Document Type
Pre-Print
Publication Date
7-16-2025
Subjects
discarding data, sufficient statistic, tournament, sequential trial
Abstract
It seems intuitively obvious that no part of a random sample should be discarded. However, for most students, the first formal justification of this idea is when sufficiency is introduced in an introductory statistical theory course. Students are often left with the idea that conditioning on the sufficient statistic always improves inference, even though the formal theory only says that for any statistical procedure there is one depending on the sufficient statistic that is no worse. Here we present an example on comparing two coins based on two consecutive tosses, where the optimal probability of guessing which coin has the higher heads probability is not improved by taking the second observation. We discuss some ramifications and introduce some generalizations, focussing on tournaments.
Rights
Copyright 2025 The Authors
This work is licensed under a Creative Commons Attribution 4.0 International License.
Persistent Identifier
https://archives.pdx.edu/ds/psu/44001
Citation Details
Portnoy, Stephen and Stein, James, "An Example Where Taking an Additional Observation Doesn't Help" (2025). Mathematics and Statistics Faculty Publications and Presentations. 431.
https://archives.pdx.edu/ds/psu/44001