El método condicionado en las tablas 2x2

Esta memoria profundiza en el estudio de los problemas que dan lugar a las tablas 2x2; en particular, esta dedicada a todas aquellas soluciones que impliquen de algún modo el principio condicionado. Esta dividida en dos capítulos: el primero esta dedicado a las soluciones exactas y en el se estudian y comparan las diferentes versiones del test exacto de fisher aparecidas en la literatura. Se presentan tambien algunas aplicaciones de este test (test de raches) y se proponen generalizaciones de los llamados test prendobayewsianos. El segundo capitulo este dedicado a las soluciones asintotices, concretamente al test de x2 del que se comparen les correcciones por continuidad usualmente utilizadas y algunas otras que se propone, estudiándose las condiciones de validez de las misma

The optimal method to make inferences about a linear combination of proportions

Asymptotic inferences about a linear combination of K independent binomial proportions are very frequent in applied research. Nevertheless, until quite recently research had been focused almost exclusively on cases of K≤2 (particularly on cases of one proportion and the difference of two proportions). This article focuses on cases of K>2, which have recently begun to receive more attention due to their great practical interest. In order to make this inference, there are several procedures which have not been compared: the score method (S0) and the method proposed by Martín Andrés et al. (W3) for adjusted Wald (which is a generalization of the method proposed by Price and Bonett) on the one hand and, on the other hand, the method of Zou et al. (N0) based on the Wilson confidence interval (which is a generalization of the Newcombe method). The article describes a new procedure (P0) based on the classic Peskun method, modifies the previous methods giving them continuity correction (methods S0c, W3c, N0c and P0c, respectively) and, finally, a simulation is made to compare the eight aforementioned procedures (which are selected from a total of 32 possible methods). The conclusion reached is that the S0c method is the best, although for very small samples (n i ≤ 10, ∀ i) the W3 method is better. The P0 method would be the optimal method if one needs a method which is almost never too liberal, but this entails using a method which is too conservative and which provides excessively wide CIs. The W3 and P0 methods have the additional advantage of being very easy to apply. A free programme which allows the application of the S0 and S0c methods (which are the most complex) can be obtained at http://www.ugr.es/local/bioest/Z_LINEAR_K.EXE

Conditional and Unconditional Tests (and Sample Size) Based on Multiple Comparisons for Stratified 2 × 2 Tables

The Mantel-Haenszel test is the most frequent asymptotic test used for analyzing stratified 2x2 tables. Its exact alternative is the test of Birch, which has recently been reconsidered by Jung. Both tests have a conditional origin: Pearson’s chi-squared test and Fisher’s exact test, respectively. But both tests have the same drawback that the result of global test (the stratified test) may not be compatible with the result of individual tests (the test for each stratum). In this paper, we propose to carry out the global test using a multiple comparisons method (MC method) which does not have this disadvantage. By refining the method (MCB method) an alternative to the Mantel-Haenszel and Birch tests may be obtained. The new MC and MCB methods have the advantage that they may be applied from an unconditional view, a methodology which until now has not been applied to this problem. We also propose some sample size calculation methods.This research was supported by the Ministerio de Economía y Competitividad, Spanish, Grant no. MTM2012-35591

Letter to the Editor

Regarding Paper “Stratified Fisher's exact test and its sample size calculation” by Sin-Ho Jung, Biometrical Journal (2014) 56(1): 129–140, http://dx.doi.org/10.1002/bimj.20130004

Inferences about a linear combination of proportions

Statistical methods for carrying out asymptotic inferences (tests or confidence intervals) relative to one or two independent binomial proportions are very frequent. However, inferences about a linear combination of K independent proportions L = Σβipi (in which the first two are special cases) have had very little attention paid to them (focused exclusively on the classic Wald method). In this article the authors approach the problem from the more efficient viewpoint of the score method, which can be solved using a free programme, which is available from the webpage quoted in the article. In addition the article offers approximate formulas that are easy to calculate, gives a general proof of Agresti’s heuristic method (consisting of adding a certain number of successes and failures to the original results before applying Wald’s method) and, finally, it proves that the score method (which verifies the desirable properties of spatial and parametric convexity) is the best option in comparison with other methods

Miettinen and Nurminen score statistics revisited

It is commonly necessary to perform inferences on the difference, ratio, and odds ratio of two proportions p1 and p2 based on two independent samples. For this purpose, the most common asymptotic statistics are based on the score statistics (S-type statistics). As these do not correct the bias of the estimator of the product pi (1–pi), Miettinen and Nurminen proposed the MN-type statistics, which consist of multiplying the statistics S by (N–1)/N, where N is the sum of the two sample sizes. This paper demonstrates that the factor (N–1)/N is only correct in the case of the test of equality of two proportions, providing the estimation of the correct factor (AU-type statistics) and the minimum value of the same (AUM-type statistics). Moreover, this paper assesses the performance of the four-type statistics mentioned (S, MN, AU and AUM) in one and two-tailed tests, and for each of the three parameters cited (d, R and OR). We found that the AUM-type statistics are the best, followed by the MN type (whose performance was most similar to that of AU-type). Finally, this paper also provides the correct factors when the data are from a multinomial distribution, with the novelty that the MN and AU statistics are similar in the case of the test for the odds ratio.</p