I am trying to compare the variability of SpO2 values within a specific time frame from different patient groups. These values are non-normally distributed (negative skew). Is it still possible to use Coefficient of Variation (CV) to calculate the variability between the two data sets (patient groups)? As CV uses mean and SD and non-normally distributed data is usually compared using median and IQR, I am unsure whether CV is still an option for my data set?
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$\begingroup$ Please explain what you mean by "variability between datasets." Evidently you intend to compare two datasets, but what properties do you wish to compare? $\endgroup$– whuber ♦Commented Mar 11, 2021 at 17:57
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2$\begingroup$ In fact normality isn't even an ideal case for the coefficient of variation. Consider that the standard normal has mean 0. That picky point aside, usefulness of coefficient of variation marches with useful of logarithmic transformation, and negative skew makes the latter unlikely. $\endgroup$– Nick CoxCommented Jan 11, 2023 at 19:21
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You can use the Coefficient of Variation (CV) to compare the homogeneity/variability between two data sets independent of distribution. So yes! You can.
The CV is given by $$CV=\frac{S}{\bar{x}}$$ where $S$ denotes the standard deviation of the sample and $\bar{x}$ the mean of the sample.
The CV is measured in percent units. Sets with values of CV less than $10\%$ tend to be interpreted as homogeneous sets.
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1$\begingroup$ Use of percentages is a common convention, but in no sense universal or binding. $\endgroup$– Nick CoxCommented Jan 11, 2023 at 19:22