A comparison of some conditional and unconditional exact tests for 2x2 contingency tables

In 1935, R.A. Fisher published his well-known “exact” test for 2x2 contingency tables. This test is based on the conditional distribution of a cell entry when the rows and columns marginal totals are held fixed. Tocher (1950) and Lehmann (1959) showed that Fisher s test, when supplemented by randomization, is uniformly most powerful among all the unbiased tests UMPU). However, since all the practical tests for 2x2 tables are nonrandomized - and therefore biased the UMPU test is not necessarily more powerful than other tests of the same or lower size. Inthis work, the two-sided Fisher exact test and the UMPU test are compared with six nonrandomized unconditional exact tests with respect to their power. In both the two-binomial and double dichotomy models, the UMPU test is often less powerful than some of the unconditional tests of the same (or even lower) size. Thus, the assertion that the Tocher-Lehmann modification of Fisher's conditional test is the optimal test for 2x2 tables is unjustified.     

On the asymptotic power and relative efficiency of the frequency X2 test

The asymptotic (Pitman) power of the X² test is investigated for particular classes of alternatives. A simple rule is introduced to identify ‘orthogonal alternatives’, for which the noncentrality parameter can be computed in a very simple way. In the sequel, restricted alternatives are considered and the ARE of the unrestricted test w.r.t. the restricted one is shown to depend only on the numbers of degrees of freedom. The concluding section discusses ‘undetectable alternatives’, i.e. alternatives for which the noncentrality vanishes.     

配额制:对妇女平等参政的快速跟进

概论 尽管十分具有争议性,但选举的性别配额制正在世界上主要地区被越来越多的国家所引入.最近几年中,大约有40个国家已经通过宪法修正案或选举法,在议会选举中引入了性别配额制.在超过50个国家中,在要求参选国家议会的各政党候选人中妇女所占最低人数的配额现在已在主要政党的纲领中出现.这一发展挑战了先前关于妇女参政的各种不同的理论.     

Quotas as a ‘fast track’ to equal representation for women

Recent years have witnessed the rapid diffusion of electoral gender quotas. Today, about fourty countries around the world have introduced gender quotas for parliamentary elections, either by constitutional amendment or electoral law. Also, quotas for public election have been laid down in major political parties' statutes in more than fifty countries. This article, which is based on the first worldwide overview of the use of quotas, presents general trends in quota adoption. It identifies two discourses: the incremental track versus the fast track to women's parliamentary representation, and argues that the Scandinavian countries – which represent the incremental track – may no longer be a valid model for ways to improve women's representation. The article also analyses the implementation process, and concludes that, without specifications of quota provisions that match the electoral system in question, and rules about the rank order of candidates as well as sanctions for non-compliance, quota provisions may be merely symbolic.     

Log-linear models for correlated marginal totals of a contingency table

The marginal totals of a contingency table can be rearranged to form a new table. If at least twoof these totals include the same cell of the original table, the new table cannot be treated as anordinary contingency table. An iterative method is proposed to calculate maximum likelihood estimators for the expected cell frequencies of the original table under the assumption that some marginal totals (or more generally, some linear functions) of these expected frequencies satisfy a log-linear model.In some cases, a table of correlated marginal totals is treated as if it was an ordinary contingency table. The effects of ignoring the special structure of the marginal table on thedistributionof the goodness-of-fit test statistics are discussed and illustrated, with special reference to stationary Markov chains.