Abstract In this paper, we develop appropriate sampling methodologies for testing hypotheses regarding the difference of mean values from two independent (or dependent) normal populations when their variances are unknown and unequal. We design two-stage and purely sequential testing methodologies of hypotheses for comparing the unknown means by determining the appropriate sample sizes while controlling both type-I and type-II error probabilities at or below preassigned levels α, β respectively. Such methodologies are constructed under both unequal and equal sample size designs. We prove that both two-stage and purely sequential testing strategies enjoy a number of practically appealing properties. Extensive sets of computer simulations and real data analyses empirically validate our theoretical findings.

中文翻译：

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两样本两阶段纯序列方法论，用于假设检验与应用：当两个方差未知且不相等时比较正态均值

摘要 在本文中，我们开发了适当的抽样方法来检验关于两个独立（或相关）正态总体的平均值差异的假设，当它们的方差未知且不相等时。我们设计了两阶段和纯顺序的假设检验方法，通过确定适当的样本大小，同时将 I 类和 II 类错误概率分别控制在或低于预先指定的水平 α、β 来比较未知均值。此类方法是在不等和等样本量设计下构建的。我们证明了两阶段和纯顺序测试策略都具有许多实际吸引人的特性。大量的计算机模拟和真实数据分析从经验上验证了我们的理论发现。