HW #20: Odds Ratio - John Uebersax
HW #20: Odds Ratio
A quality engineer wants to measure the association of customer satisfaction (low vs. high) and product design (old vs. new) and collects the following results for a sample of 100 cases.
| |Customer Satisfaction |
| | |
| |Low |High |
|Design | | |
|Old | | |
| |45 (= a) |8 (= b) |
|New | | |
| |12 (= c) |35 (= d) |
a. The odds ratio
[pic]= (45 × 35) / (8 × 12) = 1575/96 = 16.4063
b. The log of the odds ratio
[pic] = ln(16.4063) = 2.7977
c. The upper and lower limits for a 95% CI of ln(OR)
Standard error of ln(OR) =
[pic]
Critical z value for 95% CI is zcrit =1.960
Confidence interval formulae for ln(OR):
[pic]
[pic][pic]
d. The upper and lower limits for a 95% CI of OR
[pic]
[pic] (continued…)
|Odds ratio and ln(OR) calculator | | | | | |
|Variable 1 | | | |OR |16.4063 | |Variable 2 |Level 1 |Level 2 |Total | |ln(OR) |2.7977 | |Level 1 |45 |8 |53 | |std. err. ln(OR) |0.5090 | |Level 2 |12 |35 |47 | |CI width |0.95 | |Total |57 |43 |100 | |lower tail area |0.025 | | | | | | |z-crit |1.9600 | | | | | | |LL ln(OR) |1.8000 | | | | | | |UL ln(OR) |3.7954 | | | | | | |LL OR |6.049 | | | | | | |UL OR |44.495 | |
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