1a. the crude odds ratio equals (90 x 2235)/(245 x 493) = 1.67.
The stratum specific odds ratios equal (20 x 1854)/(55 x 407) =
1.66 and (70 x 381)/(190 x 86) = 1.63. The crude odds ratio and
the stratum specific odds ratios are almost equal. This suggests
that coffee and tea consumption is probably not a confounder.
1b. The following two tables display the relationship between
the potential confounder and both the predictor and the
outcome.
Cigarettes Pregnant
Coffee or Tea per Day Coffee or Tea in Six Months
Cups per Day 0 > 19 Cups per Day Yes No
0-2 2261 75 0-2 1909 427
GT 2 467 260 GT 2 571 156
The expected values for these two tables are shown below followed
by the components of the chi square tests of independence.
Expected Values
Cigarettes Pregnant
Coffee or Tea per Day Coffee or Tea in Six Months
Cups per Day 0 > 19 Cups per Day Yes No
0-2 2080.5 647.5 0-2 1891.4 444.6
GT 2 255.5 79.5 GT 2 588.6 138.4
Components of Chi Square Statistics
Cigarettes Pregnant
Coffee or Tea per Day Coffee or Tea in Six Months
Cups per Day 0 > 19 Cups per Day Yes No
0-2 15.7 50.3 0-2 0.2 0.7
GT 2 127.5 409.7 GT 2 0.5 2.2
Chi sq = 603.173 p < .001 Chi sq = 3.64, p > .05
There is a very strong relationship between the amount of
coffee or tea drunk and the amount of smoking. On the other
hand, the relationship between coffee or tea consumption and
ability to get pregnant is not significant. Since only one of
these relationships is significant, coffee or tea consumption is
not a confounder.
Return to the questions
2a. The complication rate for surgeries performed by residents
on call was 122/1840 = .066, and the complication rate for those
not on call is 237/4672 = .051. The expected values and
components to the chi square statistic are shown below.
Expected Values Chi sq Components
Complication Complication
Call Status No Yes Call Status No Yes
No 1738.6 101.4 No 0.2 4.2
Yes 4414.4 257.6 Yes 0.1 1.6
The test statistic equals 6.15, df = 1, and p = .013. Reject the
null hypothesis, and conclude that there is a relationship.
Those who were sleep deprived have a higher complication rate
than those who were not.
b. The stratum specific expected values and components to chi
square are shown below.
Emergency
Expected Values Chi sq Components
Complication Complication
Call Status No Yes Call Status No Yes
No 627.9 75.1 No 0.0 0.2
Yes 1045.1 124.9 Yes 0.0 0.1
Not Emergency
Expected Values Chi sq Components
Complication Complication
Call Status No Yes Call Status No Yes
No 1098.0 39.0 No 0.0 0.4
Yes 3382.0 120.0 Yes 0.0 0.1
The test statistics equal .35 and .57. Fail to reject the null
hypothesis. There is no relationship between call status and
complication rate after controlling for emergency status.
c. The data relating emergency status to the predictor and the
outcome are shown below.
Emergency Emergency
Call Status Yes No Complication Yes No
No 703 1137 No 1673 4480
Yes 1170 3502 Yes 200 159
Chi sq = 111.64, df = 1, p<.001 Chi sq = 134.66, df = 1, p<.001
The confounder is related to the predictor and the outcome. This
is an important type of confounder. If we fail to control for
it, we conclude that there is a relationship between the
confounder and outcome when there really is not.
Return to the questions
Return to the syllabus
Return to the home page
© J.Rice