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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: ratios |

Date |
Mon, 24 Nov 2003 20:20:14 -0000 |

There are lots of papers on the pathologies of ratios, going back at least to Karl Pearson in about 1897 and including * a debate in Systematic Zoology following a paper by Atchley et al. 1976 (Statalisters will especially prize the characteristically lucid and trenchant comment by our own Michael Hills in 1978) * a paper in Water Resources Research by Kenney in 1982. * Kronmal in JRSS a few years ago. However, I'm tempted to say that all this fear of ratios, while in a sense totally justified, can be overdone. After all, all rates, percents and proportions are ratios, at least in principle. Perhaps most are also measured as ratios. Think of physics without velocities, demography without birth or death rates, etc., and you lose much of the basic vocabulary of many sciences. Anything based on, or using, differential calculus is in the same boat. We owe to Galileo and Newton the interesting ratio free-fall velocity ------------------ elapsed time However, many ratios y/x have a most obvious rationale if y / x = constant, at least approximately, and many of the problems met in practice come from (implicitly) assuming that when it is not a fair assumption, or at the very least misses interesting fine structure. A very simple example is when people decide to summarize shape by ratios, say width/length, when in practice shapes vary more subtly than such a ratio implies. Much the same can be said about the coefficient of variation, which is a natural parameter if indeed sd / mean is really constant, but a fine source of obscurity otherwise. So I'd rather say, banally, it all depends. Some ratios are familiar and we know their vices enough to work with them; some really can bite us. Nick n.j.cox@durham.ac.uk David Airey > In the biological sciences, ratios are often used, but some > deprecate > their use. I have been told the ratio sometimes remains > correlated with > the denominator, and so the use of ratios to control for or > normalize > to the denominator may not do the trick. The distribution > of the ratio > or percent is also sometimes difficult to deal with, and > may benefit > transformation. Finally, since there are two hidden components to a > ratio, one doesn't always know whether an increase in a > ratio is due to > an increase in the numerator or a decrease in the denominator. This > would seem particularly vexing in more complex experimental > settings > with interactions. > > I recently read a note from Cornell on spurious results from using > ratios, especially when more than one ratio is used: > > <http://www.human.cornell.edu/admin/statcons/statnews/stnews03.htm> > > Now, care of Alex Tsai, I have read: > > Goldman DP, Smith JP. Methodological biases in estimating > the burden of > out-of-pocket expenses. Health Serv Res. 2001 Feb;35(6):1357-64; > discussion 1365-70. Comment on: Health Serv Res. 1999 Apr;34(1 Pt > 2):241-54. > > which is a surprisingly recent dispute on the merits and > pitfalls of > ratios in statistics between experts, with quite serious > implications > for policy change. > > So, the question I have, is it not possible to ask all the same > questions using the numerator and denominator separately in a model > that are asked by using the ratio? If all questions cannot > be answered > via analysis of the components of the ratio, in case where > they can, is > this not preferred? * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: ratios***From:*David Airey <david.airey@vanderbilt.edu>

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