### 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

** Inconceivable!