Marini E, Racugno W, Borgognini Tarli S M
Sezione di Scienze Antropologiche, Dipartimento Biologia Sperimentale, Università di Cagliari, Cittadella Universitaria di Monserrato, 09042 Monserrato, (Cagliari), Italy.
Am J Phys Anthropol. 1999 Aug;109(4):501-8. doi: 10.1002/(SICI)1096-8644(199908)109:4<501::AID-AJPA6>3.0.CO;2-7.
The difference between male and female values of quantitative traits depends on the distribution of the variables within each sex, increasing with the rise in the difference between male and female average values and with the decrease of the dispersion of measurements in both sexes. This paper deals with the sensitivity of some widely used indices (relative difference between male and female mean values (MDI), Student's t, and the so-called Bennett-Chakraborty-Majumder D coefficient) with respect to intrasexual variability. The Kolmogorov-Smirnov distance (KS) is suggested here as a further index of dimorphism, although it is not usually utilized for this purpose. The theoretical approach is accompanied by the analysis of empirical data (metric variables obtained from a sample of present Sardinians) and by computer simulations under various assumptions. Indices based on the difference between male and female average values are not able to evaluate fully the various aspects of dimorphism. Student's t proved to be an adequate measure of whole sex differences, both in real and in simulated samples, as intrasexual variability is included in its formulation. The D index also proved to be a good measure of undivided sexual dimorphism, as it is the result of formal examination, and from application to empirical or to simulated cases. The Kolmogorov-Smirnov distance gave the best performance both in formal examination and in the whole simulation results, as it takes into account intrasexual variability, and is applicable to any kind of distribution. In simulated cases it was sensitive to variations of means and variances, and it was able to evaluate variance dimorphism. Since the last three indices measure the combined effect of size and variance dimorphism, the joint use of the MDI index is suggested in order to isolate the relative contribution of the difference between the means.
数量性状的男性和女性值之间的差异取决于每个性别内变量的分布，随着男性和女性平均值之间差异的增加以及两性测量离散度的降低而增大。本文探讨了一些广泛使用的指标（男性和女性平均值的相对差异（MDI）、学生t检验以及所谓的贝内特 - 恰克拉波蒂 - 马宗德D系数）对性别内变异性的敏感性。尽管通常不用于此目的，但本文建议将柯尔莫哥洛夫 - 斯米尔诺夫距离（KS）作为二态性的进一步指标。理论方法伴随着对经验数据（从现代撒丁岛人的样本中获得的度量变量）的分析以及在各种假设下的计算机模拟。基于男性和女性平均值差异的指标无法充分评估二态性的各个方面。在实际样本和模拟样本中，学生t检验都被证明是衡量整体性别差异的适当方法，因为其公式中包含了性别内变异性。D指数也被证明是衡量整体性二态性的良好指标，这是通过形式检验以及应用于经验或模拟案例得出的结果。柯尔莫哥洛夫 - 斯米尔诺夫距离在形式检验和整个模拟结果中表现最佳，因为它考虑了性别内变异性，并且适用于任何类型的分布。在模拟案例中，它对均值和方差的变化敏感，并且能够评估方差二态性。由于最后三个指标衡量了大小和方差二态性的综合影响，因此建议联合使用MDI指数以分离均值差异的相对贡献。
