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**Santner, Thomas J. (1997): A Note on Teaching Binomial Confidence Intervals. Collaborative Research Center 386, Discussion Paper 87 [PDF, 212kB]**

## Abstract

For constructing confidence intervals for a binomial proportion $p$, Simon (1996, Teaching Statistics) advocates teaching one of two large-sample alternatives to the usual $z$-intervals $\hat{p} \pm 1.96 \times S.E(\hat{p})$ where $S.E.(\hat{p}) = \sqrt{ \hat{p} \times (1 - \hat{p})/n}$. His recommendation is based on the comparison of the closeness of the achieved coverage of each system of intervals to their nominal level. This teaching note shows that a different alternative to $z$-intervals, called $q$-intervals, are strongly preferred to either method recommended by Simon. First, $q$-intervals are more easily motivated than even $z$-intervals because they require only a straightforward application of the Central Limit Theorem (without the need to estimate the variance of $\hat{p}$ and to justify that this perturbation does not affect the normal limiting distribution). Second, $q$-intervals do not involve ad-hoc continuity corrections as do the proposals in Simon. Third, $q$-intervals have substantially superior achieved coverage than either system recommended by Simon.

Item Type: | Paper |
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Faculties: | Mathematics, Computer Science and Statistics > Statistics > Collaborative Research Center 386 Special Research Fields > Special Research Field 386 |

Subjects: | 500 Science > 510 Mathematics |

URN: | urn:nbn:de:bvb:19-epub-1480-1 |

Language: | English |

Item ID: | 1480 |

Date Deposited: | 04. Apr 2007 |

Last Modified: | 04. Nov 2020 12:45 |