Content area
Full Text
Abstract
Five myths concerning the application of parametric and nonparametric tests are discussed. Well known considerations of power, robustness, and scale of measurement are reviewed briefly. Less well known ideas about the nature of the null hypothesis and generality of application are outlined. It is concluded that in many applications behavioural researchers are using what appear to be parametric tests, but actually are evaluating nonparametric hypotheses and estimating the probability of a Type I error that would be obtained with a nonparametric test.
Statisticians have debated the relative merits of parametric and nonparametric inference for over 60 years, and increasingly that literature favours nonparametric inference when applied to data from behavioural research. Nevertheless, even a cursory look at the psychological research literature reveals that the parametric platform has been more convincing to psychologists. Why is there a schism between statisticians and researchers? We hope to answer this question by suggesting that the issue of parametric versus nonparametric inference has been dominated by a collection of interrelated myths and half - truths that have mislead researchers into using, or believing they are using, parametric tests. In debunking these myths we argue that the victory of parametric inference over nonparametric inference is more illusory than real. The myths to be discussed are:
1. Parametric tests are more powerful than nonparametric tests.
2. Parametric tests are robust.
3. Nonparametric tests are tests on non - interval data -- and t - and F - tests are exclusively parametric tests.
4. The null hypotheses evaluated by parametric tests are direct and clear, whereas the null hypotheses evaluated by nonparametric tests are indirect and vague.
5. Nonparametric tests are restricted in their application.
These myths are all tied in one way or another to evaluating the validity of statistical tests performed on real - life data -- that is, evaluating the "believability" of obtained probabilities of Type I error. Since the validity of all statistical tests relies on satisfying certain assumptions, we begin by briefly reviewing the assumptions underlying parametric and nonparametric tests.
Assumptions
The assumptions underlying the best - known and most frequently usedparametric statistics include:
1. All observations are randomly and independently sampled from their parent populations.
2. The population distributions from which samples are selected are normal.