A Bootstrap Approach for Testing Marginal Independence Between Two Categorical Variables When Subjects Have Repeated Responses

To assess independence in two-way contingency tables, the Pearson chi-square test or Fisher’s exact test are typically used. These tests assume that each subject contributes at most one count to only one table cell (e.g., sex versus blood type). In other situations, each subject may have more than one count contributing to the table and these counts may occur in different cells of the table. One may wish to test independence, adjusting for the within-subject correlation. We provide a simple nonparametric bootstrap approach and assess its performance through simulation studies. The method is illustrated on subjects with multiple mental health presentations to Emergency Departments.     

Measure of departure from symmetry for the analysis of collapsed square contingency tables with ordered categories

For square contingency tables with ordered categories, there may be some cases that one wants to analyze them by considering collapsed tables with some adjacent categories combined in the original table. This paper considers the symmetry model for collapsed square contingency tables and proposes a measure to represent the degree of departure from symmetry. The proposed measure is defined as the arithmetic mean of submeasures each of which represents the degree of departure from symmetry for each collapsed 3×3 table. Each submeasure also represents the mean of power-divergence or diversity index for each collapsed table. Examples are given.     

The asymptotic covariance structure of log-linear model estimated parameters for the multiple recapture census

This paper presents a matrix formulation for log-linear model analysis of the incomplete contingency table which arises from multiple recapture census data. Explicit matrix product expressions are given for the asymptotic covariance structure of the maximum likelihood estimators of both the log-linear model parameter vector and the predicted value vector for the observed and missing cells. These results are illustrated for data pertaining to a population of children possessing a common congenital anomaly.     

乒乓球比赛中打高球的有效战术与训练探析

乒乓球比赛中打好高球具有特别的意义。在打高球的过程中,要注意保证准确性,掌握和控制主动权,保持良好的心态、坚决果断,采用快慢杀相结合、压反手调正手和重、轻、长、短相结合的有效战术。在训练中要练好扎实的正手攻球技术,要练为战。赛前要进行有针对性的场地适应性训练。     

Partitioning Pearson's Chi-squared Statistic for Singly Ordered Two-way Contingency Tables

This paper presents a partition of Pearson's chi-squared statistic for singly ordered two-way contingency tables. The partition involves using orthogonal polynomials for the ordinal variable while generalized basic vectors are used for the non-ordinal variable. The benefit of this partition is that important information about the structure of the ordered variable can be identified in terms of locations, dispersion and higher order components. For the non-ordinal variable, it is shown that the squared singular values from the singular value decomposition of the transformed dataset can be partitioned into location, dispersion and higher order components. The paper also uses the chi-squared partition to present an alternative to the maximum likelihood technique of parameter estimation for the log-linear analysis of the contingency table.     

多标准决策表中发现概率规则的变精度粗糙集方法

用优势关系代替不可分辨关系,本文提出了一种可以从多标准决策表中获取概率规则的扩展变精度粗糙集模型,该模型能够处理多标准决策表中可能的不一相容性,获取由偏好对象组成的概率决策规则集,并导出事例决策系统的偏好模型。研究结果表明:基于优势关系,从多标准决策表中获取的最小概率规则集,使用的条件数量较少,且导出规则的数量较少、较强。     

竞技体育训练模式在普通高校乒乓球专项课程中的应用

通过实验比较、技术分析、体能测试等方法,对我校2007级新生乒乓球专项课运用竞技体育训练模式进行了教学实验探索.经过两学年的教学实践,收到了良好的效果,有效地激发了学生的学习兴趣,提高了学生的专项技术水平和体育能力,增强了学生的自信心,促进了他们身心健康的全面发展.     

Adjusted Wilcoxon signed rank test tables for ratio of percentiles

The ordinary Wilcoxon signed rank test table provides confidence intervals for the median of one population. Adjusted Wilcoxon signed rank test tables which can provide confidence intervals for the median and the 10th percentile of one population are created in this paper. Base-(n + 1) number system and theorems about property of symmetry of the adjusted Wilcoxon signed rank test statistic are derived for programming. Theorem 1 states that the adjusted Wilcoxon signed rank test statistic are symmetric around n(n + 1)/4. Theorem 2 states that the adjusted Wilcoxon signed rank test statistic with the same number of negative ranks m are symmetric around m(n+1)/2. 87.5% and 85% confidence intervals of the median are given in the table for n = 12, 13,…, 29 to create approximated 95% confidence intervals of the ratio of medians for two independent populations. 95% and 92.5% confidence intervals of the 10th percentile are given in the table for n = 26, 27, 28, 29 to create approximated 95% confidence regions of the ratio of the 10th percentiles for two independent populations. Finally two large datasets from wood industry will be partitioned to verify the correctness of adjusted Wilcoxon signed rank test tables for small samples.     

A nonparametric procedure for testing partially ranked data

In consumer preference studies, it is common to seek a complete ranking of a variety of, say N, alternatives or treatments. Unfortunately, as N increases, it becomes progressively more confusing and undesirable for respondents to rank all N alternatives simultaneously. Moreover, the investigators may only be interested in consumers’ top few choices. Therefore, it is desirable to accommodate the setting where each survey respondent ranks only her/his most preferred k (k?N) alternatives. In this paper, we propose a simple procedure to test the independence of N alternatives and the top-k ranks, such that the value of k can be predetermined before securing a set of partially ranked data or be at the discretion of the investigator in the presence of complete ranking data. The asymptotic distribution of the proposed test under root-n local alternatives is established. We demonstrate our procedure with two real data sets.     

Habits and orders of everyday life: commensal adjustment in Anglo‐French couples

This paper examines processes of habit reshuffling and change in different contexts of household formation, looking specifically at habits regarding eating and commensality. It is based on a study of 14 couples, each with one English and one French partner, half of whom live in France, half in England. We examine the interplay between partners, their determination to eat together as a couple, and the various ‘orders’ associated with their commensal pact (diets, routines, extra‐marital commensality), both when they start as couples and as parents of young children. We draw on the specificity of cross‐national couple experience to cast light on processes of adjustment – to one another, and to the new country of residence for the migrant partner. In particular, we explore the potential of notions of ‘split’ and ‘solid’ ‘patrimonies of incorporated habits’, ‘re‐shuffling’ of habits and dispositions, and ‘habit memory’, to characterize the dynamics of habits at play in each of the orders under scrutiny. Overall, the paper contributes to the analysis of habit as the ‘stuff’ of orders of everyday life.