So let’s round this up by stating that confidence intervals are useful nifty little things that are exceedingly open to misinterpretation. Use them if you want to but make sure you understand them. The following little list is useful to remember.
- A confidence interval does not say anything about the probability of the sought parameter to be inside a specific interval
- A confidence interval is a probability distribution over the data generated by a fixed parameter and not over the parameter
- Once a confidence interval has been realized (measured) by observing data it is no longer a probability; it either contains the parameter value sought or it does not