Back-transformation of log means
Maynard Williams
I'm analysing data which I log transformed prior to conducting repeated a
repeated measures ANCOVA. Because there were a number of zeros in the
original data I first added a constant of "1" to all scores prior to the
transformation. I now wish to report the ANCOVA adjusted back-transformed
groups means along with their 95% CIs.
Now, adding a constant of "1" to data to avoid trying to take the log of
zero is apparently an accepted practice. However, I suspect there is a
problem with back-transforming the log means and their 95% CI's by simply
taking the antilogs of those values and removing the original constant.
That is, the geometric mean of a set of scores will not be the same as the
back-transformed mean derived by adding 1 to those scores before conducting
a log transformation, calculating the mean, taking its antilog and removing
the original constant. How then do you back-transform such means and their
95% CIs to report them?
Hoping someone (Rich?, Bruce?) can help me.
Maynard
Rich Ulrich
the SPSS routines, instead of general statistics.
You get more statistical advice from the Usenet groups
for statistics, sci.stat.* ; but I will offer some words anyway.
On Fri, 12 Sep 2003 20:04:51 +1200, "Maynard Williams"
<maynard....@xtra.co.nz> wrote:
> Hi
>
> I'm analysing data which I log transformed prior to conducting repeated a
> repeated measures ANCOVA. Because there were a number of zeros in the
> original data I first added a constant of "1" to all scores prior to the
> transformation. I now wish to report the ANCOVA adjusted back-transformed
> groups means along with their 95% CIs.
>
> Now, adding a constant of "1" to data to avoid trying to take the log of
> zero is apparently an accepted practice.
I don't know where you got that idea, "apparently an
accepted practice," but you could do your publishing in
*that* journal. (I may seem a bit negative here, today,
but compared to some people who post in the sci.stat.*
groups, I am fairly permissive about transformations.)
It is true that some people don't care very much about
their original scores, and they are willing to take arbitrary
transformations in order to perform ANOVA with fewer
problems from odd variances, etc. That means -- it
seems to me to be implicit -- that they don't figure on
worrying much about actual scores, or Confidence intervals.
If the scales and scores do matter, that should be a
warning that you *don't* want any transformation which
is not a natural one -- No 'add-ons' should be needed,
and the power or root should be suggested by the nature
of the data collection.
Needless to say, if there are zeros in the data, then
taking the log isn't one of the possibilities. Oh, Is it
a real zero, or one owing to poor measurement? Some
folks taking bioassays figure that it is okay to replace 0
with half the lowest-measurable-amount; then there are
no zeros in the data. Does that work for you?
Further, when it comes to an "add-on," the scale of
numbers is sure to make a difference, and adding "1"
is suggested naturally, if-and-only-if the precision
of measurement is about "1". Else, not.
People who accept add-ons are going to care about
what number is added, if they know *anything* about
statistics. Otherwise, we would be well-advised to
ignore their publications.
> However, I suspect there is a
> problem with back-transforming the log means and their 95% CI's by simply
> taking the antilogs of those values and removing the original constant.
Assuming your field accepts the notion of arbitrary
transformations, I don't see the problem. Un-do what
was done, step by step.
> That is, the geometric mean of a set of scores will not be the same as the
> back-transformed mean derived by adding 1 to those scores before conducting
> a log transformation, calculating the mean, taking its antilog and removing
> the original constant. How then do you back-transform such means and their
> 95% CIs to report them?
- Yes, you set up the CI and you back-transform the mean
as well as the limits. Step-by-step. What is the problem?
--
Rich Ulrich, wpi...@pitt.edu
http://www.pitt.edu/~wpilib/index.html
"Taxes are the price we pay for civilization."