I was trying to find a suitable way to compare the relative data dispersion between two groups and also to investigate if they are statistically significant. During the last weeks, I have searched a lot and read several papers and finally come up with a solution. As I am not from statistical background, I would like your advice on this matter, if I am doing all wrong!
- According to Jeerapa [1], there are several ways to compute confidence interval for a coefficient of variation ($cv=\frac{\sigma}{\mu}$, where, $\sigma$ represents standard deviation, and $\mu$ represents mean value). I have used both Miller's Confidence interval and McKay's confidence interval. The equations can be found in the cited paper (3 and 4).
According to Altman [2], we can compute both p-value (significantly different than 0) and standard error from a given 95% CI and mean value.
According to this website, we can compute t-statistics of mean differences and then can obtain p-value from the respective t-distribution table.
My questions are:
- Is it a valid way to compare the relative data dispersion between two groups? Can we use Bonferroni correction for more than two groups?
- Basically, I have normalised a dataset using different methods and compared the relative dispersion. For example, a raw feature's cv is 12%, after normalisation this feature using method a1, the cv became 10%, and after normalisation it using method a2, the cv became 6%. As the CV is not computed from independent dataset, can we perform t test instead of paired t test? For paired t test, we need standard deviation of the differences which we cant compute (cv is a scalar value!). Using the above way, I found the p-value is less than 0.05 for method a1 and a2 where a2's cv is significantly lower than a1's cv.
- Limitations of CV are: a) same std but different mean would create different cv-value although both data dispersion are same. b) very sensitive when mean close to 0. Most of the average values from method a1 are close to 0 (e.g., 0.6). Is there any alternate way to compare the data dispersion between two or more groups?
I would really appreciate your help.
[1] Sappakitkamjorn, J. and Niwitpong, S. 2013, 'Confidence intervals for the coefficients of variation with bounded parameters', International Journal of Mathematical, Computational Science and Engineering, Vol. 7(9).
[2] Altman, D.G. and Bland, J.M. 2011, 'How to obtain the P value from a confidence interval', BMJ, 2011.
