Testing for normality in regression models: mistakes abound (but may not matter)

Area of Science:

• Ecology
• Biology
• Statistics

Background:

• Normality tests are crucial for evaluating assumptions in statistical modeling.
• Misconceptions regarding the application of normality tests are prevalent in ecological and biological research.
• Over 70% of ecology and 90% of biology papers incorrectly test raw data for normality instead of model residuals.

Purpose of the Study:

• To investigate the impact of misapplying normality tests to raw data versus model residuals in linear regression.
• To compare the statistical power of parametric (t-test) and nonparametric (Mann-Whitney U test) methods under different normality testing approaches.
• To assess the consequences of common statistical errors in ecological and biological studies.

Main Methods:

• Bibliometric review of published ecology and biology papers to identify trends in normality test application.
• Simulation of datasets with varying distributions (normal, interval, skewed) and sample sizes.
• Comparison of statistical power between testing raw data and testing model residuals for normality.

Main Results:

• Minimal differences in statistical power were observed when normality was tested on raw data compared to residuals.
• When model residuals violated normality assumptions, the Mann-Whitney U test showed a 3-4% increase in statistical power compared to incorrect approaches.
• The impact of testing raw data for normality on statistical power is negligible, particularly with large sample sizes.

Conclusions:

• Correctly testing model residuals for normality is recommended to enhance statistical model performance.
• While awareness of proper statistical practices is needed, the practical impact of testing raw data for normality on power loss is minimal.
• The study underscores the importance of adhering to statistical assumptions for robust ecological and biological research.