Standard deviation of LN transformed value So I have a set of experimentally-determined values (inhibition constants) that are given with their respective standard deviations. I used these values to calculate the free energy via the following formula:
free energy = R * T * ln (inhibition constant)

I want to also transform the standard deviations. My question is how do I do that - it seems to me that just plugging the st. deviations in the above formula is not OK.
More specifically:
Ki = 2.32 +- 0.095 uM

G = R*T*ln(Ki) = 1.9872 * 0.001 * 303.15 * ln (2.32*10E-6) = -7.8 kcal/mol +- ?????


To get to an approximate solution, you can use this rule:
$$
\sigma_{f(x)} \approx \left|\frac{\partial f}{\partial x}\right| \cdot \sigma(x)
$$
and then $\sigma(c f(x)) = c \cdot \sigma_{f(x)}$.
This comes from the first term of the Taylor expansion given here.
It's very old now, but when I was first learning this stuff I found Lyons (1991) very clear and approachable.
In comments, @whuber says:

Lognormal distributions are notorious: unless you are absolutely sure the distribution is lognormal, and you have a large amount of data, this approximation could be [...] way off. A good check is to inspect the estimated geometric s.d. Still assuming large amounts of data (hundreds or more), if the gsd is less than 0.3 or so, this approach is probably okay. If the gsd exceeds 0.5 or so, be cautious; and if it exceeds 1, the results [are] likely very unreliable.

These suggestions may not be feasible if you don't have access to the original data any more, or to summary information other than the standard deviation on the non-log-scale ...

Lyons, Louis. 1991. A Practical Guide to Data Analysis for Physical Science Students. Cambridge University Press.
