difference scores of log-transformed variables.

[Jinkuk Hong]

Dear Listers,
I need an advice on the problem of creating difference score of two variables.
I have two variables V1 and V2, from which I created two log-transformed
variables: LNV1 and LNV2 (because of skewness of the variables, it is very
common in the field using the log-transformed variable for these two variables).

Now, if I want to create a variable of difference score between V1 and V2,
which of following three would be best?
1. (V1-V2).
2. (LNV1-LNV2).
3. Ln(V1-V2).

I'm thinking of using the second one (LNV1-LNV2), but not 100% sure, and I
don't have any reference to support my decision.
Any suggestion or guide to literature to deal with this kind of problem would
be greatly appreciated.

Thanks,
Jin

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[Marta Garcia-Granero]

Jinkuk Hong wrote:

> I need an advice on the problem of creating difference score of two
> variables.
> I have two variables V1 and V2, from which I created two log-transformed
> variables: LNV1 and LNV2 (because of skewness of the variables, it is
> very
> common in the field using the log-transformed variable for these two
> variables).
>
> Now, if I want to create a variable of difference score between V1 and
> V2,
> which of following three would be best?
> 1. (V1-V2).
> 2. (LNV1-LNV2).
> 3. Ln(V1-V2).
>
> I'm thinking of using the second one (LNV1-LNV2), but not 100% sure,
> and I
> don't have any reference to support my decision.
> Any suggestion or guide to literature to deal with this kind of
> problem would
> be greatly appreciated.
>

My thoughts (a bit disperse, I haven't finished my morning coffee yet):

First of all, the fact that V1 andV2 are skewed doesn't necessarily mean
that their difference also is. If both V1 and v2 have similar degree of
skewness, and differ only in location, their difference could be roughly
symmetric. Check that before considering th need of any transformation.

If V1-V2 can take negative values, then discard option 3, obviously.
Ln(V1-V2) has the disadvantage of interpretation of the anti-log of the
mean of the log values, while Ln(V1) -Ln(V2) can be back-transformed
into something meaningful (see below).

Option number 2 can be rewritten (using a bit of log math) as:
Ln(V1/V2). Therefore, the mean of the log can be anti-logged and you
will get the geometric mean of the ratio. Is that statistic useful and
interpretable in your research?

If V1-V2 is not normal, what's the problem in using non-parametrics?

HTH,
Marta García-Granero

--
For miscellaneous statistical stuff, visit:
http://gjyp.nl/marta/

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