A compensatory approach to optimal selection with mastery scores

A Bayesian approach for simultaneous optimization of test-based decisions is presented using the example of a selection decision for a treatment followed by a mastery decision. A distinction is made between weak and strong rules where, as opposed to strong rules, weak rules use prior test scores as collateral data. Conditions for monotonicity of optimal weak and strong rules are presented. It is shown that under mild conditions on the test score distributions and utility functions, weak rules are always compensatory by nature. The authors are indebted to Wilbert Kallenberg for his valuable comments and to Jan Gulmans for providing the data for the empirical example. The names of the authors are alphabetical; they are equally responsible for the contents of this paper.     

Two simple classes of mastery scores based on the beta-binomial model

Two simple classes of mastery scores which are suitable for hand calculations are presented for beta-binomial test score distributions combined with linear and cubic referral success. The models provide a simple way to explore the consequences of selecting an arbitrary mastery score. Such assessment would be useful whenever the test user is not willing to posta priori a loss ratio, but wishes to look at the various consequences before aiming at a particular score.     

Statistical inferences about true scores

Formulas are derived for unbiased sample estimators of any raw or central moment of the frequency distribution of true scores. A general method is developed for obtaining from each examinee's observed score a least squares estimate of his true score.This research was carried out under contract Nonr-2214(00) with the Office of Naval Research, Department of the Navy.     

Using aptitude measurements for the optimal assignment of subjects to treatments with and without mastery scores

For assigning subjects to treatments the point of intersection of within-group regression lines is ordinarily used as the critical point. This decision rule is critized and, for several utility functions and any number of treatments, replaced by optimal monotone, nonrandomized (Bayes) rules. Both treatments with and without mastery scores are considered. Moreover, the effect of unreliable criterion scores on the optimal decision rule is examined, and it is illustrated how qualitative information can be combined with aptitude measurements to improve treatment assignment decisions. Although the models in this paper are presented with special reference to the aptitude-treatment interaction problem in education, it is indicated that they apply to a variety of situations in which subjects are assigned to treatments on the basis of some predictor score, as long as there are no allocation quota considerations.     

Statistical inference for false positive and false negative error rates in mastery testing

This paper describes an asymptotic inferential procedure for the estimates of the false positive and false negative error rates. Formulas and tables are described for the computations of the standard errors. A simulation study indicates that the asymptotic standard errors may be used even with samples of 25 cases as long as the Kuder-Richardson Formula 21 reliability is reasonably large. Otherwise, a large sample would be required.This work was performed pursuant to Grant No NIE-G-78-0087 with the National Institute of Education, Department of Health, Education and Welfare, Huynh Huynh, Principal Investigator. Points of view or opinions stated do not necessarily reflect NIE position or policy and no official endorsement should be inferred. The editorial assistance of Joseph C. Saunders is gratefully acknowledged.     

Statistical significance and reliability of single-subtest and cluster deviation scores

Suppose one has a battery of K subtests and a composite for the battery is defined as the mean of the K standardized subtest scores. An individual's single-subtest deviation score is the difference between the individual's score on any single subtest and his composite score. A cluster deviation score is the difference between an examinee's average for a small set (cluster) of subtests and his composite. Formulas are given for the test of statistical significance of the individual's subtest or cluster deviation score and the internal consistency reliability of such deviation scores.     

Conceptual mastery and the knowledge argument

According to Frank Jackson’s famous knowledge argument, Mary, a brilliant neuroscientist raised in a black and white room and bestowed with complete physical knowledge, cannot know certain truths about phenomenal experience. This claim about knowledge, in turn, implies that physicalism is false. I argue that the knowledge argument founders on a dilemma. Either (i) Mary cannot know the relevant experiential truths because of trivial obstacles that have no bearing on the truth of physicalism or (ii) once the obstacles have been removed, Mary can know the relevant truths. If we give Mary the epistemological capabilities necessary to draw metaphysical conclusions about physicalism, she will, while trapped in the black and white room, be able to know every truth about phenomenal experience.     

Social concomitants of cognitive mastery in Down's syndrome infants

Smiling as an index of cognitive mastery was examined in a study of seven infants clinically diagnosed as having Down's syndrome. The subjects were administered the Uzgiris-Hunt scales of infant psychological development on five occasions over a four month period of time, and their smiling responses to their successful and unsuccessful completion of the items administered were coded. Two hypothesis derived from J. McVicker Hunt's theory of intrinsic motivation were tested: (a) sense of pleasure derived from successful solutions would be greater than to tasks not solved correctly, and (b) sense of pleasure to optimally challenging tasks would be greater than to tasks which could be solved easily. The findings provided support for the first but not the second prediction. The results are interpreted in terms of similarities and differences found in the present and previous investigations, and the implications of the findings are discussed.     

基于双因子模型的测验总分和维度分的合成方法

双因子模型可以同时包含一个全局因子和多个局部因子,在描述多维测验结构时有其独特优势,近些年应用越来越广泛。文章基于双因子模型,提出了4种合成总分和维度分的方法,分别是:原始分法,加和法,全局题目加权加和法和局部题目加权加和法,并采用模拟的方法,在样本量、测验长度、维度间相关变化的条件下考察了这些方法与传统多维IRT方法的表现。最后,通过实证研究对结果进行了验证。结果显示:(1)全局加权加和法和局部加权加和法,尤其是局部加权加和法合成的总分和维度分与真值最接近、信度最高。(2)在维度间相关较高,测验长度较长的条件下,局部加权加和法的结果较好,部分条件下甚至优于多维IRT法。(3)仅有局部加权加和法合成的维度分能够反应维度间真实的相关关系。     

Maternal control style and the mastery motivation of one-year-olds

Forty-one mothers and their 12-month-old infants participated in a study of the effects of maternal control style on infant mastery motivation. Three scales were designed to assess maternal control style during a mother-infant play session. Mastery motivation was assessed in an experimenter-administered structured toy play procedure. Three components, persistence, competence, and affect, comprised the measure of mastery motivation. Mothers also completed questionnaires on child-rearing attitudes, infant temperament, and control style. Results showed that maternal attitudes and behavior were correlated with infant mastery motivation. More specifically: autonomy-oriented control behavior, sensitive care and knowledge of child-rearing were positively related to infant mastery motivation. The results provide converging evidence regarding the multiple aspects of maternal behavior which affect infant motivation.