I have two independent groups and for calculating differences in variance I want to use VR (variance ratios):
VR = variance of group A / variance of group B
So if it's correct, how I should calculate the standard error of VR? And is there a way for interpreting VR (e.g., it is small, large, or significant)?
Thank you in advance,
http://support.sas.com/documentation/cdl/en/statug/68162/HTML/default/viewer.htm#statug_surveyphreg_details30.htm
Regards!
1) The variance of a ratio is approximately:
Var(x/y)≈(E(x)E(y))2(Var(x)E(x)2+Var(y)E(y)2−2Cov(x,y)E(x)E(y))Var(x/y)≈(E(x)E(y))2(Var(x)E(x)2+Var(y)E(y)2−2Cov(x,y)E(x)E(y))
You might want to look at the answers to this question for more information.
Usually regression packages do provide at least the option to print out the estimated covariance matrix of the parameter estimates, so perhaps there's some way of getting that covariance term.
2) However, the bootstrap may give you more accurate confidence intervals, especially if your denominator variable is not many standard errors away from zero.
ME = 1.96 × SE
CI = VR ± ME
Then if the confidence interval excludes one, it’s significant (p
Majid, the solution you present is not at all suited for a ratio of variances, I would rather say it's wrong. It might be that, in some special cases, your solution could be a reasonable approximation, but in most cases the approximation will be really drastically bad.
Dear Jochen,
Thank you for your reply. In which situation, it is not a reasonable approximation? and could you please say me, what’s your suggestion instead of it?
See here: https://en.wikipedia.org/wiki/Ratio_distribution
Further, it is not clear what distributions the variances have. Under the assumption that the values are normal distributed, then the variances will have Chi²- distributions and their ratio will have an F-distribution. But unless this is all known, the best option, still! (see my 1st post here), is to bootstrap (given you have reasonably large samples).
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