Schillaci Michael A, Schillaci Mario E
Department of Social Sciences, University of Toronto Scarborough, 1265 Military Trail, Toronto, Ontario M1C 1A4, Canada.
J Hum Evol. 2009 Feb;56(2):134-8. doi: 10.1016/j.jhevol.2008.08.019. Epub 2008 Dec 2.
The use of small sample sizes in human and primate evolutionary research is commonplace. Estimating how well small samples represent the underlying population, however, is not commonplace. Because the accuracy of determinations of taxonomy, phylogeny, and evolutionary process are dependant upon how well the study sample represents the population of interest, characterizing the uncertainty, or potential error, associated with analyses of small sample sizes is essential. We present a method for estimating the probability that the sample mean is within a desired fraction of the standard deviation of the true mean using small (n<10) or very small (n < or = 5) sample sizes. This method can be used by researchers to determine post hoc the probability that their sample is a meaningful approximation of the population parameter. We tested the method using a large craniometric data set commonly used by researchers in the field. Given our results, we suggest that sample estimates of the population mean can be reasonable and meaningful even when based on small, and perhaps even very small, sample sizes.
在人类和灵长类动物进化研究中使用小样本量是很常见的。然而，评估小样本在多大程度上代表潜在总体却并不常见。由于分类学、系统发育和进化过程的判定准确性取决于研究样本对目标总体的代表性，因此描述与小样本量分析相关的不确定性或潜在误差至关重要。我们提出了一种方法，用于估计使用小样本量（n<10）或非常小的样本量（n≤5）时样本均值在真实均值标准差的期望比例范围内的概率。研究人员可以使用此方法事后确定其样本是总体参数有意义近似值的概率。我们使用该领域研究人员常用的一个大型颅骨测量数据集对该方法进行了测试。基于我们的结果，我们认为即使基于小样本量甚至非常小的样本量，总体均值的样本估计也可能是合理且有意义的。
