A-optimal partially balanced fractional 2m1+m2 factorial designs of resolution V,with 4≤m1>+m2≤6

By use of the algebraic structure, we obtain an explicit expression for the characteristic polynomial of the information matrix of a partially balanced fractional 2^m₁+m₂ factorial design of resolution V derived from a partially balanced array. For 4≤m₁+m₂≤6, A-optimal designs considered here are also presented for reasonable number of assemblies.     

Decomposing complete graphs into Kr×Kc's

We consider the problem of decomposing a complete graph into the Cartesian product of two complete graphs K_r and K_c. This problem originated from the clone library screening. We give a general method of constructing such decompositions using various sorts of combinatorial designs. In particular, for r=3 and c=3, we show that such a decomposition exists for all n satisfying some simple necessary conditions.     

2m fractional factorial designs of resolution V with high A-efficiency, 7 ⩽ m ⩽ 10

We present 111 2^m fractional factorial designs of resolution V for 7 ⩽ m ⩽ 10. These designs are the best known to the authors with respect to the A-optimality criterion (as of October 1995).     

关于单向有序R×C表的统计分析

文章对单向有序R×C列联表,指出了传统的χ2—检验方法不能反映变量之间的统计特征,用其推断两变量之间的关联性是失效的,而采用非参数统计中的秩和检验和CPD分析对单向有序R×C列联表的统计推断是合理的,它们对有序性有分辨能力。文章采用两种方法对六大洲的旅游状况进行差异分析,并排序比较,使统计信息更加丰富。     

Resampling estimation when observations are m–dependent

For m–dependent, identically distributed random observation, the bootstrap method provides inconsistent estimators of the distribution and variance of the sample mean. This paper proposes an alternative resampling procedure. For estimating the distribution and variance of a function of the sample mean, the proposed resampling estimators are shown to be strongly consistent.     

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.     

年缴m次保费的一种估算法

随着我国寿险保险公司现行缴费方式的灵活多样化,给精算工作增加了不少工作量,针对这一情况,文章讨论寿险中的年缴m次保费的一种近似估算法,给出了各种缴费方式下的转换系数与精度估计,在保持一定精度的条件下,通过模拟运算表明这种估算法是十分有用的,因而具有推广的价值。     

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.     

The power of the fisher permutation test in 2 × k tables

The power of the Fisher permutation test extended to 2 × k tables is evaluated unconditionally as a function of the under-lying cell probabilities in the table. These results are then applied in assessing the sensitivity of two-generation cancer bioassays in which a fixed number of pups from each litter born in the first generation are selected to continue on test in the second generation. In this case, the two rows of the table correspond to two treatment groups and the k columns correspond to the number of animals responding in a litter. The cell probabilities in this application are based on a suitable beta-binomial superpopulation model.     

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.     

Reverse Foldovers for Blocked 2 m−k Fractional Factorial Designs

Two-level regular fractional factorial designs are often used in industry as screening designs to help identify early on in an experimental process those experimental or system variables which have significant effects on the process being studied. When the experimental material to be used in the experiment is heterogenous or the experiment must be performed over several well-defined time periods, blocking is often used as a means to improve experimental efficiency by removing the possible effects of heterogenous experimental material or possible time period effects. In a recent article, Li and Jacroux (2007 Li , F. , Jacroux , M. (2007). Optimal foldover plans for blocked 2 ^m?k fractional factorial designs. J. Statsist. Plann. Infer 137:2434–2452. [Google Scholar]) suggested a strategy for constructing optimal follow-up designs for blocked fractional factorial designs using the well-known foldover technique in conjunction with several optimality criteria. In this article, we consider the reverse foldover problem for blocked fractional factorial designs. In particular, given a 2^(m+p)?(p+k) blocked fractional factorial design D, we derive simple sufficient conditions which can be used to determine if there exists a 2^{(m+p?1)?(p?1+k+1)} initial fractional factorial design d which yields D as a foldover combined design as well how to generate all such d. Such information is useful in developing an overall experimental strategy in situations where an experimenter wants an overall blocked fractional factorial design with “desirable” properties but also wants the option of analyzing the observed data at the halfway mark to determine if the significant experimental variables are obvious (and the experiment can be terminated) or if a different path of experimentation should be taken from that initially planned.     

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.     

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.     

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红箭飞跃冲天堂机器转动轰隆隆响,条条红箭长翅膀,     

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.     

A network algorithm for the exact treatment of the 2×k contingency table

A common statistical problem encountered in biomedical research is to test the hypothesis that the parameters of k binomial populations are all equal. An exact test of significance of this hypothesis is possible in principle, the appropriate null distribution being a normalized product of k binomial coefficients. However, the problem of computing the tail area of this distribution can be formidable since it requires the enumeration of all sets of k binomial coefficients whose product is less than a given constant. Existing algorithms, all of which rely on explicit enumeration to generate feasible binomial coefficients     

Multiple comparisons for an unbalanced a × b design under mixed models with interaction

Consider a two-way factorial experiment involving a “treatment” factor A with fixed effects, a “blocking” factor B with random effects, and interaction effects perhaps non-negligible. The degree of balance required for multiple comparison procedures to be applicable for the comparison of the treatment effects using ordinary least-squares estimates is investigated. For main effects to be estimated independently of MSAB, a sufficient condition is that the design consist of identical blocks, a strong condition of proportional frequencies. Surprisingly, under this condition of proportional frequencies, MSAB does not provide an appropriate variance estimate for inferences on each treatment contrast, even though the statistics F = MSA/MSAB is appropriate for testing equality of the treatment effects. In short, when factor B is random, standard methods of multiple comparisons apply using the interaction mean square MSAB as a variance estimator only when the treatment-block incidences n_n are constant. Nevertheless, for designs with identical blocks, appropriate variance estimates can be identified to allow for conservative or approximate multiple comparisons. This is illustrated for certain treatment balanced designs for comparisons with a control.