ANTC67 Tutorial #5
ODDS RATIOS: In class lesson
In a case control study, researchers examined the association between exposure to electromagnetic
fields and the development of childhood leukemia. The researchers were able to recruit a total of 250
participants. Of the 120 children with leukemia, 28 reported to have exposure to electromagnetic fields.
In the control group, 12 had reported to have exposure to electromagnetic fields.
1. Set up a 2 X 2 table with appropriate labels and calculate the odds ratio.
Diseased Not Diseased TOAL
(electromagnetic a 28 b 12 40
electromagnetic c 92 d 118 210
120 130 250
* This is always the set-up for the table, do not switch up things, you will get the wrong answer if not
in this format
2. We want to test if this difference is statistically different. Set up the hypotheses for this test. Hint:
what is the null and alternative hypothesis?
H o There is no relationship between the exposure and developing leukemia; OR = 1
H = OR not equal to 1.
3. We use Mantel-Haenszel chi-square test to assess statistical significance of odds ratios. What is
the decision rule for accepting or rejecting the null hypothesis? Hint: the critical value for a chi-
square test with an alpha of 0.05 is X = 3.84.
When p<0.05, our CV (critical value) = 3.84
Fail rejectoH , if X < 3.84
Reject Hoif X = (or greater than) 3.84
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4. Calculate the test statistic using the Chi-square formula. Each cell’s value must be at least 5 in
order to apply the Chi square formula.
MH chi-square= (│ad-bc│-N/2) *N
= (( )( ) ( )( )| )
C = column
R = row
5. What is your conclusion based on your calculations?
Reject H oecause the chi square value is greater than our critical value of 3.84.
1. Calculate the 95% confidence interval for the odds ratio.
95% CI for OR= e^[(ln(OR)) + 1.96SE(ln(OR))]
SE(ln(OR))] = √
= e^[(ln(OR)) + 1.96SE(ln(OR))]
= e^[(ln(OR)) + 1.96 √
= e^[(ln(2.99)) + 1.96√
= e^(1.096 1.96(0.372))
= e^(1.096 1.96(0.372))
2 ANSWERS: 1.44, 6.20
2. Interpret the odds ratio including the confidence interval.
Lower limit 1.44
Upper Limit 6.20
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2.99 fits within 95% confidence interval.
We are 95% confident that the OR falls b/w 1.44 and 6.20
The odds of leukemia in those that are exposed to electromagnetic fields are approximately three times
the odds of those who are not exposed to electromagnetic fields.