Why coefficient of variation

Since the coefficient of variation is the standard deviation divided by the mean, divide the cell containing the standard deviation by the cell containing the mean. For example, consider a risk-averse investor who wishes to invest in an exchange-traded fund ETF , which is a basket of securities that tracks a broad market index.

Then, he analyzes the ETFs' returns and volatility over the past 15 years and assumes the ETFs could have similar returns to their long-term averages. For illustrative purposes, the following year historical information is used for the investor's decision:.

Risk Management. Portfolio Management. Financial Ratios. Tools for Fundamental Analysis. Fundamental Analysis. Actively scan device characteristics for identification.

Use precise geolocation data. Select personalised content. Create a personalised content profile. Measure ad performance. Select basic ads. Create a personalised ads profile.

Select personalised ads. Apply market research to generate audience insights. Measure content performance. Develop and improve products. List of Partners vendors. The CV for a variable can easily be calculated using the information from a typical variable summary and sometimes the CV will be returned by default in the variable summary. We demonstrate below how to calculate the CV in Stata. The advantage of the CV is that it is unitless. This allows CVs to be compared to each other in ways that other measures, like standard deviations or root mean squared residuals, cannot be.

In the variable CV setting: The standard deviations of two variables, while both measure dispersion in their respective variables, cannot be compared to each other in a meaningful way to determine which variable has greater dispersion because they may vary greatly in their units and the means about which they occur.

The standard deviation and mean of a variable are expressed in the same units, so taking the ratio of these two allows the units to cancel. This ratio can then be compared to other such ratios in a meaningful way: between two variables that meet the assumptions outlined below , the variable with the smaller CV is less dispersed than the variable with the larger CV.

In the model CV setting: Similarly, the RMSE of two models both measure the magnitude of the residuals, but they cannot be compared to each other in a meaningful way to determine which model provides better predictions of an outcome. The coefficient of variation is underused rather than overused as a measure of temporal or spatial variability. Some researchers still use standard deviations for variables where the standard deviation is directly proportional to the mean - instead such variables should be log transformed, or alternatively the coefficient of variation used to describe variability.

We have included a few examples of its correct use for these purposes. Krebs discusses the use of the coefficient of variation for measuring temporal variability. He emphasizes that it is only appropriate when the slope of Taylor's Power Law is equal to 2 i. Shoukri et al. McLaughlin et al. McArdle et al. Eberhardt discusses use of the coefficient of variation in appraising variability in population studies, whilst Patel et al. Wikipedia provides a section on the coefficient of variation.

Martin Bland provides an excellent discussion on different ways to calculate the within-subject coefficient of variation. Poultry Health Services covers the intra- and interclass CVs for assay quality control, whilst Will Hopkins covers the intra-class coefficient of variation in relation to 'sports science'.