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Testing equality of two beta binomial proportions in the presence of unequal extra-dispersion parameters

机译:在存在不相等的额外色散参数的情况下测试两个beta二项式比例的相等性

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Data in the form of proportions with extra-dispersion (over/under) arise in many biomedical, epidemiological, and toxicological applications. In some situations, two samples of data in the form of proportions with extra-dispersion arise in which the problem is to test the equality of the proportions in the two groups with unspecified and possibly unequal extra-dispersion parameters. This problem is analogous to the traditional Behrens-Fisher problem in which two normal population means with possibly unequal variances are compared. To deal with this problem we develop eight tests and compare them in terms of empirical size and power, using a simulation study. Simulations show that a C() test based on extended quasi-likelihood estimates of the nuisance parameters holds nominal level most effectively (close to the nominal level) and it is at least as powerful as any other statistic that is not liberal. It has the simplest formula, is based on estimates of the nuisance parameters only under the null hypothesis, and is easiest to calculate. Also, it is robust in the sense that no distributional assumption is required to develop this statistic.
机译:在许多生物医学,流行病学和毒理学应用中,出现了具有超分散比例(过量/不足)的比例形式的数据。在某些情况下,会出现两个具有超分散比例形式的数据样本,其中的问题是要使用未指定且可能不相等的超分散参数来测试两组比例的相等性。此问题类似于传统的Behrens-Fisher问题,在该问题中比较了两个具有可能不相等方差的正态总体均值。为了解决这个问题,我们开发了八项测试,并通过模拟研究在经验大小和功效方面进行了比较。仿真表明,基于扰动参数的扩展拟似然估计的C()测试最有效地保持名义水平(接近名义水平),并且至少与任何其他不宽松的统计数据一样有效。它具有最简单的公式,仅在零假设下基于讨厌参数的估计,并且最容易计算。同样,从不需要分配假设即可发展该统计的意义上讲,它是可靠的。

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