Parametric and Nonparametric Statistics

Most of the commonly used statistical tests within the field of Applied Linguistics are based on assumptions about the underlying distribution and its parameters (e.g., means and standard deviations). These so‐called parametric statistics generally require the researcher to check, among other things, whether their data have a particular distribution or shape (i.e., an approximate normal distribution) and a comparable spread in scores across samples (i.e., homogeneity of variance). Real data, however, may violate one or more of the parametric assumptions, for example, when dealing with small samples with asymmetrical distributions and outliers. In these instances, it may be better to use a nonparametric statistical test instead. These tests generally have fewer assumptions and do not require the outcome variable to be approximately normally distributed. Because of this, they may sometimes be the better choice and sometimes they might even be the only valid option. If one or more of the assumptions of a parametric statistical test are not met, the conclusions obtained on the basis of that test might not be valid. It is thus crucial that researchers are aware of the assumptions that underlie statistical tests, that they are able to assess whether those assumptions are satisfied, and that they can consequently make an informed decision between a parametric test or its nonparametric alternative.

Homogeneity (statistics) · Nonparametric statistics · Parametric model · Parametric statistics · Probability distribution · Statistical hypothesis testing · Test (biology) · Variable (mathematics)

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