Statistical comparison of similarity tests applied to speech production data

Statistical analysis of data variability in speech production research has traditionally been addressed with the assumption of normally distributed error terms. The correct and valid application of statistical procedure requires a thorough investigation of the assumptions that underlie the methodology. In previous work [Kollia and Jorgenson, J. Acoust. Soc. Am. 102 (1997); 109 (2002)], it was shown that the error terms of speech production data in a linear regression can be modeled accurately using a quadratic probability distribution, rather than a normal distribution as is frequently assumed. The measurement used in the earlier Kollia–Jorgenson work involved the classical Kolmogorov–Smirnov statistical test. In the present work, the authors further explore the problem of analyzing the error terms coming from linear regression using a variety of known statistical tests, including, but not limited to chi‐square, Kolmogorov–Smirnov, Anderson–Darling, Cramer–von Mises, skewness and kurtosis, and Durbin. Our study complements a similar study by Shapiro, Wilk, and Chen [J. Am. Stat. Assoc. (1968)]. [Partial support provided by PSC‐CUNY and NSF to Jay Jorgenson.]