A few days ago I saw a link to a CNN-dot-com video asking if nuclear powerplants were responsible for a town in Georgia having a cancer rate 51% higher than the national average.
I didn't have time to watch the video then, and I can't find it now. If you can find it, please leave a comment.
However, we can guess basically what it said:
1. There are two nuclear powerplants in this town
2. Someone worked out some numbers and found the town had more cancer than average. CNN left out the assumptions and the confidence intervals.
3. They interviewed some locals (who are normally only on TV describing what the tornado did to the trailer park).
4. The locals assume the powerplants are responsible for the cancers, including grampa the tobacco farmer's lung cancer.
Again, you don't need to see the actual CNN bit to know where the scientific fallacies are. A better method would be to compare the town to the deep-south or Georgia cancer rate (rural Georgia; excluding Atlanta. Urbanites are statistically healthier than country folk).
I imagine using a non-biased subset for comparison would remove all statistically significant differences. A rural Georgia town will have high cancer rates due to fried food, tobacco, and alcohol. A nuclear plant is hardly needed.