假设检验中计算观察检验效能的意义的探讨

What's the Meaning of Observed Power in Hypothesis Testing

目的探讨假设检验后计算观察检验效能的意义。方法理论上推导观察检验效能与P值的函数关系。应用MonteCarlo方法,模拟产生不同参数条件下三种常用假设检验方法的观察检验效能与P值,建立两者的回归方程,计算两者的决定系数R2。根据模拟结果进一步揭示观察检验效能与P值的关系。结果定义上,观察检验效能并不等同于理论检验效能。理论上,观察检验效能是P值的单调减函数。模拟上,检验观察检验效能与P值呈负相关关系,两者存在对数二次曲线回归关系,且决定系数大于0.9。结论依据样本信息计算观察检验效能并不能提供比P值更多的信息,不能作为理论检验效能的估计值或替代值,因此,根据观察检验效能的大小判断样本量是否足够的观点不应该提倡,即使检验结果P>0.05。

Objective To explore the meaning of the observed power in hypothesis testing.Methods To confirm whether observed power is the function of P value theoretically.Monte Carlo technique was used to simulate the observed power and P value in three common hypothesis tests with parameters changed. Relationship between observed power and P value was described based on their regression equation and R square.Results In definition,the observed power is not equal to theoretical power. In theory,observed power is a monotony decrease function of P value. In simulation,observed power and P value were negatively correlative and logarithmic quadratic regression could be applied to describe their numeric relationship with R square more than 0.9.Conclusion Observed power could not provide more information than P value. It could not be used to estimate the theoretical power. Therefore,it is not recommended to calculate observed power for inferring whether sample size is enough or not even if P value is larger than 0.05 as a result of hypothesis testing.