García-Pérez Miguel A, Núñez-Antón Vicente
Departamento de Metodología, Facultad de Psicología, Universidad Complutense, Madrid, Spain.
Span J Psychol. 2009 May;12(1):288-307. doi: 10.1017/s1138741600001694.
Statistical inference about two binomial parameters implies that they are both estimated by binomial sampling. There are occasions in which one aims at testing the equality of two binomial parameters before and after the occurrence of the first success along a sequence of Bernoulli trials. In these cases, the binomial parameter before the first success is estimated by negative binomial sampling whereas that after the first success is estimated by binomial sampling, and both estimates are related. This paper derives statistical tools to test two hypotheses, namely, that both binomial parameters equal some specified value and that both parameters are equal though unknown. Simulation studies are used to show that in small samples both tests are accurate in keeping the nominal Type-I error rates, and also to determine sample size requirements to detect large, medium, and small effects with adequate power. Additional simulations also show that the tests are sufficiently robust to certain violations of their assumptions.
关于两个二项式参数的统计推断意味着它们都通过二项式抽样进行估计。在伯努利试验序列中，有时人们旨在检验首次成功出现前后两个二项式参数的相等性。在这些情况下，首次成功之前的二项式参数通过负二项式抽样进行估计，而首次成功之后的二项式参数通过二项式抽样进行估计，并且这两个估计值是相关的。本文推导了用于检验两个假设的统计工具，即两个二项式参数都等于某个指定值以及两个参数相等但未知。模拟研究用于表明在小样本中，这两个检验在保持名义第一类错误率方面都是准确的，并且还用于确定以足够的功效检测大、中、小效应所需的样本量。额外的模拟还表明，这些检验对于其假设的某些违反情况具有足够的稳健性。
