I posted a question earlier but failed miserably in trying to explain what I am looking for (thanks to those who tried to help me anyway). Will try again, starting with a clean sheet.

Standard deviations are sensitive to scale. Since I am trying to perform a statistical test where the best result is predicted by the lowest standard deviation amongst different data sets, is there a way to “normalize” it for scale, or use a different standard-deviation-type test altogether?

Unfortunately dividing the resulting standard deviation by the mean in my case does not work, as the mean is almost always close to zero.

Thanks

**Answer**

If all your measurements are using the same units, then you’ve already addressed the scale problem; what’s bugging you is degrees of freedom and precision of your estimates of standard deviation. If you recast your problem as comparing *variances*, then there are plenty of standard tests available.

For two independent samples, you can use the F test; its null distribution follows the (surprise) F distribution which is indexed by degrees of freedom, so it implicitly adjusts for what you’re calling a scale problem. If you’re comparing more than two samples, either Bartlett’s or Levene’s test might be suitable. Of course, these have the same problem as one-way ANOVA, they don’t tell you which variances differ significantly. However, if, say, Bartlett’s test did identify inhomogeneous variances, you could do follow-up pairwise comparisons with the F test and make a Bonferroni adjustment to maintain your experimentwise Type I error (alpha).

You can get details for all of this stuff in the NIST/SEMATECH e-Handbook of Statistical Methods.

**Attribution***Source : Link , Question Author : user2137 , Answer Author : Mike Anderson*