D.29 Answers: Tests for odds ratios

Answers to exercises in Sect. 31.13.

Answer to Exercise 31.1: The missing entries: Odds: 1.15; Percentage: 58.1%.

χ2=4.593; approximately z=4.593/1=2.14; expect small P-value. Software gives P=0.032. Evidence that the difference between the sample proportions is unlikely to be due to sampling variation. The test is statistically valid.

The sample provides moderate evidence (chi-square=4.593; two-tailed P=0.032) that the population odds of finding a male sandfly in eastern Panama is different at 3 feet above ground (odds: 1.15) compared to 35 feet above ground (odds: 1.71; OR: 0.67; 95% CI from 0.47 to 0.97).

Answer to Exercise 31.2: One option: H0: The population OR is one; H1: The population OR is not one. From software, χ2=0.667; P=0.414, which is large. No evidence (P=0.414) that the odds of having a smooth scar is different for women and men (chi-square: 0.667). The test is statistically valid.
Answer to Exercise 31.4: One option: H0: The population OR is one; H1: The population OR is not one. From software, χ2=3.845; P=0.050. Moderate evidence (P=0.05) that the odds of having no rainfall is different for non-positive SOI Augusts and negative-SOI Augusts (chi-square: 3.845). The test is statistically valid.
Answer to Exercise 31.5: 1. 22/366×100=6.0%. 2. 79/386×100=20.5%. 3. 22/344=0.06395349, or about 0.0640. 4. 79/307=0.257329, or about 0.257. 5. 0.257/0.0640=4.02. 6. 0.0640/0.257=0.249. 7. From 0.151 to 0.408. 8. χ2=33.763% (approximately z=5.81) and P<0.001. 9. Strong evidence (P<0.001; χ2=33.763; n=752) that the odds of wearing hat is different for males (odds: 0.257) and females (odds: 0.0640; OR: 0.249, 95% CI from 0.151 to 0.408). 10. Yes.
Answer to Exercise 31.6: 1. Low exposure (in order): 73.7%, 72.5%, 85.6%. High exposure (in order): 26.3%, 27.5%, 14.4%. 2. In order: 2.80, 2.64, 5.92. 3. Various ways; probably the easiest: H0: No association between level of exposure and type of interaction (in the population). 4. Table D.8. 5. Approximately z=20.923/2=3.23: expect small P-value. 6. Very strong evidence in the sample of an association between level of exposure and type of interaction in the population (χ2=20.923; P<0.001).
TABLE D.8: The expected counts for the phone-use data
Answer call Respond to text Reply to email
Low exposure 275.7 275.7 272.61
High exposure 81.3 81.3 80.39