(Topics: Statistics: Risks, Odds and Ratios) A survey of U.S. citizens asked each participant to indicate whether they favor or oppose the death penalty as well as whether they favor or oppose gun registration. The data are contained in the table Make sure to give an appropriate interpretation with each estimate below. Favor DP Oppose DP total Favor GR 784 236 1020 Oppose GR 311 66 377 Total 1095 302 a. Estimate with the probability that a S. citizen favors both. 784/(784+236+311+66) = 0.561 b. Estimate with the probability that someone who favors DP also favors GR. 784/(784+311) = 0.716 c. For those who favor GR, estimate their odds of opposing the DP. 236/784 = 0.301 d. For those who do not favor GR, estimate their odds of opposing the DP. 66/311 = 0.2122 e. Compute and interpret the odds 0.301/0.2122 = 1.42 Odds for group who favor GR oppose the DP are 1.42 time higher than the odds for group who not favor GR. f. Invert your odds ratio and interpret. 1/1.42 = 0.704 Odds for group who not favor GR oppose the DP are 0.704 time higher than the odds for group who favor GR. g. Compute a CI for your odds ratio. Ln (OR) = Ln(1.42) = 0.351 SEln(OR)= CI for Ln (OR) = 0.351± 1.96 (0.155) = 0.0472 to 0.6548 Actual CI for OR: e^(0.0472) to e^(0.6548) = 1.048 to 1.925 Can you check my answers?
- (Topics: Statistics: Risks, Odds and Ratios) A survey of U.S. citizens asked each participant to indicate whether they favor or oppose the death penalty as well as whether they favor or oppose gun registration. The data are contained in the table Make sure to give an appropriate interpretation with each estimate below.
|
|
Favor DP |
Oppose DP |
total |
|
Favor GR |
784 |
236 |
1020 |
|
Oppose GR |
311 |
66 |
377 |
|
Total |
1095 |
302 |
|
a. Estimate with the probability that a S. citizen favors both.
784/(784+236+311+66) = 0.561
b. Estimate with the probability that someone who favors DP also favors GR.
784/(784+311) = 0.716
c. For those who favor GR, estimate their odds of opposing the DP.
236/784 = 0.301
d. For those who do not favor GR, estimate their odds of opposing the DP.
66/311 = 0.2122
e. Compute and interpret the odds
0.301/0.2122 = 1.42
Odds for group who favor GR oppose the DP are 1.42 time higher than the odds for group who not favor GR.
f. Invert your odds ratio and interpret.
1/1.42 = 0.704
Odds for group who not favor GR oppose the DP are 0.704 time higher than the odds for group who favor GR.
g. Compute a CI for your odds ratio.
Ln (OR) = Ln(1.42) = 0.351
SEln(OR)=
CI for Ln (OR) = 0.351± 1.96 (0.155) = 0.0472 to 0.6548
Actual CI for OR:
e^(0.0472) to e^(0.6548) = 1.048 to 1.925
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d. For those who do not favor GR, estimate their odds of opposing the DP.
e. Compute and interpret the odds
f. Invert your odds ratio and interpret.
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