Testing two variances for superiority/non-inferiority and equivalence: Using the exhaustion algorithm for sample size allocation with cost

The equality of two group variances is frequently tested in experiments. However, criticisms of null hypothesis statistical testing on means have recently arisen and there is interest in other types of statistical tests of hypotheses, such as superiority/non-inferiority and equivalence. Although these tests have become more common in psychology and social sciences, the corresponding sample size estimation for these tests is rarely discussed, especially when the sampling unit costs are unequal or group sizes are unequal for two groups. Thus, for finding optimal sample size, the present study derived an initial allocation by approximating the percentiles of an F distribution with the percentiles of the standard normal distribution and used the exhaustion algorithm to select the best combination of group sizes, thereby ensuring the resulting power reaches the designated level and is maximal with a minimal total cost. In this manner, optimization of sample size planning is achieved. The proposed sample size determination has a wide range of applications and is efficient in terms of Type I errors and statistical power in simulations. Finally, an illustrative example from a report by the Health Survey for England, 1995–1997, is presented using hypertension data. For ease of application, four R Shiny apps are provided and benchmarks for setting equivalence margins are suggested.     

The Performance Diagnostic Checklist-Human Services: A brief review

The Performance Diagnostic Checklist-Human Services (PDC-HS) is an informant-based tool designed to identify the variables contributing to poor employee performance in human service settings, such as clinics, schools, and residential facilities. Upon completion of the tool, an intervention indicated by PDC-HS results is used to improve employee performance. To date, the PDC-HS has been used in a number of studies. This review describes the existing research on the PDC-HS and provides suggestions for future research.     

Mathematical Creativity: A Combination of Domain-general Creative and Domain-specific Mathematical Skills

Creativity is an understudied topic in elementary school mathematics research. Nevertheless, we argue that creativity plays an important role in mathematics, but that more research is needed to understand this relation. Therefore, this study aimed to investigate this relation, specifically between domain-general creativity, domain-specific mathematical creativity, and mathematical ability. Measures for these constructs were administered to 342 Dutch fourth graders. In order to examine the nature of the relation between creativity and mathematics, two competing models were tested, using Structural Equation Modeling. The results indicated that models in which general creativity and mathematical ability both predict mathematical creativity fitted the data better than models in which mathematical and general creativity predict mathematical ability. This study showed that both general creativity and mathematical ability are important to think creatively in mathematics.     

家庭社会经济地位对数学成绩的影响:亲子沟通和学业自我效能感的链式中介模型

采用“中国学校课程教学调查项目”中1811名八年级学生及其家长作为样本进行调查,探讨家庭社会经济地位与数学成绩的关系,考察亲子沟通和学业自我效能感的作用机制。结果显示:(1)家庭社会经济地位显著正向影响数学成绩;(2)亲子沟通、学业自我效能感在家庭社会经济地位与数学成绩之间起部分中介作用;(3)亲子沟通、学业自我效能感在家庭社会经济地位与数学成绩之间具有链式中介作用。     

A unified approach to exploratory factor analysis with missing data,nonnormal data,and in the presence of outliers

Factor analysis is regularly used for analyzing survey data. Missing data, data with outliers and consequently nonnormal data are very common for data obtained through questionnaires. Based on covariance matrix estimates for such nonstandard samples, a unified approach for factor analysis is developed. By generalizing the approach of maximum likelihood under constraints, statistical properties of the estimates for factor loadings and error variances are obtained. A rescaled Bartlett-corrected statistic is proposed for evaluating the number of factors. Equivariance and invariance of parameter estimates and their standard errors for canonical, varimax, and normalized varimax rotations are discussed. Numerical results illustrate the sensitivity of classical methods and advantages of the proposed procedures.This project was supported by a University of North Texas Faculty Research Grant, Grant #R49/CCR610528 for Disease Control and Prevention from the National Center for Injury Prevention and Control, and Grant DA01070 from the National Institute on Drug Abuse. The results do not necessarily represent the official view of the funding agencies. The authors are grateful to three reviewers for suggestions that improved the presentation of this paper.     

The "Natural" and the "Formal"

The paper presents an argument against a metaphysical conception of logic according to which logic spells out a specific kind of mathematical structure that is somehow inherently related to our factual reasoning. In contrast, it is argued that it is always an empirical question as to whether a given mathematical structure really does captures a principle of reasoning. (More generally, it is argued that it is not meaningful to replace an empirical investigation of a thing by an investigation of its a priori analyzable structure without paying due attention to the question of whether it really is the structure of the thing in question.) It is proposed to elucidate the situation by distinguishing two essentially different realms with which our reason must deal: the realm of the natural, constituted by the things of our empirical world, and the realm of the formal, constituted by the structures that we use as prisms to view, to make sense of, and to reconstruct the world. It is suggested that this vantage point may throw light on many foundational problems of logic.     

Beyond Speech Lateralization: A Review of the Variability, Reliability, and Validity of the Intracarotid Amobarbital Procedure and Its Nonlanguage Uses in Epilepsy Surgery Candidates

While the intracarotid amobarbital procedure (IAP) was originally utilized to lateralize speech functions as an aid in the surgical treatment of epilepsy, additional uses for the IAP have emerged including: (1) the use of the IAP to predict post-surgical memory changes, including both global amnesia and smaller, yet significant, material-specific memory deficits; (2) the use of the IAP to provide confirmatory evidence of lateralization of seizure focus; and (3) the use of the IAP to predict post-surgical relief from seizures. While the literature on the IAP is extensive and growing, its utility is marred by the wide variability associated with the procedure itself from epilepsy center to center. This variability renders comparisons among IAP studies problematic and conclusions about IAP efficacy difficult. The variability associated with the amobarbital procedures, as well as the reliability and the validity of the IAP in its nonlanguage uses is reviewed here. A special emphasis is devoted to research conducted in the last decade. Also discussed is the future of the IAP including anticipated research directions.     

The use of genetic test information in insurance: The argument from indistinguishability reconsidered

In the bioethical literature, discrimination in insurance on the basis of genetic risk factors detected by genetic testing has been defended and opposed on various ethical grounds. One important argument in favour of the practice is offered by those who believe that it is not possible to distinguish between genetic and non-genetic information, at least not for practical policy purposes such as insurance decision-making. According to the argument from indistinguishability, the use of genetic test information for insurance purposes should be permitted, because genetic test information is no different from non-genetic medical information in any relevant respect, therefore it would be inconsistent to prohibit the former whilst permitting the latter. This paper discusses and defends this argument and suggests a new, more tenable foundation.     

中小学生认知能力发展水平测验的研究

以皮亚杰的认知发展理论为基础,采用皮亚杰及其学生研究认知发展时的任务为测验题目,编制成测量中小学生认知能力发展水平的测验.通过对2240名中小学生施测,结果表明本测验不仅具有很好的信度和效度,而且也具有适中的难度.然后以一所中学特长班学生为被试,通过对他们进行测量,并将测验结果与同年级普通班学生的认知成绩进行比较,结果存在很明显的差异.最后对中小学生认知能力发展水平测量问题进行了探讨.