Alternatives to classical statistical procedures: Introduction to the symposium.

Abstract

AbstractMost classical statistical methods are founded on two assumptions, that the underlying distribution is normally distributed, and that the sample observations are independently and identically distributed. It did not take statisticians long to realize that these idealizations may not be true in all applied settings. In addition, the good performance of these classical procedures requires strict adherence to these assumptions. Consequently, alternatives to the classical procedures have been proposed by statisticians. The purpose of this symposium is to begin a dialogue between quantitative methodologists and substantive psychological researchers (who are voracious consumers of the classical procedures) about alternatives to the classical methods. The first three papers (Hunter & May, Zumbo & Zimmerman, and May & Hunter) will discuss a class of methods referred to as nonparametric statistics. Nonparametric procedures are an early and popular alternative to the classical procedures. Lind & Zumbo will discuss methods which are designed to deal with violations of normality. In closing, Thomas will discuss alternatives to classical statistical procedures when the second assumption is violated.The primary goal of the symposium is to expose generalists and specialists in the behavioural and social sciences to statistical procedures which are not usually part of their standard statistical repertoire. As well, we believe that it is important to begin communication among methodologists and substantive psychological researchers in a direct and clear manner (i.e., avoiding as much jargon as possible). Pursuant to these goals we solicited the participation of two statistically literate substantive psychological researchers who use clever data - analytic strategies in their substantive fields of cognition and development and have written an elementary introductory textbook on behavioural science statistics (Hunter & May). As well, some social science methodologists/statisticians (Lind, Thomas, Zimmerman, & Zumbo) were invited to present papers on recent developments in their work. In the spirit of the demolition of the Berlin Wall, we were interested in removing the disciplinary boundaries which usually isolate us.The dialogue is vital to both disciplines. Speaking for the methodologists, many of the problems we deal with are fueled by substantive issues and problems. As well, the substantive researchers are often the authors of social and behavioural science statistics textbooks. The authors of introductory elementary textbooks and instructors in introductory courses in Psychology departments almost inevitably fall short of being leading experts in statistics, but they are shapers of opinion and practice, having the effect of primacy in their favour. Yet, often advances in substantive areas are based upon the results of statistical tests. Therefore, it is important and vital for these substantive researchers to be as current as possible in their statistical knowledge.Topic of the SymposiumThe topic of the symposium was alternatives to classical statistical procedures, also referred to as alternatives to normal theory. We use the term classical statistics in the title because this is often used in the statistical literature and because of the historical precedence of these techniques. However, we prefer the term alternatives to normal theory not only because these techniques rely on the normal distribution but also because they are what are normally used (please excuse the pun).Normal theory includes common statistical tests using t, F, or z distributions such as ANOVA or regression. Also, multivariate techniques such as MANOVA, discriminant analysis, factor analysis, and covariance structural modelling/structural equation modelling are included. Most of these methods are the ordinary realizations of the Gaussian based (normal distribution) general linear model via least - squares estimation. …