Methods and formulas for Test mean / reference mean (by log transformation) for 2-Sample Equivalence Test

The difference (D) the standard error of the difference (SE) and the confidence interval (CI) are calculated as described for Test mean - reference mean. However, the calculations are performed using the natural log of the data values and the natural log of the equivalence limits.

The ratio, ρ, is calculated by converting the difference, D, back into the original units as follows:

The CI for equivalence for the ratio is calculated by converting the CI for equivalence based on the difference back into the original units as follows:

where LL_D is the lower limit for the CI for equivalence for the difference and UL_D is the upper limit for the CI for equivalence for the difference.

T-values and p-values are calculated as described for Test mean - reference mean. However, the calculations are performed using the natural log of the data values and the natural log of the equivalence limits.