### 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.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science |

Editors | S.E. Nikoletseas |

Pages | 67-76 |

Number of pages | 10 |

Volume | 3503 |

Publication status | Published - 2005 |

Externally published | Yes |

Event | 4th International Workshop on Experimental and Efficient Algorithms, WEA 2005 - Santorini Island, Greece Duration: 10 May 2005 → 13 May 2005 |

### Other

Other | 4th International Workshop on Experimental and Efficient Algorithms, WEA 2005 |
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Country | Greece |

City | Santorini Island |

Period | 10/5/05 → 13/5/05 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science (miscellaneous)

### Cite this

*Lecture Notes in Computer Science*(Vol. 3503, pp. 67-76)

**Don't compare averages.** / Bast, Holger; Weber, Ingmar.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science.*vol. 3503, pp. 67-76, 4th International Workshop on Experimental and Efficient Algorithms, WEA 2005, Santorini Island, Greece, 10/5/05.

}

TY - GEN

T1 - Don't compare averages

AU - Bast, Holger

AU - Weber, Ingmar

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=24944522333&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24944522333&partnerID=8YFLogxK

M3 - Conference contribution

VL - 3503

SP - 67

EP - 76

BT - Lecture Notes in Computer Science

A2 - Nikoletseas, S.E.

ER -