声调研究中的一种新统计方法——“增长曲线分析”法在汉语方言研究中的运用

A new statistical approach in the studies of tones:Two case studies on Chinese dialects using Growth Curve Analysis

声调基频是一种连续的非线性数据。长期以来,针对基频数据多采用T检验、方差分析等“点对点”的统计方法,但这类方法本质上是将连续的数据作离散化处理,并不符合基频数据的特点。本文旨在介绍一种新的统计方法——“增长曲线分析”法。这种统计方法能将基频曲线作为一个整体来考量,通过正交多项式拟合声调曲线,采用均值、斜率和凹凸程度等特征系数来比较曲线的异同。这种统计方法不仅能够较有效地解决传统“点对点”统计方法所带来的诸多弊端,还能将声调数据中的个体差异考虑在内。此外,本文还通过两个实例研究——黎里方言单字调和天津方言两字组连调,展示了“增长曲线分析”法对解决汉语方言声调研究争议问题的有效性。

Fundamental frequency(f 0)contours of lexical tones are a type of non-linear continuous data.Previous studies typically represent tonal f 0 contours with discrete points and conduct“point-by-point”statistical analyses such as T-test and ANOVA.Such tests,however,face challenges given by the continuous and non-linear nature of f 0 data.The current paper introduces a new statistical method,the“Growth Curve Analysis(GCA)”,which treats a continuous f 0 contour as a whole.With orthogonal polynomial structures,f 0 contours are fitted independently in terms of intercept,slope,and high-order(e.g.quadratic)terms.This approach can not only avoid the problems of traditional“point-by-point”statistical analyses,but also take speaker individual differences into consideration.Two case studies are discussed to illustrate the method:one is on lexical tonal realization in the Lili黎里Wu吴Chinese,and the other is on tone sandhi in Tianjin天津Mandarin.Both studies show that debates in the existing literature on tones can be more effectively resolved via statistical modeling with GCA.