Using the range to calculate the coefficient of variation.
ABSTRACT In this research a coefficient of variation (CVhigh-low) is calculated from the highest and lowest values in a set of data. Use of CVhigh-low when the population is normal, leptokurtic, and skewed is discussed. The statistic is the most effective when sampling from the normal distribution. With the leptokurtic distributions, CVhigh-low works well for comparing the relative variability between two or more distributions but does not provide a very "good" point estimate of the population coefficient of variation. With skewed distributions CVhigh-low works well in identifying which data set has the more relative variation but does not specify how much difference there is in the variation. It also does not provide a "good" point estimate.
- SourceAvailable from: Elke U Weber[show abstract] [hide abstract]
ABSTRACT: This article examines the statistical determinants of risk preference. In a meta-analysis of animal risk preference (foraging birds and insects), the coefficient of variation (CV), a measure of risk per unit of return, predicts choices far better than outcome variance, the risk measure of normative models. In a meta-analysis of human risk preference, the superiority of the CV over variance in predicting risk taking is not as strong. Two experiments show that people's risk sensitivity becomes strongly proportional to the CV when they learn about choice alternatives like other animals, by experiential sampling over time. Experience-based choices differ from choices when outcomes and probabilities are numerically described. Zipf's law as an ecological regularity and Weber's law as a psychological regularity may give rise to the CV as a measure of risk.Psychological Review 05/2004; 111(2):430-45. · 9.80 Impact Factor
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ABSTRACT: The relative efficiency and biasedness of using the standardized mean range to estimate σ is discussed. The effect σ parental non-normality on the relative efficiency of the range estimator of σ is found to be minimal for n20. This further establishes the robustness of using this method of estimating σ in quality control analysis. For larger sample sizes and non-normal distributions, the use of the standardized mean range often results in extremely biased estimates of σ. This can be problematic when selecting proper sample sizes. With populations which are grossly leptokurtic, sample sizes which are too large occur, and an extra cost may be incurred. With platykurtic distributions, sample sizes which are too small occur, and additional sampling may be necessary to obtain a proper sample size.Journal of Statistical Computation and Simulation 03/1986; 24(1):71-82. · 0.63 Impact Factor