The rolling totals method of computing sums,sums of squares,and sums of cross-products

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.ABITIBI POWER AND PAPER COMPANY     

The calculation of sums of squares for interactions in the analysis of variance

A method is described for the calculation of the sum of squares for a second-order interaction. It is then shown that the method is general and can be used for the calculation of the sum of squares for any higher-order interaction.     

IBM computation of sums of products for positive and negative numbers

The wiring of the plugboard of the IBM type 405 machine for the computation of sums of squares and cross products of positive and negative numbers is described. The method makes greater demands on the X distributor and class selector capacity of the machine than does the method of wiring the plugboard when the numbers all have the same sign.WORLD BOOK COMPANY     

A simplified method for approximating multiple regression coefficients

A method of exhaustion has been described for calculating regression coefficients. This method dispenses with the solution of simultaneous equations but utilizes a process of successive extraction in obtaining's, where each successive is maximized. This procedure permits the worker to discard as he goes along those weights which are deemed unsatisfactory for purposes of prediction. The coefficients and theR in a problem involving a criterion and six independent variables were calculated in sixty minutes. TheR's obtained by this method are smaller than those yielded by the Doolittle technique, but in problems which have been considered this discrepancy has not exceeded .05.     

Emotion-based learning on a simplified card game: the Iowa and Bangor Gambling Tasks

The Iowa Gambling Task (IGT) has been widely used in the assessment of neurological patients with frontal lesions. Emphasis has been placed on the complexity of the task (i.e., four decks of varying contingency pattern) with the suggestion that the participant must use emotion-based learning to deal with a complex decision-making process. The present study used a single deck card game (the Bangor Gambling Task, BGT), matched in many respects with the Iowa Gambling Task, in which the contingencies varied over time (gradually becoming worse for the participant) rather than across deck (as in the IGT). Forty participants performed both tasks. Performance on the tasks showed many similarities, with participants showing a comparable pattern of incremental learning on both tasks, reaching an analogous final level of performance. More importantly, there was a high correlation (r(2) = .93) in performance between the two tasks, the most salient feature of which was that virtually every participant who fell below categorisation of impaired IGT performance, also did very poorly on the BGT. These findings bear on the question of whether arguments about the 'complexity' of the Iowa Gambling Task necessarily explain why it appears to require emotion-based learning. The Bangor Gambling Task might also be a useful tool for clinical neuropsychologists, in the assessment of patients with executive dysfunction-given that the task is easier and quicker to administer than the Iowa Gambling Task, but appears to share the same performance features.     

Inconsistent communication: A simplified method for selecting messages

In examining the family's role in the development and perpetuation of disordered behavior, studies of inconsistent communication have focused on the frequency and impact of such communications in disturbed versus non-disturbed groups. For these and other lines of study, current methods for defining and selecting inconsistent messages are extremely time-consuming, and as a result, large-scale efforts have been discouraged. To address this problem, the current study attempted to develop and evaluate an efficient procedure for selecting inconsistent communications which would be comparable to the standard method. Most important, it was found that raters are capable of accurately judging affect in a particular channel when presented with several channels simultaneously, and as such, it is unnecessary to artificially separate channels when affect ratings are to be obtained. Future research should be facilitated by the method developed in the current study.     

A method of determining unbiased distribution in the latin square

The paper describes a method of constructing Latin-square designs in which treatment sequences are unbiased with regard to serial order as well as position of treatment. The procedure is useful for those Latin squares in which the number of cells in each column (or row) is an even number, which, when written in ascending and descending series, contain corresponding ordered numbers prime to each other. Such numbers are 2, 4, 6, 10, 12, 16, 18, 22, 28, 30, 36, etc.     

A psychophysical method for determining the effect of studded tires on safety

A method was presented for determining the safety effect of studded tires independently of other driver and vehicle centered variables which covariate with the use of studs. It is based on psychophysical functions between the friction coefficient and accident risk, or driver behavior, separately produced for studded and unstudded cars. From the two functions, the effect of studded tires can be calculated at different levels of friction as far as the respective effect of studs on friction is known. A pilot study was conducted concerning the risk of skidding in a curve. The friction coefficient was periodically measured on an off-ramp of a motorway and, for each passing car, the spot speed and the use of studs was recorded. The probability of skidding, calculated from the distribution of safety margins, was plotted as a function of friction and the effects of studded tires and other driver and vehicle centered variables were demonstrated.     

The incremental priming technique: A method for determining within-condition priming effects

A novel priming technique is applied in two experiments using an alphabetic decision and a lexical decision task to study effects of repetition, and form-related priming on letter and word recognition. The incremental priming technique consists of a gradual increase of the prime’s informational value (operationalized as prime intensity). The minimum prime-intensity level serves as a within-condition baseline for each priming condition. Thus, we can define any priming effect with respect to two baseline conditions: one is the minimum-intensity condition of the particular priming condition (within-condition baseline), and the other is a different priming condition (across-condition baseline). This double-baseline approach makes measuring of priming effects more reliable and imposes stronger constraints on our interpretations of these effects.     

Item synonymization: A method for determining the total meaning of pencil-paper reactions

Items have been studied heretofore for their value as elements of particular tests to the neglect of more fundamental research into the multiple potentiality of items. This article proposes a method of grouping items into synonymies comprising all of the items which correlate with a given key item. These synonymies can be used for interpretation of the total meaning of the key item: (1) by inspection of the constituent items and (2) by correlational study of obtained single scores of individual persons. The method is illustrated by four items with inter- and intra-correlations, and characteristics of an ideal background reservoir of items are pointed out.     

A simplified version of the maximum information per time unit method in computerized adaptive testing

In this article, we propose a simplified version of the maximum information per time unit method (MIT; Fan, Wang, Chang, & Douglas, Journal of Educational and Behavioral Statistics 37: 655–670, 2012), or MIT-S, for computerized adaptive testing. Unlike the original MIT method, the proposed MIT-S method does not require fitting a response time model to the individual-level response time data. It is also computationally efficient. The performance of the MIT-S method was compared against that of the maximum information (MI) method in terms of measurement precision, testing time saving, and item pool usage under various item response theory (IRT) models. The results indicated that when the underlying IRT model is the two- or three-parameter logistic model, the MIT-S method maintains measurement precision and saves testing time. It performs similarly to the MI method in exposure control; both result in highly skewed item exposure distributions, due to heavy reliance on the highly discriminating items. If the underlying model is the one-parameter logistic (1PL) model, the MIT-S method maintains the measurement precision and saves a considerable amount of testing time. However, its heavy reliance on time-saving items leads to a highly skewed item exposure distribution. This weakness can be ameliorated by using randomesque exposure control, which successfully balances the item pool usage. Overall, the MIT-S method with randomesque exposure control is recommended for achieving better testing efficiency while maintaining measurement precision and balanced item pool usage when the underlying IRT model is 1PL.     

The regression equation method of determining academic discrepancy

This article discusses the regression equation approach to quantifying academic discrepancy, which is an aspect of most generally accepted learning disability definitions. The concept of regression toward the mean and its relevance to determining underachievement is presented. Variations of the expectancy formula and IQ-achievement difference approaches fail to fully consider regression effects and therefore will produce the serious identification errors of including too many children with above-average IQs and too few with below-average IQs. The parameter estimation variation of the regression equation approach is advocated as the best method for quantifying the academic discrepancy aspect of learning disabilities.     

A simplified duality for implicative lattices and l-groups

A topological duality is presented for a wide class of lattice-ordered structures including lattice-ordered groups. In this new approach, which simplifies considerably previous results of the author, the dual space is obtained by endowing the Priestley space of the underlying lattice with two binary functions, linked by set-theoretical complement and acting as symmetrical partners. In the particular case of l-groups, one of these functions is the usual product of sets and the axiomatization of the dual space is given by very simple first-order sentences, saying essentially that both functions are associative and that the space is a residuated semigroup with respect to each of them.The author is supported at the Mathematical Institute of Oxford by a grant of the Argentinian Consejo de Investigations Cientificas y Tecnicas (CONICET). The author wishes to acknowledge the CONICET and the kind hospitality of the Mathematical Institute.     

Note on the least squares solution for the method of successive categories

The problem of estimation in the method of successive categories is reconsidered and a new least squares solution is obtained. An empirical comparison of this solution with Gulliksen's solution is presented.Preparation of this paper has been supported by the Quartermaster Food and Container Institute for the Armed Forces. Views or conclusions expressed herein are those of the author and do not necessarily reflect the views or indorsement of the Department of Defense.