Custom Designs and Log Transforms for Variables with Zeros

Question

Another customer question...

Customer is creating a liquid solution containing salt (NaCl).  This isn't a mixture problem, so he's wanting to set up a DOE with the actual salt content, not a percentage.

He wants to cover a large range, say 10 to 1e6, so he wants to use log(amount), so his inputs range from 1(=log(10)) to 6(=log(1e6)).

However, he would also like to include "No Salt", which of course is not allowed (No Salt = log(0) = undefined).

What's the best way to handle this?  He suggested just running a few extra custom trials at Salt=0 just to see what was happening, but excluding them from the analysis.  Thoughts?

JerryFish · Answer

Thanks Team!  I'll communicate these suggestions to the customer, and repost here when I hear back from him.

Jerry

DonMcCormack · Answer

Is the response over the range of salt expected to be linear? If so, I'd opt for using the transform Log(x+1) over adding a small amount to 0. I've run into situations where different arbitrary small amounts led to different significance results. If the response isn't expected to be linear, why not treat the factor as categorical?

jiancao · Answer

A workaround for dealing with 0 values is add very very small values like 1e-7 so that log transformation can be made.