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Preliminary testing for normality: some statistical aspects of a common concept
V Schoder1, A Himmelmann, K P Wilhelm
1proDERM, Institute for Applied Dermatological Research, Schenefeld, Hamburg, Germany. vschoder@proderm.de
Background:
Statistical methodology has become an increasingly important topic in dermatological research. Adequacy of the statistical procedure depends among others on distributional assumptions. In dermatological articles, the choice between parametric and nonparametric methods is often based on preliminary goodness-of-fit tests.
Aim:
For the special case of the assumption of normally distributed data, the Kolmogorov-Smirnov test is the most popular choice. We investigated the performance of this test on four types of non-normal data, representing the majority of real data in dermatological research.
Methods:
Simulations were run to assess the performance of the Kolmogorov-Smirnov test, depending on sample size and severity of violations of normality.
Results:
The Kolmogorov-Smirnov test performs badly on data with single outliers, 10% outliers and skewed data at sample sizes < 100, whereas normality is rejected to an acceptable degree for Likert-type data.
Conclusion:
Preliminary testing for normality is not recommended for small-to-moderate sample sizes.
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