I have computed the mean, variance, min and max from multiple samples of a distribution. Now I have also computed the sample mean and standard error of these statistics. How can I give these values meaning ? The statistics are all within different ranges and so are their standard error. Can I set the standard error relation to the corresponding sample mean and then judge its effects ?
Concretely, it's accelerometer data of multiple mice individuals. I have computed the statistics for each individual and the mean plus standard error of those statistics across the mouse population. Now I want to judge whether the deviation of the statistics among the individuals is large or not. For example the mean of the mean across the population is 0.5, and the standard error is 0.7. Now is it a big error ? The variance on the other hand has a mean of 7e+03 and a standard error of 4e+3. Is this error big ?
Best Answer
One metric you could use is the coefficient of variation, which is simply the standard deviation divided by the mean. This will tell you about the relative proportion of variability in the samples compared to the magnitude of the samples themselves. A variance of 1e9 might seem large, but not for a variable whose mean is 1e1000. You will still have to draw a cutoff somewhere to delineate "high" and "low" error, but at least you will have a statistic that looks at the error compared to the mean.