When is it right to use the log of responses in a relative potency test? We have two preparations, standard and test described. There is evidence of heteroscedasticity, and less than ten units(unequal for both test). I learnt that assuming normal distribution, gives better and valid confidence interval than the arrived at using log_10 values. When is using log appropriate and ani adjustment for small sample size assay,RP test, generalizable for population's (\Rho value.). Thanks
 A: The choice between non-transformed and transformed data depends on the nature of the data. The standard t-test for comparing the means between 2 groups assumes that there is a normal distribution of values within each group, with the same variance within each group. If that's close enough to true, then there's no need to transform. If there's normality in each group but different variances between them, then there's no need to transform and Welch's t-test can be used.
If normality doesn't hold within groups, then a log or other transformation might help. But then you are comparing the means on the transformed scale, not the original scale.
With as few samples as you have, it would be difficult to judge whether or not the normality and equal-variance assumptions hold. With that few samples, however, you could easily do a permutation test instead to get an estimate of the reliability of your mean difference. Say that you have $N_S$ cases of "standard" and $N_T$ cases of "test." After you calculate the mean difference on the original data, you take all the $N_S+ N_T$ values and re-calculate the mean difference for all possible combinations of $N_S$ "standard" and $N_T$ "test" labels. For example, if $N_S = 6$ and $N_T = 4$, there are only 210 such combinations. The two-sided p-value for your original mean difference is the fraction of those mean values whose absolute value is greater than that of your original (correctly labeled) mean difference.
