. "Appendix 3-7: Marginal Mean and Variance of Transformed Response Variables." Gender Differences at Critical Transitions in the Careers of Science, Engineering, and Mathematics Faculty. Washington, DC: The National Academies Press, 2010.
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Gender Differences at Critical Transitions in the Careers of Science, Engineering, and Mathematics Faculty
Given an MLE and an estimate of the least squares mean in the transformed scale, we compute and as follows:
Given a point estimate of the least squares mean in the original scale and an approximation to its variance, we can compute an approximate 100(1–α)% confidence interval for the true mean in the original scale in the usual manner:
where df is the appropriate degrees of freedom. In our case, and due to relatively large sample sizes everywhere, the t critical value can be replaced by the corresponding upper α/2 tail of the standard normal distribution.
and an estimate of 
the least squares mean in the transformed scale, we compute 
and 
as follows:
