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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Manning, C.D., Schütze, H.: Foundations of statistical natural language processing. MIT Press, Cambridge (1999)
Teh, Y.W., Jordan, M.I., Beal, M.J., Blei, D.M.: Sharing clusters among related groups: Hierarchical dirichlet processes. In: Proceedings of the Advances in Neural Information Processings Systems Conference (NIPS 2004), MIT Press, Cambridge (2004)
Lavrenko, V., Croft, W.B.: Relevance based language models. In: Proceedings of the 24th annual international ACM SIGIR conference on Research and development in information retrieval (SIGIR 2001), pp. 120–127. ACM Press, New York (2001)
Mori, S., Nagao, M.: A stochastic language model using dependency and its improvement by word clustering. In: Proceedings of the 17th international conference on Computational linguistics (COLING 1998), pp. 898–904. Association for Computational Linguistics (1998)
Grimmett, G., Stirzaker, D.: Probability and Random Processes. Oxford University Press, Oxford (1992)
Siegel, A.: Median bounds and their application. Journal of Algorithms 38, 184–236 (2001)
Basu, S., Dasgupta, A.: The mean, median and mode of unimodal distributions: A characterization. Theory of Probability and its Applications 41, 210–223 (1997)
Munro, J.I., Paterson, M.S.: Selection and sorting with limited storage. Theoretical Computer Science 12, 315–323 (1980)
Manku, G.S., Rajagopalan, S., Lindsay, B.G.: Approximate medians and other quantiles in one pass and with limited memory. In: Proceedings of the ACM SIGMOD International Conference on Management of Data (SIGMOD 1998), pp. 426–435 (1998)
Motulsky, H.: The link between error bars and statistical significance, http://www.graphpad.com/articles/errorbars.htm
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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
eBook Packages: Computer ScienceComputer Science (R0)