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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

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The Kolmogorov-Smirnov test is unreliable for detecting non-normal data in dermatology research, especially with small sample sizes. Preliminary normality testing is not recommended for small-to-moderate sample sizes.

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Area of Science:

  • Dermatological research
  • Statistical methodology

Background:

  • Statistical methods are crucial in dermatology, with distributional assumptions impacting procedure adequacy.
  • Goodness-of-fit tests are commonly used to choose between parametric and nonparametric methods in dermatological studies.

Purpose of the Study:

  • To evaluate the performance of the Kolmogorov-Smirnov test for normality assumption.
  • To assess the test's reliability on various non-normal data types common in dermatology.

Main Methods:

  • Simulations were conducted to analyze the Kolmogorov-Smirnov test's performance.
  • The study examined the impact of sample size and the severity of normality violations.

Main Results:

  • The Kolmogorov-Smirnov test showed poor performance on data with single/multiple outliers and skewed distributions for sample sizes under 100.
  • Normality was acceptably rejected for Likert-type data.

Conclusions:

  • Preliminary normality testing using the Kolmogorov-Smirnov test is not advisable for small-to-moderate sample sizes in dermatological research.
  • Researchers should reconsider relying on preliminary normality tests due to performance limitations.