linear constellations. This definition lacks only a statistical test to compare with possible chance results. A computational procedure is also described for searching for linear constellations. This procedure is very laborious and might best be accomplished on high-speed automatic computers. There is no guarantee that the procedure will find all linear constellations, but it probably would yield satisfactory results for well-designed studies.
F-Test Bias for Experimental Designs in Educational Research
Authors: Gourlay Neil
Published: January 2006

Reference is made to Neyman's study of F-test bias for the randomized blocks and Latin square designs employed in agriculture, and some account is given of later statistical developments which sprang from his work—in particular, the classification of model-types and the technique of variance component analysis. It is claimed that there is a need to carry out an examination of F-test bias for experimental designs in education and psychology which will utilize the method and, where appropriate, the known' results of this new branch of variance analysis. In the present paper, such an investigation is carried out for designs which may be regarded as derivatives of the agricultural randomized blocks design. In a paper to follow, a similar investigation will be carried out for experimental designs of the Latin square type.
Test Reliability and Effective Test Length
Authors: Angoff William H.
Published: January 2006

Measures of effective test length are developed for speeded and power tests, which are independent of the number of items in the test or of the time required for administration. These measures are used in determining reliability for (1) speeded and power tests, where a separately timed short parallel form is administered in addition to the full-length test; (2) power tests, where a subset of items is imbedded within the total test, parallel to the total test; and (3) power tests, where the subset of items is correlated with the complementary parallel subset in the test.
An Analytical Solution for Approximating Simple Structure in Factor Analysis
Authors: Carroll John B.
Published: January 2006

It is proposed that a satisfactory criterion for an approximation to simple structure is the minimization of the sums of cross-products (across factors) of squares of factor loadings. This criterion is completely analytical and yields a unique solution; it requires no plotting, nor any decisions as to the clustering of variables into subgroups. The equations involved appear to be capable only of iterative solution; for more than three or four factors the computations become extremely laborious but may be feasible for high-speed electronic equipment. Either orthogonal or oblique solutions may be achieved. For illustrations, the Johnson-Reynolds study of “flow” and “selection” factors and the Thurstone box problem are reanalyzed. The presence of factorially complex tests produces a type of hyperplanar fit which the investigator may desire to adjust by graphical rotations; the smaller the number of such tests, the closer the criterion comes to approximating simple structure.
A Factor Analysis of Intra-Task Performance on two Psychomotor Tests
Authors: Fleishman Edwin A.
Published: January 2006

There are indications that even during the short time of administration of a single psychomotor test, the ability or abilities sampled may shift materially in importance. It then becomes important to know the stages in which these fluctuations occur, the stage at which the test is most complex, and the stage at which the test most nearly measures one ability at a time. This paper describes an application of factorial methods to this problem. Factor analysis of inter-trial correlations on two models of the Rudder Control Test revealed three factors, “Steadiness-Control,” “Precision of Movement,” and “Strength.” The same factor pattern was confirmed in a separate factor analysis on another sample in which the order of administration of the tests was reversed. Implications are pointed out for future psychomotor test development.
The Estimation of the Discriminal Dispersion in the Method of Successive Intervals
Authors: Burros Raymond H.
Published: January 2006

A new algebraic formula is derived for estimation of the discriminal dispersion in the method of successive intervals. The legitimate use of the formula requires that as many normal deviates as possible be present in the matrix. For this reason, it is recommended that deviates corresponding to the interval (0.01, 0.99) of the cumulative proportions be used, instead of those corresponding to (0.05, 0.95), the interval used by Edwards and Thurstone. Computations on data published by Edwards and Thurstone showed that when adjustment was made for variability in dispersions calculated by the formula of this paper, a reduction of fifty per cent in mean absolute discrepancy was produced. Since the formula is easy to use and avoids the disadvantages of its predecessors, it should have fairly wide applicability in psychological research.
The Law of Comparative Judgment in the Successive Intervals and Graphic Rating Scale Methods
Authors: Rimoldi H. J. A. , Hormaeche M.
Published: January 2006

The law of comparative judgment is applied to the successive intervals and graphic rating scale methods. A procedure for estimating the modal discriminal process and discriminal dispersion of the stimuli, as well as the value of the boundaries of the intervals on the continuum, is given. From the estimated values it is possible to determine the theoretical proportions and to compare them with the actual experimental proportions. The agreement between these values is an indication of the adequacy of the assumptions made.
The Discrimination of Two Racial Samples
Authors: Horst Paul , Smith Stevenson
Published: January 2006

Nineteen different anthropometric measures were obtained on all members of each of two racial groups. A procedure was developed and applied to the data to give maximum differentiation between the groups. The method is applicable wherever we have a large number of independent variables and a dependent variable. In such cases, the conventional methods for determining multiple regression constants are very laborious. An iteration method is presented which is more rapid than any with which the writers are familiar. The method selects in sequence those variables which together yield the largest multiple correlation with the criterion. At each step in the procedure, rapid estimates of the regression weights and the multiple correlation at that point are available.
A Component Model for Stimulus Variables in Discrimination Learning
Authors: Burke C. J. , Estes W. K.
Published: January 2006

A general function is derived describing the conditioning of a single stimulus component in a discriminative situation. This function, together with the combinatorial rules of statistical learning theory [5, 12], generates empirically testable formulas for learning of classical two-alternative discriminations, probabilistic discriminations, and discriminations based on the outcomes of preceding trials in partial reinforcement experiments.
A General Least Squares Solution for Successive Intervals
Authors: Diederich Gertrude W. , Messick Samuel J. , Tucker Ledyard R
Published: January 2006

A general least squares solution for successive intervals is presented, along with iterative procedures for obtaining stimulus scale values, discriminal dispersions, and category boundaries. Because provisions for weighting were incorporated into the derivation, the solution may be applied without loss of rigor to the typical experimental matrix of incomplete data, i.e., to a data matrix with missing entries, as well as to the rarely occurring matrix of complete data. The use of weights also permits adjustments for variations in the reliability of estimates obtained from the data. The computational steps involved in the solution are enumerated, the amount of labor required comparing favorably with other procedures. A quick, yet accurate, graphical approximation suggested by the least squares derivation is also described.
Approximating Maximum Test Validity by a Non-Parametric Method
Authors: Webster Harold
Published: January 2006

The Gleser-DuBois conditions for selecting from a number of test items those which will maximize the correlation between total test score and criterion will degenerate into expressions requiring only item counts on total distributions and the upper halves of distributions. A grouping convention for scores near medians is recommended. The inefficiency of the method is easily compensated for, because, regardless of the size of the sample, only standard test-scoring equipment and brief computations are required. A procedure is outlined, and some applications are discussed.
Reliability Formulas that do not Assume Experimental Independence
Authors: Guttman Louis
Published: January 2006

Tautologies are established for the reliability coefficient ρ2t of the sum of n part scores. It is not assumed that the part scores are experimentally independent of each other nor that the parts are equivalent to each other. The tautologies show the exact role played by experimental dependence and nonequivalence of parts, respectively, in the reliability of the sum. The formal algebra is appropriate to reliability in the sense of repeated trials of the same test, as well as in the sense of a universe of parallel tests, although the empirical meanings are different. Emphasis is on practical formulas that require information from only a single experiment (or test). These can take the form only of lower bounds to ρ2t, four of which are developed.
A Rationale for the Measurement of Traits in Individuals
Authors: Coombs Clyde H.
Published: January 2006

Hypotheses presented in a previous paper conceive of an individual's position on an attitude scale as represented by a mean position (status score) and a sigma (dispersion score). The testing of these hypotheses requires a determination of these two scores for each individual. A rationale is presented here for the determination of these two scores for an individual from his forced choice responses to pairs of items of nearly equal scale value.
On the Computation of Zero-Order Correlation Coefficients
Authors: Kossack Carl F.
Published: January 2006

There appears to be a gap in published computational techniques inasmuch as nowhere in the literature nor in textbooks can one find a model to be followed in computing the numerous zero-order correlation coefficients for a correlation matrix. The purpose of this paper is to present, by means of an illustration, such a model. The model consists of two computational matrices, matrix one being the Summation Matrix and matrix two the Computational Matrix. The entries on these matrices are arranged so as to facilitate the future computations.
Remarks on the Method of Paired Comparisons: II. The Effect of an Aberrant Standard Deviation when Equal Standard Deviations and Equal Correlations are Assumed
Authors: Mosteller Frederick
Published: January 2006

If customary methods of solution are used on the method of paired comparisons for Thurstone's Case V (assuming equal standard deviations of sensations for each stimulus), when in fact one or more of the standard deviations is aberrant, all stimuli will be properly spaced except the one with the aberrant standard deviation. A formula is given to show the amount of error due to the aberrant stimulus.
Remarks on the Method of Paired Comparisons: III. A Test of Significance for Paired Comparisons when Equal Standard Deviations and Equal Correlations are Assumed
Authors: Mosteller Frederick
Published: January 2006

A test of goodness of fit is developed for Thurstone's method of paired comparisons, Case V.

The test involves the computation of \documentclass[12pt]{minimal}
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\begin{document}
$$\chi ^2 = n\Sigma(\theta '' - \theta ')^2 /821,$$
\end{document}, where n is the number of observations per pair, and θ″ and θ′ are the angles obtained by applying the inverse sine transformation to the fitted and the observed proportions respectively. The number of degrees of freedom is (k−1) (k−2)/2.
Rate of Addition as a Function of Difficulty and Age
Authors: Birren James E. , Botwinick Jack
Published: January 2006

Rate of addition was studied as a function of difficulty as measured by problem length. The hypothesis was tested that the rate of addition would decline as a function of the logarithm of the number of addition operations per problem. The test material required the rapid addition of single columns of digits ranging from two to twenty-five digits in length. Rate of uncorrected addition declined as a power function of problem length and the rate of correct addition declined as an exponential function of length. Results indicated that subjects who varied in age and mental status could be differentiated according to the parameters defining the curves of addition rate as a function of length.
A Correlational Analysis of Tracking Behavior
Authors: Knowles W. B. , Holland J. G. , Newlin E. P.
Published: January 2006

This study reveals the usefulness of multiple correlation techniques in estimating the relative importance of different aspects of a tracking task in the operator's tracking behavior. The technique is applied to a compensatory tracking task with a position control.
The Upper and Lower Twenty-Seven Per Cent Rule
Authors: Cureton Edward E.
Published: January 2006

A simplified re-derivation of the formula underlying the rule is presented, followed by a derivation of the comparable rule for the unitrectangular distribution, which turns out to be a 33-per cent rule. Critical comments are offered concerning two assumptions: normality of the score distribution and equality of mean standard errors of measurement in the high and low groups.
The Matching Problem
Authors: Gilbert Edgar J.
Published: January 2006

Tables of the exact distributions of number of matches are given for small decks having the same number of cards in each suit. Several approximate distributions are considered for use with larger decks, and some indication of the goodness of the approximations is given.
A Comparison of Game Theory and Learning Theory
Authors: Simon Herbert A.
Published: January 2006

It is shown that Estes' formula for the asymptotic behavior of a subject under conditions of partial reinforcement can be derived from the assumption that the subject is behaving rationally in a certain game-theoretic sense and attempting to minimax his regret. This result illustrates the need for specifying the frame of reference or set of the subject when using the assumption of rationality to predict his behavior.
A Nomogram for Factor Analysts
Authors: Deuel P. D.
Published: January 2006

When a new reference vector is chosen graphically from the plane of two old ones, its direction cosines as well as the projections of the tests on it are most easily computed by applying certain multipliers d and Sd to quantities which are already known. The nomogram quickly supplies d, after S has been read from the graph.
Further Notes on Differences between Percentages
Authors: Swineford Frances
Published: January 2006

In certain problems dealing with percentage differences, it frequently happens that one is interested in a critical value different from zero rather than in the usual hypothesis of no population difference. Moreover, one may be concerned with differences greater than (or less than) a given magnitude, so that only one tail of the distribution of chance values is used. Tables are here presented to facilitate evaluating results of such problems. One per cent and 5 per cent values can be read from the tables, such values corresponding to the more usual 2 per cent and 10 per cent confidence limits.
A Simplified Punch Card Method of Determining Sums of Squares and Sums of Products
Authors: Castore George F. , Dye William S.
Published: January 2006

A simplified method of obtaining sums of squares and sums of cross products by the use of punch card equipment is described. Application of the method has revealed several advantages, which are noted.
A Least Squares Solution for Successive Intervals Assuming Unequal Standard Deviations
Authors: Gulliksen Harold
Published: January 2006

A least squares solution has been presented for the Law of Categorical Judgment and the Method of Successive Intervals, which is formally equivalent to Horst's solution for the matrix of incomplete data. A simplified approximation which is recommended for use with any matrix of complete data is also given. A procedure, analogous to that originally devised by Thurstone and presented by Saffir, is outlined for the typical experimental matrix of incomplete data. It is essentially a “point and slope” method of fitting a straight line which comes rather directly from the least squares solution.
A Device for Facilitating the Computation of the First Four Moments about the Mean
Authors: Lyman John , Marchetti Pietro V.
Published: January 2006

A mechanical device is described which materially reduces the time, labor, and probability of errors which are involved in the computation of certain moments about the mean. The use of the device is illustrated with the computation of the mean, standard deviation, g1 as a measure of skewness, and g2 as a measure of kurtosis of data from a given study.
An Analytical Method for Simple Structure
Authors: Thurstone L. L.
Published: January 2006

One of the most difficult parts of multiple-factor analysis for the student to learn is the rotation of the coordinate axes to simple structure. The complete graphical methods have been the most dependable. The work of interpreting these diagrams is not only tedious but it requires the development of a skill that many otherwise competent students are unable to master. The writer has tried many times to develop an analytical method which would eliminate the graphical methods of successive approximation. The method to be described here seems at last to be successful and practically feasible. It is equally applicable to unimodal and bimodal hyperplanes so that no restrictive assumptions need to be made about the positive or negative signs of the factorial components.
A Method for the Study of Interstimulus Similarity
Authors: Coombs Clyde H.
Published: January 2006

A generalized method for collecting data on interstimulus similarity is presented and its special cases evaluated by use of information theory. A method of analyzing the data by the Unfolding Technique is presented which permits the study of the latent attribute structure underlying the similarity of stimuli for a single individual.