How to calculate confidence intervals of $1/\sqrt{x}$-transformed data after running a mixed linear regression in stata? I have run a series of mixed linear regressions in Stata, some with inverse-square-root ($1/\sqrt{x}$) transformations and others with square root ($\sqrt{x}$) transformations.  
How do I calculate untransformed confidence intervals from the transformed results??
 A: You calculate the full transformed confidence interval and then transform it back.
Let's say the transformed confidence interval is 5 ± 3, or CI95% = [2, 8].  You would take the 2, and 8 values and transform them back.  You do NOT transform the 3 (the width of the confidence interval).  The result in this example CI95% = [0.25, 0.016].
Be careful of interpretation because you're switching around what is larger and what is smaller.  Also, the CI inferences only hold in the transformed space and these back transformed values would just be referece / orientation values for the reader rather than primary values for inference.  If this is something like a beta coefficient you can't even do the back transform because the line is no longer straight and you wouldn't be able to interpret it (you could calculate the whole line and error curves and back transform them though).  There may be other interpretation issues.  
Generally, it's best to interpret in the transformed space and present back transformed values only for convenience and where they aid that interpretation.  It would be best if you can ascribe some meaning to the transformed value.
