bluuebunny/crossref_metadata_2025 huggingface dataset:
Studies in Measurement of the Relations Among Sovereign States
Authors: Klingberg Frank L.
Published: January 2006

This article describes the application of three psychometric methods to
the problem of measurement of the friendly or hostile relations among states
of the world today. To secure judgments, schedules were sent to students of
international affairs at several times during the last five years. The
method of equal-appearing intervals was used to determine the relative
probability of war for 88 pairs of states in January, 1937; the method of
“triadic combinations” to determine relative friendliness among the Great
Powers in November, 1938; and the method of “multidimensional” or group rank
order to measure the attitudes of important states toward the Great Powers
in March and April, 1939; June, 1940; and June, 1941. A chart of scale
values for the pairs of Great Powers shows the changing trends since 1937.
The last two methods were used to depict the Great Powers in
multidimensional space according to their mutual friendliness, thus
permitting the application of a type of factor analysis. The reliability of
the methods employed was high, and various types of evidence support the
general validity of the results.
Clinical Psychology—Art or Science
Authors: Sarbin Theodore R.
Published: January 2006

This paper questions the oft-repeated statement that clinical psychology
is an art by examining the main functions of clinical psychologists, i.e.,
diagnosis and treatment. In examining the concept of diagnosis, evidence is
presented which supports the notion that a diagnostic statement has meaning
only when it has a referent in the future—when it provides a prediction. A
prediction (probability-statement) is determined empirically and may be
stated in terms of a regression equation or in terms of a crude
generalization from clinical experience. Treatment likewise is determined by
tacit or expressed predictions of behavior under alternative conditions. The
various conceptions of art as applied to clinical psychology are examined
and the conclusion is drawn that clinical psychology is a scientific as
opposed to an artistic or intuitive enterprise.
Portable Response Timer
Authors: Libby J. E. P. , Hunsicker A. L.
Published: January 2006

The instrument to be described was developed from apparatus the original
design of which, by Landahl and Bechtoldt, was unpublished. Its function is
to measure the times of simple reaction, choice, perception of projected
patterns, and perception of dim patterns after light adaptation. It may also
be used to time verbal response to multiple-choice material when combined
with the response relay described by Libby elsewhere in the present
journal.

The complete instrument, including chronoscope, subject keys, and
experimenter keys, may be carried in a case ll"x6.5"x6.5". The chronoscope,
M, occupies the left half of the case. The upper half of the right-hand
section serves for carrying the subject key (H)
or, as shown in the accompanying cut, the microfilm container and projector
slides. All remaining apparatus is in the lower half of this
compartment.
The Measurement of Conformity
Authors: Katzoff E. T.
Published: January 2006

Allport's J-curve hypothesis of conforming behavior and its attendant treatment of appropriate data are criticized on the following points: (1) narrowness of application; (2) flexibility of interpretation of results; (3) arbitrary selection of a criterion of conformity; (4) lack of a means by which the extent of conformity in one situation can be compared with that in another; (5) inequality of “telic” units. As an alternative treatment of such data, the method of higher moments is suggested and rationalized. Data from Allport and Solomon are reworked by this method and results compared.
The Scaling of Test Scores by the Method of Paired Comparisons
Authors: Grossnickle Louise T.
Published: January 2006

The purpose of this study is to investigate, by the method of paired comparisons, a possible scaling of individuals who have made certain test scores, such that the additive property will be satisfied and such that a stability in scaling will be maintained,—in other words, a scaling such that the scaled score of an individual will remain relatively the same regardless of the grouping of individuals in which he may be placed. The results show that it is possible to utilize psychophysical methods in psychological and educational test situations. Among the major findings are that Case V of the Law of Comparative Judgment is applicable to the data in this problem, the method of dividing the intermediate category equally between the greater and the less was the best of three possible methods, internal consistency was satisfied, and, finally, when a new test of stability was applied, it was found that the distances between the hypothetical individuals remain the same.
A Method of Estimating Accuracy of Test Scoring
Authors: Deemer Walter L.
Published: January 2006

When errors of test scoring obey a Poisson frequency law (theoretical considerations suggest that they do), the method described may be used for finding the upper fiducial limits of scoring errors per paper. A criterion is suggested for establishing tolerance limits on scoring errors, and a method is given (1) for finding the probability of being wrong in the statement that the tolerance limit is being met for a given size sample or (2) for finding the size of sample that will make this probability not greater than some fixed value.
Why do People Factor?
Authors: Holzinger Karl J.
Published: January 2006

This is a very simple explanation of factor analysis primarily for the “factorial layman.” The interpretation of factors and the comparisons of various factor solutions are illustrated with a hypothetical example so designed that the reader can visualize all the relationships in a two-dimensional graph.
Note on the Relationship between Internal Consistency and Test-Retest Estimates of the Reliability of a Test
Authors: Jackson Robert W. B.
Published: January 2006

A comparison of the “test-retest” and “internal consistency” estimates of reliability coefficients is given, and it is shown that the two methods give different results. Application of the analysis of variance and covariance method reveals that there is not just one but a number of reliability coefficients involved, and that an estimate of each of these may be obtained. The analysis shows that in using the test-retest method the error or remainder effects are not independent on the two trials, possibly because the individuals remember the items and their responses to them on the previous trial.
An Analysis of Learning Data Which Distinguishes Between Initial Preference and Learning Ability
Authors: Gulliksen Harold
Published: January 2006

Several sets of learning data furnished by I. Krechevsky have been analyzed in terms of meaningful parameters of the learning curve, and the changes in the frequency distributions of these parameters with changes in the experimental conditions have been studied. One of the parameters represents the animal's initial preference for the light or dark, the other represents learning ability. The analysis shows that destruction of about ten or fifteen per cent. of the cortex, increases the animal's preference for the light and decreases the learning ability slightly. By ordinary methods of analysis, it is not possible to discover that both initial preference and learning ability have been changed by any given factor.
A General Factor in Improvement with Practice
Authors: Heese K. W.
Published: January 2006

Results of 10 trials on 6 tests for 50 subjects were analyzed, first, by applying the centroid method to actual improvement or practice scores and, second, by applying a formula developed by Woodrow for determining factor loadings for practice scores from the differences between factor loadings of initial and final scores. Contrary to expectation, the two methods yielded discrepant results, for the explanation of which a hypothesis is advanced. The operation of a general factor was not demonstrated. Tentative interpretations of the factors extracted by the centroid method are offered.
A Factorial Study of Auditory Function
Authors: Karlin J. E.
Published: January 2006

Tests of auditory function in the fields of pitch, loudness, quality (timbre), and time, auditory analysis, synthesis, and memory, together with age, intelligence, and four tests of visual memory, were studied factorially. The subjects were 200 high-school students. The intercorrelations were factored to nine factors by a modification of the centroid technique and rotated to an oblique simple structure. No general auditory factor appeared. Instead there appeared group factors tentatively identified as pitch-quality discrimination, loudness discrimination, “auditory integral for perceptual mass,” auditory resistance (synthesis and analysis), speed of closure, auditory span formation, memory span (auditory and visual), memory or incidental closure and an unidentifiable residual plane. The average intercorrelation among the primary vectors was low, only one intercorrelation being greater than .34. A number of queries are answered by the interpretation of the results.
Derivation and Application of a Unit Scoring System for the Strong Vocational Interest Blank for Women
Authors: Harper Bertha P. , Dunlap Jack W.
Published: January 2006

Scoring keys, based upon unit weights, were made up for fourteen occupations of the Strong Vocational Interest Blank for Women. The study here presented of scores obtained in using these keys, in comparison with scores obtained from Dr. Strong's keys, indicates, for 551 women at the University of Rochester, that the new, unit-weighted keys are valid for all practical purposes and make possible a great saving in scoring time.
On the Interpretation of Common Factors: A Criticism and a Statement
Authors: Reyburn H. A. , Taylor J. G.
Published: January 2006

The concept of simple structure is criticized for lack of objectivity and for failure to produce invariance of (a) factor loadings under change of battery, and (b) individual scores on primary traits under change of tests. It is also criticized on the grounds that simple structure yields at best the factors which were put in and that, by suitable manipulation of tests, any set of factors may be represented in a battery by tests which will yield a simple structure. A procedure for rotation is developed which locates the first rotated axis to pass through a cluster of tests which, by hypothesis, contain a common factor and to project all tests into a hyperplane orthogonal to this factor. The second factor is then located to pass through the projections of a second cluster of tests defining the second factor, and so on, until all hypothecated factors have been located. Any residual interrelations may then be rotated graphically to the most plausible arrangement.
Contributions to the Theory of Human Relations: VII. Outline of a Mathematical Theory of the Sizes of Cities
Authors: Rashevsky N.
Published: January 2006

In generalization of a previous study, a mathematical approach to the theory of the average size of cities as well as of the distribution of city sizes is outlined.
A Coefficient of Imbalance for Content Analysis
Authors: Janis Irving L. , Fadner Raymond H.
Published: January 2006

This article presents a Coefficient of Imbalance applicable to any type of communication that may be classified into favorable content, unfavorable content, neutral content, and non-relevant content. The combined influence of the average presentation of relevant content and the average presentation of total content is reduced to two components, the coefficients of favorable imbalance and of unfavorable imbalance. A precise definition of imbalance is developed and measured against ten criteria.
An Exact Test of Significance for Means of Samples Drawn from Populations with an Exponential Frequency Distribution
Authors: Festinger Leon
Published: January 2006

The mathematical derivation of a test for determining the fiducial limits of, and significance of difference between, means when the samples are drawn from exponential populations is presented. The test for differences between means takes the particularly simple form of the F test (the ratio of the larger to the smaller mean) with each mean possessed of 2n degrees of freedom, n being the number of cases in the sample. Random sampling, a range of scores upwards from a lower limit of zero, and independence of means from each other are necessary assumptions for the use of the test. Examples of situations in which the test should be used are given, together with a description of the necessary computational procedures. Comparisons of the results of the application of this test with the erroneous application of the critical ratio on actual data show that rather large discrepancies exist between the two tests. Results obtained by applying tests which assume normality to exponential distributions are subject to much error.
On the Reliability of a Weighted Composite
Authors: Mosier Charles I.
Published: January 2006

A general formula for the reliability of a weighted composite has been derived by which that reliability can be estimated from a knowledge of the weights whatever their source, reliabilities, dispersions, and intercorrelations of the components. The Spearman-Brown formula has been shown to be a special case of the general statement. The effect of the internal consistency or intercorrelation of the components has been investigated and the conditions defining the set of weights yielding maximum reliability shown to be that the weight of a component is proportional to the sum of its intercorrelations with the remaining components and inversely proportional to its error variance.
Multiple Rectilinear Prediction and the Resolution into Components: II
Authors: Guttman Louis , Cohen Jozef
Published: January 2006

Given a battery of n tests that has already been resolved into r orthogonal common factors and n unique factors, procedures are outlined for computing the following types of linear multiple regressions directly from the factor loadings: (i) the regression of any one test on the n−1 remaining tests; (ii) all the n different regressions of order n−1 for the n tests, computed simultaneously; (iii) the regression of any common factor on the n tests; (iv) the regressions of all the common factors on the n tests computed simultaneously; (v) the regression of any unique factor on the n tests; (vi) the regressions of all the unique factors on the n tests, computed simultaneously. Multiple and partial correlations are then determined by ordinary formulas from the regression coefficients. A worksheet with explicit instructions is provided, with a completely worked out example. Computing these regressions directly from the factor loadings is a labor-saving device, the efficiency of which increases as the number of tests increases. The amount of labor depends essentially on the number of common factors. This is in contrast to computations based on the original test intercorrelations, where the amount of labor increases more than proportionately as the number of tests increases. The procedures evaluate formulas developed in a previous paper (2). They are based essentially on a shortened way of computing the inverse of the test intercorrelation matrix by use of the factor loadings.
A Preferential Matching Problem
Authors: Greenwood J. A.
Published: January 2006

A matching method proposed by Dr. C. E. Stuart is presented in some detail and the essentials for a test of significance are derived. This method differs from the older matching methods in that partial credit is allowed for a near miss. A slight variation of the method permits the matching of one item with M sets of n traits.
A Statistical Test for Means of Samples from Skew Populations
Authors: Festinger Leon
Published: January 2006

This paper presents a test for determining significance of differences between means of samples which are drawn from positively skewed populations, more specifically, those having a Pearson Type III distribution function. The quantity 2npxg/xp (where p equals the mean squared divided by the variance and n is the number of cases in the sample), which distributes itself as Chi Square for 2np degrees of freedom, may be referred to the tables of Chi Square for testing hypotheses about the value of the true mean. For two independent samples, the larger mean divided by the smaller mean, which distributes itself as F for 2n1p1 and 2n2p2 degrees of freedom, may be referred to the F distribution tables for testing significance of difference between means. The test assumes that the range of possible scores is from zero to infinity. When a lower theoretical score limit (c) exists which is not zero, the quantity (Mean − c) should be used instead of the mean in all calculations.
The Significance of Rank difference Coefficients of Correlation
Authors: Thornton G. R.
Published: January 2006

The coefficients of rank difference correlation that are barely significant at six different levels of significance are given for N's of 2 to 30. Most of the values were obtained by translation of Olds' tables of probabilities for various values of Σd2. Comparison of these data with those obtained by four other methods indicates that one method yields values more appropriate than those obtained from Olds' data for coefficients significant at the .01 level for N's from 11 to 25. This method also provides a convenient means of obtaining approximate values of coefficients significant at the .01 level for N's above 30. Need for caution in evaluating the significance of coefficients obtained from data involving tie rankings is indicated. The article concludes with recommendations as to choice of methods of determining the significance of rank difference coefficients.
The Concept of Test and Item Reliability in Relation to Factor Pattern
Authors: Wherry Robert J. , Gaylord Richard H.
Published: January 2006

It is shown that approaches other than the internal consistency method of estimating test reliability are either less satisfactory or lead to the same general results. The commonly attendant assumption of a single factor throughout the test items is challenged, however. The consideration of a test made up of K sub-tests each composed of a different orthogonal factor disclosed that the assumption of a single factor produced an erroneous estimate of reliability with a ratio of (n−K)/(n−1) to the correct estimate. Special difficulties arising from this error in application of current techniques to short tests or to test batteries are discussed. Application of this same multi-factor concept to item-analysis discloses similar difficulties in that field. The item-test coefficient approaches √1/K as an upper limit rather than 1.00 and approaches √1/n as a lower limit rather than .00. This latter finding accounts for an over-estimation error in the Kuder-Richardson formula (8). A new method of isolating sub-tests based upon the item-test coefficient is proposed and tentatively outlined. Either this new method or a complete factor analysis is regarded as the only proper approach to the problem of test reliability, and the item-sub-est coefficient is similarly recommended as the proper approach for item analysis.
General Theory and Methods for Matric Factoring
Authors: Guttman Louis
Published: January 2006

Methods are developed for factoring an arbitrary rectangular matrix S of rank r into the form FP, where F has r columns and P has r rows. For the statistical problem of factor analysis, S may be the score matrix of a population of individuals on a battery of tests. Then F is a matrix of factor loadings, P is a matrix of factor scores, and r is the number of factor variates. (As in current procedures, there remains a subsequent problem of rotation of axes and interpretation of factors, which is not discussed here.) Methods are also developed for factoring an arbitrary Gramian matrix G of rank r into the form FF′, where F has r columns and F′ denotes F transposed. For the statistical problem of factor analysis, G may be the matrix of intercorrelations, R, of a battery of tests, with unity, communalities, or other parameters in the principal diagonal. R is proportional to SS′, and it is shown that S can be factored by factoring R. This may usually be the most economical procedure in practice; it should not be overlooked, however, that S can be factored directly. The general methods build up an F (and P) in as many stages as desired; as many factors as may be deemed computationally practical can be extracted at a time. Perhaps it will usually be found convenient to extract not more than three factors at a time. Current procedures, like the centroid and principal axes, are special cases of a general method presented here for extracting one factor at a time.
Interrelationships of Number-Correct and Limen Scores for an Amount-Limit Test
Authors: Lorr Maurice
Published: January 2006

For an amount-limit test homogeneous as to content and varied as to difficulty it is established that an individual's number-right score and his limen score as estimated by the constant process are mathematically related. The experimental and the theoretic relationship between normal deviate and limen score are shown to be in good agreement. It is also found that the two methods of evaluating individual test performance yield equally reliable sets of scores for the procedures used. Accordingly where the assumptions basic to the relationship obtain, the more conveniently computed raw score may be considered to be as valid and reliable an index of individual test performance as the limen score. The concept of the dispersion parameter of the individual as a measure of change or error in test score found no experimental verification. Estimates of individual variability are unrelated to differences in score on equivalent forms.
The Application of Probit Analysis to the Results of Mental Tests
Authors: Finney D. J.
Published: January 2006

The application of the Müller-Urban constant process to item selection, as considered in a recent paper in this journal, is shown to be closely analogous to a method now in general use for the analysis of insecticidal and other toxicological tests. This method of probit analysis gives the maximum likelihood estimates of the unknown parameters and, with the aid of published tables, the necessary computations can be rapidly performed. The present paper contains an outline of the method and an illustration of the most convenient form of computations for use in analyses of psychometric data.
The Determination of Successive Principal Components Without Computation of Tables of Residual Correlation Coefficients
Authors: Tucker Ledyard R.
Published: January 2006

A procedure is presented for determining the successive principal components of a correlation matrix where it is not necessary to compute the successive tables of residual correlations. The original correlation matrix is bordered with a new row and column for each principal component that is determined.
Factoring Test Scores and Implications for the Method of Averages
Authors: Holzinger Karl J.
Published: January 2006

The general procedure and detailed steps for attaining complete factor analyses of scores are presented. Both orthogonal and oblique factors are considered. It is shown that a single average by conventional procedure gives an incomplete summarization of the data when the rank exceeds one. There should be as many averages as there are common factors.
The Interpretation of a Test Validity Coefficient in Terms of Increased Efficiency of a Selected Group of Personnel
Authors: Richardson Marion W.
Published: January 2006

The predictive efficiency of a test used to select personnel is defined in terms of total effectiveness of the group thus selected, as compared with chance selection. The formula developed requires the use of an estimate of the ratio of average effectiveness of men selected to the average effectiveness of men not selected by the test. The predictive efficiency of the test varies directly with the magnitude of this ratio and also directly with the percentage rejected.
A Simple Method of Factor Analysis
Authors: Holzinger Karl J.
Published: January 2006

A simple method for extracting correlated factors simultaneously is described. The method is based on the idea that the centroid pattern coefficients for the sections of unit rank of the complete matrix may be interpreted as structure values for the entire matrix. Only the routine centroid average process is required.
Maximal Weighting of Qualitative Data
Authors: Wherry Robert J.
Published: January 2006

A method whereby biographical or other questionnaire data of a purely qualitative nature may be used to predict success or failure on an independent criterion is presented. The method is not new but the present least-squares derivation and the transformation equation for punched card coding were not available in the literature. The proper weights are found to be proportional to the per cent of passers in the various categories. The method is suggested as a suitable substitute for non-linear approaches in connection with purely quantitative data as well. The implications of reweighting in connection with multiple regression is discussed. The lavish use of degrees of freedom makes cross-validation extremely desirable.
“Parallel Proportional Profiles” and other Principles for Determining the Choice of Factors by Rotation
Authors: Cattell Raymond B.
Published: January 2006

The choosing of a set of factors likely to correspond to the real psychological unitary traits in a situation usually reduces to finding a satisfactory rotation in a Thurstone centroid analysis. Seven principles, three of which are new, are described whereby rotation may be determined and/or judged. It is argued that the most fundamental is the principle of “parallel proportional profiles” or “simultaneous simple structure.” A mathematical proof of the uniqueness of determination by this means is attempted and equations are suggested for discovering the unique position.
Some Examples of Multivariate Analysis in Educational and Psychological Research
Authors: Tyler Fred T.
Published: January 2006

This paper provides the formulas necessary for testing the significance of the differences between mean values of different multivariate normal populations by Hotelling's generalization of “Student'” ratio. It also indicates the methods, proposed by Mahalanobis, and by Rao, of classifying different multivariate populations and individuals. The methods are illustrated by means of personality test data obtained from students preparing for the General Elementary and the General Secondary Teaching Credentials.
The Rolling Totals Method of Computing Sums, Sums of Squares, and Sums of Cross-Products
Authors: Ayers J. Douglas , Stanley J. Perham
Published: January 2006

The rolling totals method of computing sums, sums of squares, and sums of cross-products appears to have several advantages over usual methods, in that it saves time and requires less equipment. Only an IBM sorter and a tabulator equipped with Card Cycle Total Transfer Device are used. The method provides an immediate independent visual check on the accuracy of the sums of cross-products of each successive variable as it is run. Since controlling is done by sorting, the necessity for re-wiring after each run on the tabulator is eliminated. The wiring, illustrated by a diagram, is simple and straightforward.
On the Economies of a Pre-Screening Technique for Aptitude Test Batteries
Authors: Arbous A. G. , Sichel H. S.
Published: January 2006

Test battery selection is justified on the grounds that it is more efficient than the conventional methods. More precise definitions of efficiency have shown that the additional cost of test administration can often outweigh the gains of selecting a more competent group of persons. Final evaluation of the profit and loss account can be made only when no further economies can be effected in the selection procedures themselves. A psychometric pre-screening technique which will reduce this cost considerably is developed here. Its psychometric structure is mathematically defined, and its advantages illustrated in terms of testing economy (E) and losses (L) of good material for different selection ratios (S.R.). It is shown that, under many circumstances, the testing economy can be considerable, and that in all practical cases “Losses” will be ≤ 1.5% for all values of ρ ≥ .8 (between the pre-screening test and the final battery). The technique in practice is illustrated from a set of data.
Efficiency of Multiple-Choice Tests as a Function of Spread of Item Difficulties
Authors: Cronbach Lee J. , Warrington Willard G.
Published: January 2006

The validity of a univocal multiple-choice test is determined for varying distributions of item difficulty and varying degrees of item precision. Validity is a function of σd2 + σy2, where σd measures item unreliability and σy measures the spread of item difficulties. When this variance is very small, validity is high for one optimum cutting score, but the test gives relatively little valid information for other cutting scores. As this variance increases, eta increases up to a certain point, and then begins to decrease. Screening validity at the optimum cutting score declines as this variance increases, but the test becomes much more flexible, maintaining the same validity for a wide range of cutting scores. For items of the type ordinarily used in psychological tests, the test with uniform item difficulty gives greater over-all validity, and superior validity for most cutting scores, compared to a test with a range of item difficulties. When a multiple-choice test is intended to reject the poorest F per cent of the men tested, items should on the average be located at or above the threshold for men whose true ability is at the Fth percentile.
An Internal Consistency Check for Scale Values Determined by the Method of Successive Intervals
Authors: Edwards Allen L. , Thurstone L. L.
Published: January 2006

The method of successive intervals is a psychological scaling procedure in which stimuli are classified into successive intervals according to the degree of some defined attribute which they are judged to possess. A psychological continuum is defined and the scale values are then taken as the medians of the distributions of judgments on the psychological continuum. It is assumed that the distributions of judgments for each stimulus are normal on the psychological continuum as defined.

An internal consistency check indicates that the cumulative distributions of empirical judgments for the various stimuli can be reproduced by means of a limited number of parameters with an average error that compares favorably with that usually reported for paired comparison data. Furthermore, the scale values obtained by successive interval scaling, for the data reported, are shown to be linearly related to those obtained by the method of paired comparisons.
The Selective Efficiency of a Test Battery
Authors: Sichel Herbert S.
Published: January 2006

In industrial acceptance sampling one frequently makes use of operating characteristic curves to describe the discriminating power of a particular sampling plan. Similarly, it is possible to demonstrate the selective efficiency of a test battery in terms of (a) the Applicant's Operating Characteristic (A.O.C.); (b) the Selector's Operating Characteristic (S.O.C.). The A.O.C. determines the chance of selection by means of a test for any given level of true ability. The S.O.C. connects functionally probability of success on the criterion with the predictor scores of a battery. For the case of a normal bivariate distribution the exact mathematical expressions of the OC curves are derived in terms of the correlation coefficient ρ, the cut-off points α and β, and the predictor and criterion scores X and Y (in standard measures). The Efficiency Index H is defined as the percentage of successful subjects gained by the use of a test battery, taking chance selection as a yardstick for comparison. Its optimum, for fixed ρ and α, is derived. The distribution law of the criterion scores of selectees is deduced and its first four moments are shown to depart little from normality for cases usually encountered in practice. A “Quality-Gainae” diagram graphically illustrates the improvements secured. Another simple device, the “Cost-Utility” diagram, explains to management the full implications of selecting personnel by means of a test battery. Neither of the diagrams requires an understanding of the correlation coefficient. The confidence belt of the OC curves, the standard error of the mean criterion score of selectees and the standard error of the predicted number of successful applicants are determined. Finally, the full theory is applied in detail to a real test battery.
Note on the Computation of Biserial Correlations in Item Analysis
Authors: Siegel Laurence , Cureton Edward E.
Published: January 2006

A rapid method is described for machine computation of biserial correlations in item analysis with several criteria. This method has been found to yield biserial correlations from punched IBM cards at the rate of about 41 per hour.
A Factorial Study of Temperament
Authors: Baehr Melany E.
Published: January 2006

The theory is advanced that personality factors obtained in the first order may often represent combinations of temperament traits that occur in the experimental population. Under these circumstances an investigation of the second order represents a purification process and yields factors which represent the more basic or pervasive characteristics of the original behavior items included in the factorial study. These second-order factors can be obtained directly in the first order by a careful selection of the variables which enter into the analysis. A second-order analysis was undertaken of the nine factors inherent in three of J. P. Guilford's inventories, and four clearly interpretable second-order factors were obtained. Three of these factors were obtained directly in the first order in a new factorial study of twenty-two behavior items. Attention is drawn to the similarities between these factors and traits of temperament postulated by an independent investigator.
Mathematical Structures and Psychological Measurements
Authors: Weitzenhoffer André M.
Published: January 2006

The nature of psychological measurements in relation to mathematical structures and representations is examined. Some very general notions concerning algebras and systems are introduced and applied to physical and number systems, and to measurement theory. It is shown that the classical intensive and extensive dimensions of measurements with their respective ordinal and additive scales are not adequate to describe physical events without the introduction of the notions of dimensional units and of dimensional homogeneity. It is also shown that in the absence of these notions, the resulting systems of magnitudes have only a very restricted kind of isomorphism with the real number system, and hence have little or no mathematical representations. An alternative in the form of an extended theory of measurements is developed. A third dimension of measurement, the supra-extensive dimension, is introduced; and a new scale, the multiplicative scale, is associated with it. It is shown that supra-extensive magnitudes do constitute systems isomorphic with the system of real numbers and that they alone can be given mathematical representations. Physical quantities are supra-extensive magnitudes. In contrast, to date, psychological quantities are either intensive or extensive, but never of the third kind. This, it is felt, is the reason why mathematical representations have been few and without success in psychology as contrasted to the physical sciences. In particular, the Weber-Fechner relation is examined and shown to be invalid in two respects. It is concluded that the construction of multiplicative scales in psychology, or the equivalent use of dimensional analysis, alone will enable the development of fruitful mathematical theories in this area of investigation.
Estimation of the Reliability of Ratings
Authors: Ebel Robert L.
Published: January 2006

A procedure for estimating the reliability of sets of ratings, test scores, or other measures is described and illustrated. This procedure, based upon analysis of variance, may be applied both in the special case where a complete set of ratings from each of k sources is available for each of n subjects, and in the general case where k1, k2, ..., kn ratings are available for each of the n subjects. It may be used to obtain either a unique estimate or a confidence interval for the reliability of either the component ratings or their averages. The relations of this procedure to others intended to serve the same purpose are considered algebraically and illustrated numerically.
The Comparability of Scores from Three Mathematics Tests of the College Entrance Examination Board
Authors: Schultz Douglas G.
Published: January 2006

Scores from three mathematics tests of the College Entrance Examination Board were examined in order to determine the effect on the scores of (1) choice of test, (2) amount of training in mathematics, and (3) recency of training in mathematics. Groups of candidates were paired in a number of comparisons and matched by means of a regression technique which is described. On the average, students of similar ability made comparable scores on the mathematical section of the Scholastic Aptitude Test and on the Comprehensive Mathematics Test. The scores of candidates who took the Intermediate Mathematics Test averaged substantially higher than those of comparable students who took either of the other two tests. A greater amount of mathematical training and more recent training were both found to be positively related to scores on the mathematical section of the Scholastic Aptitude Test and on the Intermediate Mathematics Test, but the effect of recency appeared to be less than one might expect.
Maximizing Predictive Efficiency for a Fixed Total Testing Time
Authors: Taylor Calvin W.
Published: January 2006

For any fixed total time of testing it is possible, through proper item-and-time allotment, to combine tests into a battery so that the multiple correlation with a pre-assigned criterion will be maximized. By holding constant the ratio of the length in number of items to the time length for each test, a set of general equations has been derived which will yield this maximum value of the multiple R and will enable one to determine, in any given case, the optimal fraction of total testing time that should be devoted to each type of test under consideration. The set of general equations is applied to a two-test-battery problem to obtain the optimal length of each type of test for one hour total testing time. If two other tests had been selected for the two-test sample problem, different subdivisions of the total time would generally occur. The manner in which the results would change when using other tests with different initial reliability, validity, and intercorrelation values is briefly presented. Some general implications of this method of battery development are also discussed.
Predicted Differences and Differences between Predictions
Authors: Mollenkopf William G.
Published: January 2006

When K tests are given to N individuals, and for each individual there are two criterion measures, then (1) the multiple regression weight to be applied to the standard score for each test to predict the criterion-difference score equals the difference of the weights for predicting each criterion separately; (2) the difference between the predicted scores equals the predicted difference (each test being assigned the appropriate multiple regression weight); (3) the square of the multiple correlation between predicted and actual criterion-difference scores equals the sum of squares of the multiple correlations of the battery with each criterion less the product of these correlations and the correlation between predicted scores all divided by twice the quantity one minus the criterion intercorrelation; and (4) the variance of errors of estimating the criterion-difference score equals the sum of the variances of errors of estimating each criterion score minus twice the criterion intercorrelation, plus twice the correlation between predicted scores multiplied by the product of the square root of one minus the variance of errors of estimating one criterion and the corresponding square root for the second criterion.
Factor Analysis Calculations by Tabulating Machines
Authors: Hall D. M. , Welker E. L. , Crawford Isabelle
Published: January 2006

I.B.M. tabulating equipment can be of considerable help in reducing the time and increasing the accuracy of multiple factor analysis, even if used for only a part of the calculations. Once the plugboard is wired and those cards punched which are used over and over again, problems involving any number of variables can be handled with dispatch. The correlation matrix is listed, the totals verified, and the signs changed on the tabulator. Then the factors and the residual coefficients are calculated by means of a calculator. Tucker's procedure has been modified by using a calculator instead of a multiplying punch, by reducing the number of cards used, by simplifying checks on calculations, by simplifying plugboard wiring, and by preparing work sheets on tabulator paper. Extraction of factors from 24 variables at the rate of one in four hour's time seems to justify the use of the tabulating equipment on small problems.
Factorial Design and Covariance in the Study of Individual Educational Development
Authors: Johnson Palmer O. , Tsao Fei
Published: January 2006

This is the report of the application of the principles of factorial design to an investigation of individual educational development. The specific type of factorial design formulated was a 2 Χ 3 Χ 3 Χ 3 arrangement, that is, the effect of sex, grade location, scholastic standing, and individual order, singly and in all possible combinations was studied in relation to educational development as measured by the Iowa Tests of Educational Development. An application of the covariance method was introduced which resulted in increased precision of this type of experimental design by significantly reducing experimental error. The two concomitant measures used to increase the sensitiveness of the experiment were initial status of individual development and mental age. Without these statistical controls all main effects and two first-order interactions would have been accepted as significant. With their use only sex (doubtful), scholastic standing, and individual order demonstrated significant effects. The chief beauty of the analysis of variance and covariance as an integral part of a self-contained experiment is demonstrated in the complete single analysis of the data. The statistical utilization of the experimental results has also been developed for purposes of estimation and prediction. The mathematical statistician is being continuously required to develop and analyze experimental designs of increasing complexity since the introduction of the analysis of variance and covariance. The mathematical formulation and solution of the problem of this investigation is carried out. The methods illustrated and explained in this study, and modifications and extensions of them are capable of very wide application. The general principles can be used to various degrees and in a number of ways.
A Factorial Analysis of Olfaction
Authors: Hsü E. H.
Published: January 2006

Twenty-one reagents were rated on a pleasantness scale by 182 subjects. The tetrachoric correlation coefficients were determined for the variables. The correlation matrix thus obtained was subjected to a Thurstone analysis which gave rise to a 6-dimensional structure. Two of these were not clear-cut, and the last one appeared to be a residual factor. One factor, the benzene-ketone, revealed the chemical property of unsaturation and the physiological quality of possible trigeminal stimulation. The other two factors were marked by the presence of oxygen and nitrogen, respectively, and were tentatively labelled as a plant factor and an animal factor accordingly. The intercorrelations of the primaries are high.
Graphical and Tabular Aids for Determining Sample Size When Planning Experiments Which Involve Comparisons of Percentages
Authors: Swineford Frances
Published: January 2006

When one knows in advance the minimum percentage difference which will be of practical interest in an investigation, principles of economy suggest the desirability of an accurate estimate of the size of the sample to be used. Charts are presented which eliminate any computation where the two groups involved are to be equal. A table is included for the case where one group will be from one to three times the size of the other. The charts are also useful for determining whether or not obtained differences are statistically significant at the 5 per cent or the 1 per cent level.
A New Descriptive Statistic: The Parabolic Correlation Coefficient
Authors: Peters Charles C.
Published: January 2006

This article proposes a new descriptive statistic related to the second order parabola in the same manner in which the familiar correlation coefficient is related to the regression coefficient. The parabolic r describes in standard terms simultaneously the general trend of the regression and the extent and nature of its curvilinearity, and is relatively easy to compute and easy to communicate. Formulas for its standard error and its limits are derived and it is applied to a number of regressions.
The Orthogonal Approximation of an Oblique Structure in Factor Analysis
Authors: Green Bert F.
Published: January 2006

A procedure is derived for obtaining an orthogonal transformation which most nearly transforms one given matrix into another given matrix, according to some least-squares criterion of fit. From this procedure, three analytic methods are derived for obtaining an orthogonal factor matrix which closely approximates a given oblique factor matrix. The case is considered of approximating a specified subset of oblique vectors by orthogonal vectors.
A Single Plane Method of Rotation
Authors: Thurstone L. L.
Published: January 2006

The method of rotation described here is applied to one hyperplane at a time. The method seems to be simple and quite effective and it can be applied by a relatively inexperienced computer. The method does not postulate a positive manifold, and hence it is applicable also to bipolar factors.
Ultimate Choice between two Attractive Goals: Predictions from a Model
Authors: Mosteller Frederick , Tatsuoka Maurice
Published: January 2006

A mathematical model for two-choice behavior in situations where both choices are desirable is discussed. According to the model, one or the other choice is ultimately preferred, and a functional equation is given for the fraction of the population ultimately preferring a given choice. The solution depends upon the learning rates and upon the initial probabilities of the choices. Several techniques for approximating the solution of this functional equation are described. One of these leads to an explicit formula that gives good accuracy. This solution can be generalized to the two-armed bandit problem with partial reinforcement in each arm, or the equivalent T-maze problem. Another suggests good ways to program the calculations for a high-speed computer.
A Criterion for Selecting Variables in a Regression Analysis
Authors: Linhart H.
Published: January 2006

Methods are given for deciding whether to use some or no predictor variables in a regression analysis. Previously obtained results on the more general problem, whether to use k or k − r predictor variables are reviewed with emphasis on applications.