Abstract
We point out that for two sets of measurements, it can happen that the average of one set is larger than the average of the other set on one scale, but becomes smaller after a non-linear monotone transformation of the individual measurements. We show that the inclusion of error bars is no safeguard against this phenomenon. We give a theorem, however, that limits the amount of “reversal” that can occur; as a by-product we get two non-standard one-sided tail estimates for arbitrary random variables which may be of independent interest. Our findings suggest that in the not infrequent situation where more than one cost measure makes sense, there is no alternative other than to explicitly compare averages for each of them, much unlike what is common practice.
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© 2005 Springer-Verlag Berlin Heidelberg
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Bast, H., Weber, I. (2005). Don’t Compare Averages. In: Nikoletseas, S.E. (eds) Experimental and Efficient Algorithms. WEA 2005. Lecture Notes in Computer Science, vol 3503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427186_8
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DOI: https://doi.org/10.1007/11427186_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25920-6
Online ISBN: 978-3-540-32078-4
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