What does the 95% confidence interval mean?
My take on interpreting the 95% CI:
Predictor: Riding a fixed gear bicycle
Outcome: Low-rise jeans
Result: Riding a fixie is associated with a 50% (95% CI: 25%-75%) higher probability of wearing low-rise jeans
Bias/confounding: None, of course
Here is a generally agreeable statement:
If the study were repeated again an infinite number of times, 95% of those studies would have the true risk difference in the 95% CI.
Here is what SOME call a crime against inference:
There is a 95% probability that the true risk difference is between 25% and 75%.
Image I flip a coin, it lands on the ground and I step on it before you can see how it landed.
Q: What is the probability that it is heads?
A1: 50% - Infidel, you have committed a crime against inference and are condemned to death*.
A2: 0% or 100%: Congratulations, you can join the League of Pedantic Professors
The source of confusion? The LPP uses a technical definition of probability that involves repeated observations. Meanwhile in the real world, 99% of us say that while the coin IS heads up (100%) or tails up (0%), because we don't know which we still say it has a 50% probability of being either. [Insert obligatory Schrodinger's cat here.]
Unless I am wrong, and I'm never wrong**, there is no problem with the stronger statement because the kind of people that interpret the CI that way are the kind of people that say 50%.
* At the age of 80 years, 95% CI: 50-120