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From |
"Michael Blasnik" <michael.blasnik@verizon.net> |

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

Subject |
Re: st: ratios first or last? |

Date |
Mon, 24 Nov 2003 10:08:32 -0500 |

It's not that the denominator is skewed right, it's that the ratio itself varies between smaller and larger denominators. Quoting myself: "If you find that the ratio of averages is giving larger estimates, then the individual ratios tend to be larger with larger values of x." Michael Blasnik michael.blasnik@verizon.net ----- Original Message ----- From: "David Airey" <david.airey@vanderbilt.edu> To: <statalist@hsphsun2.harvard.edu> Sent: Sunday, November 23, 2003 3:11 PM Subject: re: st: ratios first or last? > This is helpful, Michael. So, if I understand this correctly, for > denominators that are skewed right, we should expect the ratio of > averages to give a greater animal estimate than the average of ratios? > I'll test this. > > Thank you for these thoughts. > > -Dave > > > The ratio of averages gives greater weight to observations with larger > > values in the denominator than the average of the ratios. In fact, > > you can > > get both estimates from weighted regressions: > > > > ratio of averages: > > reg y x [aw=1/x], nocons > > > > average of ratios: > > reg y x [aw=1/x^2], nocons > > > > which allows you to see the implicit weighting of each approach. Each > > estimator can be considered the "best" (BLUE) estimator for a given > > assumption about the variance. The ratio of averages approach is > > commonly > > referred to as a "ratio estimator" in survey sampling literature. In > > most > > applications, the average of ratios approach is thought to be less > > representative of the variance structure. > > > > If you find that the ratio of averages is giving larger estimates, > > then the > > indivdual ratios tend to be larger with larger values of x. > > > > Michael Blasnik > > michael.blasnik@verizon.net > > > > ----- Original Message ----- > > From: "David Airey" <david.airey@vanderbilt.edu> > > To: <statalist@hsphsun2.harvard.edu> > > Sent: Saturday, November 22, 2003 8:27 PM > > Subject: st: ratios first or last? > > > > > > > Recently I was surprised to find a difference between two methods of > > > calculating a ratio during an experiment. Each animal has two > > measures > > > taken repeatedly over time. The ratio is of the two measures. I could > > > take the ratio at each time point, and then average the ratios to get > > > my animal ratio. Alternatively, I could average each of the two > > > measures and then form a ratio of the two averages, again getting my > > > animal ratio. The second method consistently gets a higher ratio than > > > the first method. Why would this occur? The second method is standard > > > in my literature base. > > > > > > -Dave * * 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**:**re: st: ratios first or last?***From:*David Airey <david.airey@vanderbilt.edu>

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