Comparing coefficients of variation from numerous datasets

Question

Question 1) Is it valid to calculate a coefficient of variation (CV) for each dataset if there is some spatial correlation in the datapoints?

I have 30 datasets. Each dataset is from an independent trial and has ~2,000 data points in it. However, the data points within each trial are not necessarily independent from each other, they have some spatial correlation.

Furthermore, each data set has ~1000 datapoints from control and ~1000 datapoints from treatment. So if I calculate the CV for each within each dataset, I will have

control_cvs   = [cv1, cv2, cv3 ... cv30]  
treatment_cvs = [cv1, cv2, cv3 ... cv30]

Question 2) Can I treat each CV as independent and use them in a paired t-test to determine if control_cvs are significantly different than the treatment_cvs?

Given, of course, that the distribution of CVs is normal and the control and treatment have similar variances.

Each dataset represents an independent trial, to me it seems reasonable to treat the overall CV as a randomly sampled point. However, I have a limited understanding of statistics, any help in understanding this better would be appreciated.

Answer 1

There are several levels here to your question and possible answers. I will pick out three.

1. You have two sets of 30 scores or results (which happen to be coefficients of variation) for control and treatment conditions.

So, why not plot those scores? You don't say explicitly whether control and treatment samples are paired, but if so then natural plots are (1) a scatter plot of treatment versus control (2) often also a scatter plot of the difference versus the mean of those two (noting that the median is identical with the mean for two values).

Whether paired or unpaired, a plot of the distributions of the two sets of scores is also a possibility. Apart from more commonly seen plots, I suggest quantile plots as allowing easy comparison of both the general level, spread and shape of the distribution and any details (e.g. outliers).

Here are two examples:

How to present box plot with an extreme outlier?

How to visualize independent two sample t-test?

2. You write

Given, of course, that the distribution of CVs is normal and the control and treatment have similar variances.

where I hope that "[g]iven, of course, that" means "subject to checking whether". Non-normality is not necessarily fatal here and different variances can be accommodated often by using an appropriate version of the test. But coefficients of variation I would expect to be substantially skewed, as bounded by zero, not so strongly bounded upwards, and certainly unstable as a ratio of two quantities, so advice to tread carefully is likely to seem obvious.

3. Why use coefficients of variation at all? They provoke polarised opinions from statistical people. There are several threads bearing on this under the tag you cite, some fairly negative. My personal view is that coefficients of variation being helpful goes with variation being best considered on logarithm scale, in which case the variability of the logarithms is of direct interest.

For more see How to interpret the coefficient of variation?

The question of spatial dependence of the raw measurements is tricky as well as interesting. I would feel tempted to regard it as a side-issue, trusting that the coefficients of variation being based on independent sources is the major issue. There could easily be more authoritative views on this from people with deeper technical understanding.