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Using the range to calculate the coefficient of variation
1Department of Information Systems/Decision Sciences, College of Business and Public Administration, Old Dominion University, Norfolk, VA 23529, USA. grhiel@odu.edu
Psychological Reports
|January 26, 2005
Summary
This study introduces a coefficient of variation (CVhigh-low) using extreme values. It performs best with normal distributions but offers limited point estimates for leptokurtic and skewed data, though it can compare relative variability.
Area of Science:
- Statistics
- Data Analysis
- Probability Distributions
Background:
- Traditional measures of statistical dispersion are essential for understanding data variability.
- The coefficient of variation (CV) is a standardized measure of dispersion, but its calculation can be sensitive to outliers or require the entire dataset.
- Exploring alternative methods for estimating variability, especially from limited data points, is valuable.
Purpose of the Study:
- To introduce and evaluate a novel coefficient of variation (CVhigh-low) derived from the highest and lowest values in a dataset.
- To assess the performance and limitations of CVhigh-low across different probability distributions: normal, leptokurtic, and skewed.
- To determine the utility of CVhigh-low as a point estimate and for comparative analysis of variability.
Main Methods:
- Calculation of a coefficient of variation (CVhigh-low) using only the maximum and minimum values of a dataset.
- Theoretical analysis and discussion of the application of CVhigh-low to normal, leptokurtic, and skewed population distributions.
- Evaluation of CVhigh-low's effectiveness as a point estimate of population variation and its capability in comparative variability assessments.
Main Results:
- CVhigh-low is most effective and provides a good point estimate when sampling from a normal distribution.
- For leptokurtic distributions, CVhigh-low is useful for comparing relative variability between datasets but yields a poor point estimate.
- With skewed distributions, CVhigh-low effectively identifies which dataset has greater relative variation but does not provide a precise measure of that variation or a good point estimate.
Conclusions:
- The CVhigh-low statistic is a viable, albeit limited, measure of data variability, particularly useful for quick comparisons.
- Its accuracy as a point estimate is highly dependent on the underlying data distribution, being most reliable for normal distributions.
- Further research may explore modifications or specific contexts where CVhigh-low can be optimized for leptokurtic and skewed data.