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Many statistical tests assume normal distribution. This paper explores alternative data distributions when normality is not met, offering better analytical options than non-parametric methods.

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Area of Science:

  • Statistics
  • Data Analysis

Background:

  • Classical statistical tests often rely on the assumption of normally distributed data.
  • Violating this assumption can lead to the inappropriate use of non-parametric methods or normal distributions.
  • Existing non-parametric methods may have limitations or not be suitable for all data types.

Purpose of the Study:

  • To highlight the importance of selecting appropriate data distributions beyond the normal distribution.
  • To introduce researchers to alternative distributions available in modern statistical software.
  • To guide the selection of distributions that accurately represent the data generating process.

Main Methods:

  • Discussion of various non-normal probability distributions.
  • Categorization of distributions based on suitability for different data types.
  • Review of modern statistical software capabilities for distribution selection.

Main Results:

  • Identified several alternative distributions suitable for non-normally distributed data.
  • Provided guidance on matching data characteristics to appropriate distributions.
  • Emphasized that selecting a correct distribution is a critical, often overlooked, step in data analysis.

Conclusions:

  • Choosing a distribution that reflects the data generating process improves analytical accuracy.
  • Researchers should explore alternatives to the normal distribution when its assumptions are violated.
  • Utilizing a wider range of distributions enhances the robustness of statistical analyses.