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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 ?

Momo
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Grunwalski
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  • What you mean give it "meaning" and "standard error relation"? What you're doing sounds like part of a Monte Carlo procedure... – Lucas Farias May 10 '17 at 23:14
  • Well, I want to judge how spread the data is. 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 ? – Grunwalski May 11 '17 at 07:21
  • See here for conceptually similar problem: https://stats.stackexchange.com/questions/132536/how-to-choose-a-confidence-level/132538#132538 Basically there is **no statistical method** that return results that can be no matter of context considered as "high" or "low" depending on their values alone. – Tim May 11 '17 at 07:39
  • Maybe there's another way for you to achieve the kind of conclusion you want. Because, as @Tim stated, such numbers don't speak by themselves. It is to say, for example, that If there was another study like this, you could at least compare your results with theirs. – Lucas Farias May 11 '17 at 17:40

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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.

Nuclear Hoagie
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