基于C~2R及C~2GS~2模型的物流配送效率差异评价

文章综合运用数据包络模型中的C2R模型和C2GS2模型,选取我国东中西部电子商务物流配送的宏观统计数据,构建了物流投入与产出效率评价体系,并对我国电子商务的区域差异进行研究。研究显示:我国东部地区实现了物流配送技术的有效性与物流配送效率的最大化,中部地区处于物流配送技术的弱有效状态,西部地区物流配送技术与效率发展滞后。     

枫桥镇农家户均存款突破2．2万元

枫桥镇农家户均存款突破２．２万元陆全楠金融机构最新统计数据显示，苏州新区枫桥镇经济水平稳步提高，１９９５年末，农村存款余额为２．８５亿元，比上年末增长４７．７％，其中，村民年末储蓄存款２．０９亿元，比１９９４年末增长４３．２％，户均存款突破２．２万元...     

Selection of the best in 2×2 factorial designs

Selection of the cell in a 2×2 -factorial design with the greatest mean is considered. A general class of ranking and selection procedures (RSP) is constructed to include methods based on the largest marginal cell means (SP1) or on the largest cell mean (SP3). Using the preference zone approach the minimum probability of a correct solution is found, In this paper a RSP which maximizes the minimum probability of a correct solution over the preference zone is found. In this way selection of the cell with the greatest observed mean is proven to be admissible.     

浙江省高校“2＋2”选拔考试成绩比较分析

引言浙江省高校“2 2”选拔考试,是针对浙江省的大学生在本校学习两年后,符合一定条件可参加部分高校重点专业的选拔考试,成绩合格者可转入选拔学校完成本科学制后二年的学习,列入选拔学校的普通本科生管理。浙江省教育厅从2003—2006连续4年进行了“2 2”选拔考试的试点工作,选拔学校通过2     

Logratio approach to statistical analysis of 2×2 compositional tables

Compositional tables represent a continuous counterpart to well-known contingency tables. Their cells contain quantitatively expressed relative contributions of a whole, carrying exclusively relative information and are popularly represented in proportions or percentages. The resulting factors, corresponding to rows and columns of the table, can be inspected similarly as with contingency tables, e.g. for their mutual independent behaviour. The nature of compositional tables requires a specific geometrical treatment, represented by the Aitchison geometry on the simplex. The properties of the Aitchison geometry allow a decomposition of the original table into its independent and interactive parts. Moreover, the specific case of 2×2 compositional tables allows the construction of easily interpretable orthonormal coordinates (resulting from the isometric logratio transformation) for the original table and its decompositions. Consequently, for a sample of compositional tables both explorative statistical analysis like graphical inspection of the independent and interactive parts or any statistical inference (odds-ratio-like testing of independence) can be performed. Theoretical advancements of the presented approach are demonstrated using two economic applications.     

Structural properties of UMPU-tests for 2×2 tables and some applications

The paper is concerned with structural properties of the acceptance regions of uniformly most powerful unbiased tests (UMPU-tests) for one- and two-sided hypotheses for 2×2 tables as, for instance, the comparison of two proportions or testing for association. These tests can be considered as randomized versions of Fisher's exact tests. A series of monotonicity and unimodality properties will be proved. These properties are equivalent to a symmetry and convexity condition often required for powerful unconditional tests. Knowledge of such properties allows a fast and in some sense recursive calculation of the critical values of the UMPU-tests which is important if a repeated calculation of all critical values for different sample sizes or different levels is required. This is, for example, the case if the unconditional power has to be controlled over a certain subset of the alternative, or, if one is interested in powerful unconditional non-randomized tests generated by a UMPU-test. Our results also imply some useful properties of the two-dimensional unconditional power function. On the other hand, we found some less nice properties of the UMPU-tests, too.     

Inference using attributable risk for a 2×2 case–control study

Asymptotic variance plays an important role in the inference using interval estimate of attributable risk. This paper compares asymptotic variances of attributable risk estimate using the delta method and the Fisher information matrix for a 2×2 case–control study due to the practicality of applications. The expressions of these two asymptotic variance estimates are shown to be equivalent. Because asymptotic variance usually underestimates the standard error, the bootstrap standard error has also been utilized in constructing the interval estimates of attributable risk and compared with those using asymptotic estimates. A simulation study shows that the bootstrap interval estimate performs well in terms of coverage probability and confidence length. An exact test procedure for testing independence between the risk factor and the disease outcome using attributable risk is proposed and is justified for the use with real-life examples for a small-sample situation where inference using asymptotic variance may not be valid.     

动态分析2:统计指数

动物园,总使我们想到一些很快活的事情。跟家人、跟朋友,在小时候、或长大时,我们去那里游玩。我想,谁都喜欢到动物园看动物,但恐怕没人喜欢看到动物们被关在笼子里。当我在电视看到野生动物园时,我非常向往那里人与动物亲密无间的接触。当然,就近的动物园里,孔雀开屏、熊猫绕竹、猴山打闹、懒狮贪睡、河马探头、百鸟啾啾、天鹅悠游、虎啸猿啼……哈哈,无不带来欢畅。您知道,泰国是“大象之国”,大象除了会表演外,还会帮人拖木头,会做很多事,大象真是个高智商的动物。不久前,我到泰国旅游,看了大象表演,对大象又有了更深的喜爱。喜爱之余,忍…     

Chance-Corrected Measures of Reliability and Validity in 2 × 2 Tables

It is customary to use two groups of indices to evaluate a diagnostic method with a binary outcome: validity indices with a standard rater (sensitivity, specificity, and positive or negative predictive values) and reliability indices (positive, negative and overall agreements) without a standard rater. However neither of these classic indices is chance-corrected, and this may distort the analysis of the problem (especially in comparative studies). One way of chance-correcting these indices is by using the Delta model (an alternative to the Kappa model), but this means having to use a computer program to work out the calculations. This paper gives an asymptotic version of the Delta model, thus allowing simple expressions to be obtained for the estimator of each of the above-mentioned chance-corrected indices (as well as for its standard error).     

Bayesian P-Values for Testing Independence in 2 × 2 Contingency Tables

This article considers Bayesian p-values for testing independence in 2 × 2 contingency tables with cell counts observed from the two independent binomial sampling scheme and the multinomial sampling scheme. From the frequentist perspective, Fisher's p-value (p _F ) is the most commonly used p-value but it can be conservative for small to moderate sample sizes. On the other hand, from the Bayesian perspective, Bayarri and Berger (2000 Bayarri , M. J. , Berger , J. O. ( 2000 ). P-values for composite null models (with discussion) . J. Amer. Statist. Assoc. 95 : 1127 – 1170 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) first proposed the partial posterior predictive p-value (p _PPOST ), which can avoid the double use of the data that occurs in another Bayesian p-value proposed by Guttman (1967 Guttman , I. ( 1967 ). The use of the concept of a future observation in goodness-of-fit problems . J. Roy. Statist. Soc. Ser. B 29 : 83 – 100 . [Google Scholar]) and Rubin (1984 Rubin , D. B. ( 1984 ). Bayesianly justifiable and relevant frequency calculations for the applied statistician . Ann. Statist. 12 : 1151 – 1172 .[Crossref], [Web of Science ®] , [Google Scholar]), called the posterior predictive p-value (p _POST ). The subjective and objective Bayesian p-values in terms of p _POST and p _PPOST are derived under the beta prior and the (noninformative) Jeffreys prior, respectively. Numerical comparisons among p _F , p _POST , and p _PPOST reveal that p _PPOST performs much better than p _F and p _POST for small to moderate sample sizes from the frequentist perspective.     

Improved P-Values for Testing Marginal Homogeneity in 2 × 2 Contingency Tables

This article considers the problem of testing marginal homogeneity in a 2 × 2 contingency table. We first review some well-known conditional and unconditional p-values appeared in the statistical literature. Then we treat the p-value as the test statistic and use the unconditional approach to obtain the modified p-value, which is shown to be valid. For a given nominal level, the rejection region of the modified p-value test contains that of the original p-value test. Some nice properties of the modified p-value are given. Especially, under mild conditions the rejection region of the modified p-value test is shown to be the Barnard convex set as described by Barnard (1947 Barnard , G. A. ( 1947 ). Significance tests for 2 × 2 tables . Biometrika 34 : 123 – 138 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). If the one-sided null hypothesis has two nuisance parameters, we show that this result can reduce the dimension of the nuisance parameter space from two to one for computing modified p-values and sizes of tests. Numerical studies including an illustrative example are given. Numerical comparisons show that the sizes of the modified p-value tests are closer to a nominal level than those of the original p-value tests for many cases, especially in the case of small to moderate sample sizes.     

The Vanishing 2×2 Table: Linking the Hypergeometric,Binomial and Poisson

A simple procedure for establishing minimum sample size in X ² goodness-of-fit tests is presented. Samples of this size will automatically satisfy Yarnold's criterion.     

A More Powerful Average Bioequivalence Analysis for the 2 × 2 Crossover

The 2 × 2 crossover is commonly used to establish average bioequivalence of two treatments. In practice, the sample size for this design is often calculated under a supposition that the true average bioavailabilities of the two treatments are almost identical. However, the average bioequivalence analysis that is subsequently carried out does not reflect this prior belief and this leads to a loss in efficiency. We propose an alternate average bioequivalence analysis that avoids this inefficiency. The validity and substantial power advantages of our proposed method are illustrated by simulations, and two numerical examples with real data are provided.     

全球保险费用逾2万亿美元

据最新一期英国（经济学家）杂志刊登的数字，1995年全球保险费用首次超过了2万亿美元。工业化国家的保险费用总额占全球的 90％以     

The Robustness of Common Measures of 2×2 Association to Bias Due to Misclassifications

The strength of association between two dichotomous characteristics A and B can be measured in many ways. All of these statistics are biased when there is misclassification, and all are prevalence dependent whether or not their population values are. Measures lacking fixed endpoints for random and perfect association, such as sensitivity, specificity, risk ratios, and odds ratio, have a bias either so unpredictable or so large that the observable and true measures of association may bear little resemblance to each other. Reexpressions of these measures that fix the endpoints and other measures with fixed endpoints, such as kappa, phi, gamma, risk difference, and attributable risk, produce attenuated estimates of their true values. Disattenuating such estimators is possible using test—retest data.     

The impact of a preliminary test for interaction in a 2 × 2 factorial trial

Preliminary tests of significance on the crucial assumptions are often done before drawing inferences of primary interest. In a factorial trial, the data may be pooled across the columns or rows for making inferences concerning the efficacy of the drugs {simple effect) in the absence of interaction. Pooling the data has an advantage of higher power due to larger sample size. On the other hand, in the presence of interaction, such pooling may seriously inflate the type I error rate in testing for the simple effect.

A preliminary test for interaction is therefore in order. If this preliminary test is not significant at some prespecified level of significance, then pool the data for testing the efficacy of the drugs at a specified α level. Otherwise, use of the corresponding cell means for testing the efficacy of the drugs at the specified α is recommended. This paper demonstrates that this adaptive procedure may seriously inflate the overall type I error rate. Such inflation happens even in the absence of interaction.

One interesting result is that the type I error rate of the adaptive procedure depends on the interaction and the square root of the sample size only through their product. One consequence of this result is as follows. No matter how small the non-zero interaction might be, the inflation of the type I error rate of the always-pool procedure will eventually become unacceptable as the sample size increases. Therefore, in a very large study, even though the interaction is suspected to be very small but non-zero, the always-pool procedure may seriously inflate the type I error rate in testing for the simple effects.

It is concluded that the 2 × 2 factorial design is not an efficient design for detecting simple effects, unless the interaction is negligible.     

统计学原理题解(2)

1985年第1期习题(2)的解答:(一)甲国粮食产量年平均增长速度=1.06－1=0．06或6‰乙国粮食产量年平均增长速度=1.02－1=0.02或2‰设:在第n年甲国粮食产量和乙国相等,