Problems with using the normal distribution--and ways to improve quality and efficiency of data analysis

Area of Science:

• Statistics
• Data Analysis
• Scientific Methodology

Background:

• The Gaussian (normal) distribution and its summary statistics (mean ± SD/SEM) are standard for characterizing quantitative data variation.
• Current methods often fail to adequately represent skewed data distributions, potentially leading to incorrect conclusions.

Purpose of the Study:

• To question the adequacy of the Gaussian model for all data types.
• To propose an alternative characterization for skewed data using a multiplicative (log-normal) approach.

Main Methods:

• Evaluating the limitations of symmetric characterizations (mean ± SD) for skewed data.
• Introducing the log-normal distribution as a suitable model for data with multiplicative variation.
• Utilizing a new notation (mean * x/s*) for the geometric mean and multiplicative standard deviation.

Main Results:

• Symmetric characterizations are inappropriate for skewed distributions, as indicated by the "95% range check".
• Multiplicative causes of variation are generally more significant than additive ones.
• The log-normal distribution, characterized by geometric mean and multiplicative SD, provides a more accurate representation of skewed data.

Conclusions:

• Shifting from symmetric to asymmetric data views enhances recognition and interpretation quality.
• Adopting the log-normal model can lead to considerable savings in sample size.
• Accurate data modeling improves scientific insight and aligns with ethical responsibilities.