A note on statistical power in multi‐site randomized trials with multiple treatments at each site

We derive the statistical power functions in multi‐site randomized trials with multiple treatments at each site, using multi‐level modelling. An F statistic is used to test multiple parameters in the multi‐level model instead of the Wald chi square test as suggested in the current literature. The F statistic is shown to be more conservative than the Wald statistic in testing any overall treatment effect among the multiple study conditions. In addition, we improvise an easy way to estimate the non‐centrality parameters for the means comparison t‐tests and the F test, using Helmert contrast coding in the multi‐level model. The variance of treatment means, which is difficult to fathom but necessary for power analysis, is decomposed into intuitive simple effect sizes in the contrast tests. The method is exemplified by a multi‐site evaluation study of the behavioural interventions for cannabis dependence.     

Using Cook's distance in polytomous logistic regression

The previously unknown asymptotic distribution of Cook's distance in polytomous logistic regression is established as a linear combination of independent chi‐square random variables with one degree of freedom. An exhaustive approach to the analysis of influential covariates is developed and a new measure for the accuracy of predictions based on such a distribution is provided. Two examples with real data sets (one with continuous covariates and the other with both qualitative and quantitative covariates) are presented to illustrate the approach developed.     

BRIEF REPORT: BARTLETT'S TEST OF SPHERICITY AND CHANCE FINDINGS IN FACTOR ANALYSIS

Bartlett's test of sphericitg: was applied to a correlation matrix computed on random normal deviates by Armstrong and Soelberg (1968), and returned a chi square value indicating that the matrix could have been generated from a population where the correlation coefficients are zero. These results re- emphasize the desirability of computing this test prior to proceeding t o factor extraction, and in accord with the findings of other writers, indicate this test to be sensitive in detecting results which can be ascribed to chance.     

Intragroup differentiation in terms of ingroup and outgroup attributes

An experiment (n = 36) was conducted to test the hypothesis that attribute typicality moderates intragroup differentiation. The predicted reversal from perceived relative ingroup homogeneity on typical ingroup attributes to perceived relative outgroup homogeneity on typical outgroup attributes was confirmed for both homogeneity measures (standard deviation and probability of differentiation). But the ingroup homogeneity effects were more reliable than the outgroup homogeneity effects. Relative ingroup size (minority versus majority) was included in the experimental design as a between-subjects factor but did not qualify the reversal of perceived relative homogeneity.     

Distributions of the Kullback–Leibler divergence with applications

The Kullback–Leibler divergence (KLD) is a widely used method for measuring the fit of two distributions. In general, the distribution of the KLD is unknown. Under reasonable assumptions, common in psychometrics, the distribution of the KLD is shown to be asymptotically distributed as a scaled (non‐central) chi‐square with one degree of freedom or a scaled (doubly non‐central) F. Applications of the KLD for detecting heterogeneous response data are discussed with particular emphasis on test security.     

Exploring the Vocational Rehabilitation Acceptance Rates for Hispanics Versus Non‐Hispanics in the United States

Compared with other ethnic minorities in the United States, numbers for the Hispanic population are significantly escalating. In the study described here, a chi‐square test of proportions was used to examine the vocational rehabilitation (VR) acceptance rates among Hispanics and non‐Hispanics. The test statistic revealed a statistically significant difference between race/ethnicity and VR acceptance. In particular, Hispanics are more likely to be accepted for VR services than are non‐Hispanics in the United States. Implications for VR counselors are discussed.     

Note on the sampling error of the difference between correlated proportions or percentages

Two formulas are presented for judging the significance of the difference between correlated proportions. The chi square equivalent of one of the developed formulas is pointed out.     

Teaching students to recognize structural similarities between statistics word problems

An important skill in mathematical problem solving is recognizing that the problem one is working on (target problem) can be solved using the same method as a problem one already knows (source problem). In a preliminary study, college students displayed a higher level of structural awareness (i.e. sorting word problems on the basis of structural features) at the end rather than the beginning of their first statistics course. In the main study, we taught college students to sort statistics word problems on the basis of structural features (i.e. whether the problem could be solved by t‐test, correlation, or chi‐square statistics) rather than surface features (i.e. the problem's cover story). These results support a structural awareness theory in which students learn to form problem schemas by abstracting the underlying structural features of a problem statement and organizing them into a generalized problem model. Copyright © 2002 John Wiley & Sons, Ltd.     

Parental Loss in Children as Reflected in Projective Responses

Fisher and Cleveland originally proposed that individuals differ in exterior-interior body awareness. A study was conducted in a population of 61 men and 43 women to examine this hypothesis. Tachistocopic recognition times for picture categories depicting the exterior and interior (E and I) body sectors were ascertained. A chi square analysis revealed that these recognition times were significantly related (P = 0.01) to Rorschach measures reflecting E-I awareness. An additional finding was that men recognized the I category more rapidly. This was considered to provide further support for the hypothesis that men have accentuated I awareness. An outline was given of ongoing work designed to measure the extent of the tachistoscope's regional specificity.     

A note on the standard length of a test

This paper describes a relationship between the variance-covariance matrix of test items and Woodbury's concept of the standard length of a test. An index of item-test relationship is described in standard length terms. The sum of these indices for the items in a test is equal to the square of Jackson's coefficient of sensitivity.     

测验信度估计：从α系数到内部一致性信度

沿用经典的测验信度定义, 简介了信度与a 系数的关系以及a系数的局限。为了推荐替代a系数的信度估计方法, 深入讨论了与a 系数关系密切的同质性信度和内部一致性信度。在很一般的条件下, 证明了a 系数和同质性信度都不超过内部一致性信度, 后者不超过测验信度, 说明内部一致性信度比较接近测验信度。总结出一个测验信度分析流程, 说明什么情况下a 系数还有参考价值; 什么情况下a 系数不再适用, 应当使用内部一致性信度(文献上也常称为合成信度)。提供了计算同质性信度和内部一致性信度的计算程序, 一般的应用工作者可以直接套用。     

Helping Those Who Help Themselves: Does Counseling Enhance Retention?

This study examined how academic distress changed over the course of counseling and predicted retention. The sample comprised students receiving services at the campus counseling center (n = 404), students from a psychology department subject pool (n = 311), and students from the general campus population (n = 75,748). The analyses performed included t test, analysis of covariance, chi‐square test, and logistical regression. The results suggested that students whose academic distress did not decrease had lower retention rates than both clients whose academic distress improved and the general student body.     

The phi coefficient and chi square as indices of item validity

Two new methods of item analysis are described. One involves the computation of the coefficient (correlation of a fourfold point distribution) and the other involves chi square. The only data required are the proportions of passing individuals in the upper and lower criterion groups, for the determination of , and in addition,N, for the determination of chi square. Abacs are presented for graphic solution of the two indices of validity, and tests of significance are provided.     

Type I errors and power of the parametric bootstrap goodness‐of‐fit test: Full and limited information

In sparse tables for categorical data well‐known goodness‐of‐fit statistics are not chi‐square distributed. A consequence is that model selection becomes a problem. It has been suggested that a way out of this problem is the use of the parametric bootstrap. In this paper, the parametric bootstrap goodness‐of‐fit test is studied by means of an extensive simulation study; the Type I error rates and power of this test are studied under several conditions of sparseness. In the presence of sparseness, models were used that were likely to violate the regularity conditions. Besides bootstrapping the goodness‐of‐fit usually used (full information statistics), corrected versions of these statistics and a limited information statistic are bootstrapped. These bootstrap tests were also compared to an asymptotic test using limited information. Results indicate that bootstrapping the usual statistics fails because these tests are too liberal, and that bootstrapping or asymptotically testing the limited information statistic works better with respect to Type I error and outperforms the other statistics by far in terms of statistical power. The properties of all tests are illustrated using categorical Markov models.     

Analysis of trend: a permutation alternative to the F test

When the categories of the independent variable in an analysis of variance are quantitative, it is more informative to evaluate the trends in the treatment means than to simply compare differences among the treatment means. A permutation alternative to the conventional F test is shown to possess significant advantages when analyzing trend among quantitative treatments in a one-way analysis of variance. An example with and without an extreme data point illustrates the effectiveness of the permutation alternative for the analysis of trend when homogeneity of variance is compromised.     

The self-serving attributional bias: Beyond self-presentation

An experiment was conducted to provide empirical support for the notion that asymmetrical causal attributions for favorable and unfavorable outcomes result from a self-serving attributional bias that occurs independently of self-presentational concerns. Subjects did either well or poorly on an ego-involving test for which their performance, attributions, and evaluations of the test were either public or private. A pattern of self-serving responses for subjects' attributions and evaluations of the test was found in the private conditions, thus providing evidence of the influence of outcome favorability on individuals' perceptions of causality. Theoretical and practical implications of these finding are discussed and suggestions for future research are offered.     

Shape constancy and a perceptual bias towards symmetry

In attempting to judge whether a briefly presented rotated figure was symmetrical (circle or square) or asymmetrical (ellipse or rectangle), a bias towards perceiving symmetry was evident. This bias appears to be perceptual rather than judgmental in origin in that it was affected neither by variations in the probability of occurrence of symmetrical figures nor by familiarization with the stimuli. A characterization of the stimulus similarity space based on the shape-slant invariance hypothesis is presented, and a model which incorporates both the similarity space and the symmetry bias is proposed. The model can account for our paradoxical finding that the more asymmetrical some projected images, the more likely they will be perceived as symmetrical. This model can also account for Massaro’s (1973, 1975) results on shape constancy. However, Massaro’s theory was not supported in that extension in depth did not account for increased difficulty of shape judgments.     

基于人格特征的即时通讯软件用户分类模型

根据即时通讯(instantmessaging,IM)软件工具使用行为的差异将用户划分为两类,使用“大五人格问卷”获取了该两类IM用户的人格特征测量数据。统计分析结果表明,上述两类用户在“适应性”和“社交性”因子上的得分存在显著差异,而在“开放性”、“利他性”和“道德感”三个因子上的得分差异不显著。据此,以用户在“适应性”与“社交性”因子上的得分为输入和用户的分类类别为输出,构建了IM用户基于人格特征的BP神经网络分类模型。对模型的拟合度检验表明,该模型可利用人格测量数据对IM用户进行有效分类。