Improving Data Analysis in Second Language Acquisition by Utilizing Modern Developments in Applied Statistics

Abstract

In this article we introduce language acquisition researchers to two broad areas of applied statistics that can improve the way data are analyzed. First we argue that visual summaries of information are as vital as numerical ones, and suggest ways to improve them. Specifically, we recommend choosing boxplots over barplots and adding locally weighted smooth lines (Loess lines) to scatterplots. Second, we introduce the reader to robust statistics, a tool that can provide a way to use the power of parametric statistics without having to rely on the assumption of a normal distribution; robust statistics incorporate advances made in applied statistics in the last 40 years. Such types of analyses have only recently become feasible for the non-statistician practitioner as the methods are computer-intensive. We acquaint the reader with trimmed means and bootstrapping, procedures from the robust statistics arsenal which are used to make data more robust to deviations from normality. We show examples of how analyses can change when robust statistics are used. Robust statistics have been shown to be nearly as powerful and accurate as parametric statistics when data are normally distributed, and many times more powerful and accurate when data are non-normal.