At my work, we have used a 'modified Coefficient of Variation', defined as the Standard Error over the mean, and I wanted to ask if there is any statistical justification for this. We are interested in determining the necessary sample size needed to be confident in our estimates of a mean value (like a simple, rule-of-thumb power analysis). I've been told that for our work, a value of 20% is an acceptable cutoff for SE/Mean. I recently encountered a different group of plant ecologists using SE/Mean in the same manner: to assess whether they had done enough surveys; however, I can not find broad online support for this statistical technique.
Based on searches here at CrossValidated and the internet more broadly, true CV is defined as standard deviation over the mean and lets you assess relative variability between separate sample groups that otherwise might have different units. I also know that SE is already a measure of how confident we are in the estimate of the mean. Does it make sense to standardize SE by the mean as a rule-of-thumb estimate for the variability in your sample?
I think the appeal of using SE/mean is that there is a clear decline in this metric with increasing sample size - but it feels arbitrary. Any insight would be appreciated.
EDIT: Real life examples
In my own work: We 'over sampled' an area of interest by doing a number of marine fish surveys within an area (say 20), then used SE/mean and bootstrapping to estimate how this metric changed with sample size. It was determined that the SE/mean had reduced to .20 or 20% by ~6 surveys so that in future years, we will now only use 6 surveys.
From the plant ecologist: SE/mean can be used post-hoc to determine if you collected enough transect data using the rule of thumb that SE/mean should be 10% or less. If SE/mean is greater than 10% - then you didn't survey enough and cannot be as confident in your results
Though one of these examples is from a terrestrial ecologist, both of these uses seem a little fishy..