A problem with logarithms
It is not pleasant to go where statisticians fear to tread.
The article on how difficult it is to treat irritable bowel syndrome
(1) ran into a quagmire of graphs (Figs 2, 3, 4). According to one rapid
response (2), the x- axis wrongly implied there could be a negative
Relative risk is a ratio that can range from zero beyond 1 and then
possibly to infinity. Infinity here would be merely theoretical, as so
much unfortunately is in statistics. Relative risk compares control to
treatment, non- exposed to exposed (3).
So why were there negative values of relative risk on the graphs?
What hellish error had been made?
Ah, the spacings are not linear, but logarithmic. We have a
logarithmic x- axis. And logarithms can be negative for fractions below
one. The logarithm of one in base ten is- zero. So Figs 2, 3, and 4 would
seem valid after all if they were in the form of logarithmic graphs.
Still, they have proved confusing. They were not defined as logarithmic in
the forest plots.
And why choose logarithms? These would make the relative risk appear
less than it actually was. Perhaps there was not enough space for an
ordinary linear graph.
Maybe the intention was to give the data an unfair graphical spin.
And here is the twist in this statistical tale. By picking a log or a
linear axis, we can make the data look as we would wish it to on a graph,
for all sorts of malevolent purposes. We can squeeze it in or stretch it
There are lies, damned lies, statistics- and graphs.
(1) Effects of fibre, antispasmodics, and peppermint oil in the
treatment of irritable bowel syndrome: systematic review and meta-
analysis. Alexander C Ford et al. BMJ 2008;337:a2313
(2) Error in figs 2,3, 4. BMJ Rapid Response. Mitchell Levine and
benjamin Asa. 6 May. 2009.
(3) Statistical Methods in Medical Research. P. Armitage, G.Berry,
J.N.S.Matthews. Blackwell. Fourth edition. 2002. Psgs. 671- 673.
Competing interests: No competing interests