Hi @MSN : Are you after confidence intervals etc for the ratio of GMs (GMR), or just the GM of a single variable? If question is about the latter, so here are the steps.
Suppose you have a column X. Make another column Y= ln(X).
1. Use the distribution platform to get a CI on the mean of Y (based on arithmetic mean, AM).
2. Back transform the interval to get the CI on the Geometric Mean (GM) of X.
3. An Equivalence Test via TOST is, effectively, carried out via calculating a 90% CI (if your desired type 1 error rate, alpha, is 0.05) via (2) above and comparing it to your equivalence limits (if the interval is entirely contained within the limits then equivalence is confirmed).
You'll notice the interval calculated in (1) above is symmetric around the AM if Y. But the interval for the GM calculated in (2) is not symmetric around the estimated GM of X.
The steps are similar if you are interested the ratio of GMs (GMR); Carry out a one-way ANOVA on Y=ln(X), then back transform the confidence interval on the difference in means to get a confidence interval on the GMR. Then for TOST, compare that interval to your equivalence limits.
Strictly speaking, all the above assume your data is log-normal; but if your sample size is large enough, the CLT (Central Limit Theorem) saves you.
