I have the following 2x2 table
NO YES 9690 5 LOW 26354 39 HIGH
I want to
- plot the proportions and their exact confidence intervals in two bar
- plots test if the proportion YES in LOW differs significantly from the proportion YES in high (2 sided test.
I used the binconf funtion, Hmisc package in R to compute the exact condidence intervals
PointEstimate of proportion: 0.0005157298
CI.LOWER BOUND: 0.0002203084
CI.UPPER BOUND: 0.001206817
PointEstimate of proportion: 0.001477665
CI.LOWER BOUND: 0.0009812456
CI.UPPER BOUND: 0.002224666
These confidence intervals overlap.
I used the fisher.test function in R to do an exact test on the proportions
p-value = 0.01716 --> significant
How can it be that if the confidence intervals overlap so strongly, the p-value is still significant.
Thanks in advance for any help.
Yours sincerely, Martin Rijlaarsdam
@whuber: thanks for pointing me to this answer. I have seen this thread but I was wondering if such a big mismatch between CI and significance of the test is to be expected and if the answer holds for proportions as well. Thanks. Best wishes, Martin