变量变换对假设检验效能影响的研究

To Explore How to Improve the Power of the Test by Variable Transformation

目的探讨变量变换对假设检验效能的影响。方法以两样本率假设检验为例,建立变量变换后统计量的渐近分布,通过计算机模拟,比较经过各种变量变换后假设检验第一类错误和第二类错误的变化,从而确定较优的变换。结果在不同总体率的条件下,找到几个能改变小样本χ2检验效能的变换函数。结论变量变换能有效地提高假设检验的效能。

Objective This paper explored how to improve the power of the test by variable transformation. Methods In this paper, the authors made the statistic based on the two- sample rate by transformation. In order to search better transformation, Type Ⅰ error and Type Ⅱ error were compared among the all kinds of statistic. Results Based on the scale of population rate, we have found the some transformation that can improve the power of test, especially X^2 test of the small sample size. Conclusion The variable transformation can improve the power of test.