两个独立样本均数比较时各自样本含量的最佳搭配

Estimating sample size for quantative data when comparing two parallel groups with optimal allocation ratio

目的结合实例，介绍两个独立样本均数比较时在不同限制条件下最优样本含量计算公式的推导与应用。方法根据研究中纳入样本的难易程度与经费限制，分3种情况讨论，阐明各种条件下的最优样本含量估算公式的推导与应用。结果①在总样本含量N一定时n1=n2=1/2 N使假设检验功效最大；②在总经费C一定时，n1=C/c1＋√c1c2,n2=C/c2＋√c1c2使假设检验功效最大；③在检验功效1-β与第一组样本含量n1一定时，n2=（z1-α/2＋z1-β）2σ2n1/n1δ2-（z1-α/2-z1-β）2σ2 使总样本含量N最小。结论按照各个条件下的公式计算，可以获得该条件限制下的最优样本含量估计。

Objective To introduce the development and application of sample size formulas under various situations ac- cording to practical examples. Methods With the considerations of cost and the difficulty of enrolling volunteers, we discuss thetopic under 3 situations. Results 1 ①For a given total sample size N, n1 =n2 =1/2N, may lead to a maximum power; ②For agiven total cost C, n1=C/c1＋√c1c2,n2=C/c2＋√c1c2may lead to a maximum power; ③For a given power 1-β and sample size ofthe first group n1, n2=（z1-α/2＋z1-β）2σ2n1/n1δ2-（z1-α/2-z1-β）2σ2 will lead to a minimum sample size in total. Conclusion These proposed formulascan provide the optimal sample sizes under the various specific situations.