Smothers C D, Sun F, Dayton A D
Central Research Division, Pfizer Inc., Groton, CT 06340, USA.
Vet Parasitol. 1999 Mar 1;81(3):211-24. doi: 10.1016/s0304-4017(98)00206-4.
Efficacy calculations in anthelmintic studies require estimates of the central tendency for the nematode populations. Confusion exists among practitioners regarding which measures of central tendency are most appropriate; although the arithmetic mean is frequently used, there are theoretical reasons for preferring the geometric mean. To investigate this controversy, arithmetic and geometric means were compared for their suitability for use in measuring efficacy. Arithmetic and geometric means were compared as measures of central tendency for skewed distributions. The following criteria were developed to facilitate the comparison: (1) probability around the parameter, (2) influence of extreme values, and (3) proximity to the median. Under log-normality, theoretical results demonstrated the superiority of the geometric mean. Modified-bootstrap simulations using empirical data from cattle were used to confirm theoretical expectations. Simulations on log-normal data supported the geometric mean as the better indicator of the central tendency. Additionally, for data not confirmed as log-normal, the superiority of geometric means was demonstrated. In a comparison of precision, it was shown that mean squared error was always smaller for sample geometric means than for arithmetic means when n> or =2. Simulation results added support to that conclusion.
驱虫研究中的疗效计算需要对线虫种群的集中趋势进行估计。从业者对于哪种集中趋势度量最为合适存在困惑；尽管算术平均数经常被使用，但从理论上来说，更倾向于几何平均数。为了研究这一争议，对算术平均数和几何平均数在衡量疗效方面的适用性进行了比较。将算术平均数和几何平均数作为偏态分布的集中趋势度量进行比较。为便于比较制定了以下标准：(1) 参数周围的概率，(2) 极端值的影响，以及(3) 与中位数的接近程度。在对数正态分布下，理论结果证明了几何平均数的优越性。使用来自牛的经验数据进行的修正自展模拟被用于证实理论预期。对对数正态数据的模拟支持几何平均数作为集中趋势的更好指标。此外，对于未确认为对数正态的数据，也证明了几何平均数的优越性。在精度比较中，结果表明当n≥2时，样本几何平均数的均方误差总是小于算术平均数。模拟结果为该结论提供了进一步支持。
