You’re right about this. It is true that the mean differences are much smaller than the means so, if the populations are Gaussian, (L-R)/(L+R) may not be too badly behaved. I gave the exact form of the distribution in my comment. My point was that ratio distributions have the potential to have a sting in their tails and that this should be checked (and can be checked quite easily). They did not comment on these issues in their reply. They did show the histogram but that doesn’t really settle much.

Peter

]]>Thinking more about this: I expect you are right that if L and R conform to Gaussian (normal) distributions then (L-R)/(L+R) conforms to a Cauchy distribution. (I’ve not checked the integrations.) But:

1. It won’t change conclusions very much provided that the difference (L-R) is much smaller in magnitude than the sum (L+R), so that the the distribution of (L-R(/(L+R) is tight; and

2. If the distribution is not tight, then you can’t assume normal distributions for L and R because these quantities cannot be negative. (The normal distribution runs from minus infinity to infinity.)

Did the authors say anything like this in their published reply?

Anton

]]>More worrying is the prevalence of ad hoc statistical tests in areas such as manufacturing quality control of aeroplane parts, and drug safety tests…

Anton

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