Is calculating the standard deviation of a group of standard deviations an appropriate way to represent volatility between groups?

This thread provides an excellent explanation of the calculation of the standard deviation of the sample standard deviation. However, I'm not sure if it's appropriate in my case.

I'm attempting to measure the stability of a classification scheme across groups of documents across years. My data contain 10 variables for ~20,000 observations. The observations are groups of documents and the variables are the fraction of each group assigned to one part of a binary classification each year. For instance (using 6 instead of all 10 to save space):

Group 2010 2011 2012 2013 2014 2015
Group1 0.27 0.28 0.27 0.26 0.26 0.28
Group2 0.62 0.64 0.61 0.60 0.66 0.64
Group3 0.00 0.00 0.01 0.00 0.02 0.00

To measure the stability of the fractional classification within a group across years, the population standard deviation seems to make the most sense. Using the sample above, this would be: $$$$\sigma = \sqrt\frac{\sum{(X-\mu)^2}}{N}$$$$

Group 2010 2011 2012 2013 2014 2015 SD
Group1 0.27 0.28 0.27 0.26 0.26 0.28 0.0082
Group2 0.62 0.64 0.61 0.60 0.66 0.64 0.0203
Group3 0.00 0.00 0.01 0.00 0.02 0.00 0.0076

Now, I want to find the stability between groups. Would it be appropriate to simply calculate the population SD of the population SD values? It's important to note that the distribution of SDs by group is not normal in my complete data (e.g., Skewness = 1.58, Kurtosis = 5.39)

• Use counts instead of fractions, because the fractions have lost almost all information about how much variability to expect.
– whuber
Jun 1, 2022 at 16:09