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

The following methods and formulas are used for testing the ratio between the test mean and the reference mean using the log transformation.

Difference, standard error, and confidence interval

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.

Ratio and confidence interval for equivalence

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 LLD is the lower limit for the CI for equivalence for the difference and ULD is the upper limit for the CI for equivalence for the difference.

T-values and p-values

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.
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