什么时候曼泽拉斯-阿尔特曼定律在数学上是微不足道的？一种新的方法
When is Menzerath-Altmann law mathematically trivial? A new approach
摘要：
孟泽拉特定律，Z的趋势，部分的平均大小，随着X的减少，部分的数量，在语言，音乐和基因组中发现。最近，有人认为，基因组中的定律的存在是Z = Y/X这一事实的必然结果，这意味着Z与X的比例为Z~1/X。这种比例是曼泽拉斯-阿尔特曼定律的一个非常特殊的例子，它已经被基因组中X和Y之间的相关性检验所否定，X是一个物种的染色体数量，Y是基因组的碱基大小，Z是平均染色体大小。在这里，我们回顾了该测试的统计基础，并考虑基于不同的相关性度量的三个非参数测试和一个参数测试，以评估基因组中的Z~1/X。最有效的检验是一种新的基于相关比的非参数检验，它能够在11个分类组中的9个中拒绝Z~1/X，并检测出边缘组。Z~1/X不是事实，而是真实基因组不符合的基线。认为孟泽拉特-奥特曼定律是不可避免的观点是有严重缺陷的。
英文摘要：
Menzerath's law, the tendency of Z, the mean size of the parts, to decrease as X, the number of parts, increases is found in language, music and genomes. Recently, it has been argued that the presence of the law in genomes is an inevitable consequence of the fact that Z = Y/X, which would imply that Z scales with X as Z ~ 1/X. That scaling is a very particular case of Menzerath-Altmann law that has been rejected by means of a correlation test between X and Y in genomes, being X the number of chromosomes of a species, Y its genome size in bases and Z the mean chromosome size. Here we review the statistical foundations of that test and consider three non-parametric tests based upon different correlation metrics and one parametric test to evaluate if Z ~ 1/X in genomes. The most powerful test is a new non-parametric based upon the correlation ratio, which is able to reject Z ~ 1/X in nine out of eleven taxonomic groups and detect a borderline group. Rather than a fact, Z ~ 1/X is a baseline that real genomes do not meet. The view of Menzerath-Altmann law as inevitable is seriously flawed.
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