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).
Answer call | Respond to text | Reply to email | |
---|---|---|---|
Low exposure | 275.7 | 275.7 | 272.61 |
High exposure | 81.3 | 81.3 | 80.39 |