# 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.