Bartlett统计量的修正公式

MODIFICATION OF BARTLETT'S STATISTIC

Bartlett统计量在多母体方差齐性检验中有着重要的应用。通常认为Bartlett统计量近似服从χ2分布,但是工程应用中发现,当样本较小时Bartlett统计量与其χ2分布之间的误差较大,导致小样本情况下检验精度不高。对此,文中根据Bartlett统计量与其χ2分布之间均值相等的原则,提出一种修正的Bartlett统计量。该统计量在大样本和小样本情况下均能更好地服从χ2分布,可以有效地提高检验精度。并给出Bartlett统计量与修正Bartlett统计量之间对比结果。此外,还建立两正态母体标准差比例、两指数母体均值比例的仿真结果检验方法和多母体标准差比例仿真结果检验的两步仿真法。

Bartlett＇ s statistic is widely used in test for homogeneity of variances. It is well known that Bartlett＇ s statistic is an approximate Х^2 distribution. However, Bartlett＇s statistic departs far from its Х^2 distribution and results in low test precision in small sample situation. Based on mean equality of both Bartlett＇ s statistic and its Х^2 distribution, a new modified formulation of Bartlett＇ s statistic is proposed. It can not only be well distributed as Х^2 distribution in both large and small sample situation, but also effectively increase test precision. Comparison between modified and traditional Bartlett＇s statistic is also presented. Furthermore, test methods for simulation results are established, including standard deviation ratio test for two normal populations, mean ratio test for two exponent populations, and two-step simulation method of standard deviation ratio test for multiple populations.