### Abstract

The standard confidence intervals for proportions and their differences used in introductory statistics courses have poor performance, the actual coverage probability often being much lower than intended. However, simple adjustments of these intervals based on adding four pseudo observations, half of each type, perform surprisingly well even for small samples. To illustrate, for a broad variety of parameter settings with 10 observations in each sample, a nominal 95% interval for the difference of proportions has actual coverage probability below .93 in 88% of the cases with the standard interval but in only 1% with the adjusted interval; the mean distance between the nominal and actual coverage probabilities is .06 for the standard interval, but .01 for the adjusted one. In teaching with these adjusted intervals, one can bypass awkward sample size guidelines and use the same formulas with small and large samples.

Original language | English (US) |
---|---|

Pages (from-to) | 280-288 |

Number of pages | 9 |

Journal | American Statistician |

Volume | 54 |

Issue number | 4 |

State | Published - Nov 2000 |

Externally published | Yes |

### Fingerprint

### Keywords

- Binomial distribution
- Score test
- Small sample
- Wald test

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

**Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures.** / Agresti, Alan; Caffo, Brian S.

Research output: Contribution to journal › Article

*American Statistician*, vol. 54, no. 4, pp. 280-288.

}

TY - JOUR

T1 - Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures

AU - Agresti, Alan

AU - Caffo, Brian S

PY - 2000/11

Y1 - 2000/11

N2 - The standard confidence intervals for proportions and their differences used in introductory statistics courses have poor performance, the actual coverage probability often being much lower than intended. However, simple adjustments of these intervals based on adding four pseudo observations, half of each type, perform surprisingly well even for small samples. To illustrate, for a broad variety of parameter settings with 10 observations in each sample, a nominal 95% interval for the difference of proportions has actual coverage probability below .93 in 88% of the cases with the standard interval but in only 1% with the adjusted interval; the mean distance between the nominal and actual coverage probabilities is .06 for the standard interval, but .01 for the adjusted one. In teaching with these adjusted intervals, one can bypass awkward sample size guidelines and use the same formulas with small and large samples.

AB - The standard confidence intervals for proportions and their differences used in introductory statistics courses have poor performance, the actual coverage probability often being much lower than intended. However, simple adjustments of these intervals based on adding four pseudo observations, half of each type, perform surprisingly well even for small samples. To illustrate, for a broad variety of parameter settings with 10 observations in each sample, a nominal 95% interval for the difference of proportions has actual coverage probability below .93 in 88% of the cases with the standard interval but in only 1% with the adjusted interval; the mean distance between the nominal and actual coverage probabilities is .06 for the standard interval, but .01 for the adjusted one. In teaching with these adjusted intervals, one can bypass awkward sample size guidelines and use the same formulas with small and large samples.

KW - Binomial distribution

KW - Score test

KW - Small sample

KW - Wald test

UR - http://www.scopus.com/inward/record.url?scp=0034554907&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034554907&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0034554907

VL - 54

SP - 280

EP - 288

JO - American Statistician

JF - American Statistician

SN - 0003-1305

IS - 4

ER -