Coefficient of variation calculated from the range for skewed distributions

Area of Science:

• Statistics
• Data Analysis
• Psychometrics

Background:

• Skewed distributions are prevalent in real-world data, particularly in psychology and education.
• Traditional measures of variation may be less reliable with skewed data.
• Accurate estimation of population variation is crucial for robust statistical inference.

Purpose of the Study:

• To develop a novel coefficient of variation (CVS(high.low)) robust to skewed distributions.
• To assess the utility of CVS(high.low) as a dose estimate for population coefficient of variation.
• To validate the method using both theoretical and empirical skewed distributions.

Main Methods:

• A new coefficient of variation, CVS(high.low), was formulated using the maximum and minimum values of a dataset.
• A correction factor was derived to enhance the accuracy of CVS(high.low).
• The performance of CVS(high.low) was evaluated against population coefficient of variation using chi-squared and empirical skewed distributions.

Main Results:

• The developed CVS(high.low) with its correction factor provides a reliable dose estimate of the population coefficient of variation.
• The method demonstrated effectiveness across three distinct skewed chi-squared distributions.
• Validation using three skewed empirical datasets from psychology and education confirmed the method's practical applicability.

Conclusions:

• CVS(high.low) offers a practical and effective approach for estimating population variation from skewed data.
• This method is particularly valuable when dealing with real-world datasets in fields like psychology and education.
• The findings suggest a new tool for statistical analysis where data skewness is a concern.