## D.24 Answers: CIs for odds ratios

Answers to exercises in Sect. 25.9.

**Answer to Exercise 25.1**:

**1.**\(99/62 = 1.596774\); about 1.60.

**2.**\(216/115 = 1.878261\); about 1.88.

**3.**\(1.596774/1.878261 = 0.850\), as in the output.

**4.**A few ways; for example: For every 100 men with a smooth scar, about 85 women with a smooth scar.

**5.**(Graph not shown, but use a stacked or side-by-side bar chart.)

**6.**Table D.4.

**7.**Exact 95% CI for the OR, from the output: 0.576 to 1.255.

**8.**If study repeated study many times (with the same numbers of men and women), about 95% of the CIs would contain population OR. In practice: population OR is probably between 0.576 and 1.255.

Odds with smooth scars | Percentage with smooth scars | Sample size | |
---|---|---|---|

Women: | 1.60 | 61.5% | 161 |

Men: | 1.88 | 65.3% | 331 |

Odds ratio: | 0.850 |

**Answer to 25.2**:
The output can be interpreted in one of two ways
(Sect. 25.2):

- Odds are the odds of swimming at the beach; OR compares these odds between those without an ear infection, to those with an ear infection.
- Odds are the odds of
*not*having an ear infection; OR compares these odds for beach swimmers to non-beach swimmers.

**Answer to 25.3**:

**1.**Table D.5.

**2.**Table D.6.

**3.**OR: Odds of a 1800-hr turbine getting a fissure is 0.389 times the odds of a 3000-hr turbine getting a fissure.

**4.**CI from 0.133 to 1.14. Plausible values for the population OR that may have produced the sample OR likely to be between these values.

Fissures | No fissures | Total | |
---|---|---|---|

About 1800 hours | 7 | 66 | 73 |

About 3000 hours | 9 | 33 | 42 |

Total | 16 | 106 | 122 |

Odds with fissures | Percentage with fissures | Sample size | |
---|---|---|---|

About 1800 hours | 0.1061 | 9.59% | 73 |

About 3000 hours | 0.2727 | 21.43% | 42 |

Odds ratio | 0.389 |

**Answer to Exercise 25.4**: Odds of no rainfall (non-positive SOI): \(14/40 = 0.35\). Odds of no rainfall (negative SOI): \(7/53 = 0.1320755\). Required OR is \(0.35/0.1320755 = 2.65\), as in output. 95% CI from 0.979 to 7.174.

**Answer to Exercise 25.5**: The 95% CI is from 0.151 to 0.408. The OR of not wearing a hat, comparing males to females (males

*less*likely to be

*not*wearing a hat; rewording, males

*more*likely to be wearing a hat).