Testing for normality: a user's (cautionary) guide.

Area of Science:

• Statistics
• Biostatistics
• Data Analysis

Background:

• The normality assumption, central to inferential statistics, posits data originates from a normal (Gaussian) distribution.
• Violating this assumption can render statistical outputs, like p-values, inoperable and lead to resource waste.
• Accurate assessment of normality is vital for reliable statistical inference.

Purpose of the Study:

• To provide an overview of diagrammatical and statistical methods for evaluating data normality.
• To highlight common pitfalls and challenges in applying normality tests.
• To critically examine the practical utility and necessity of preliminary normality testing.

Main Methods:

• Review of graphical methods for normality assessment (e.g., histograms, Q-Q plots).
• Discussion of common statistical tests for normality (e.g., Shapiro-Wilk, Kolmogorov-Smirnov).
• Analysis of potential misinterpretations and limitations of these methods.

Main Results:

• No method perfectly confirms normality; natural variables rarely conform to an ideal normal distribution.
• Graphical methods offer visual inspection but can be subjective.
• Statistical tests provide quantitative measures but are sensitive to sample size and assumptions.

Conclusions:

• Preliminary normality testing is often questioned due to the ideal nature of normality and the robustness of methods with large sample sizes.
• Careful consideration of methods and potential pitfalls is essential for valid statistical analysis.
• Alternative approaches or robust statistical methods may be preferable when normality is questionable.