A 95% confidence level means that the method used, applied repeatedly to many samples, would produce intervals containing the true value 95% of the time.
A 95% confidence level means that the method used, applied repeatedly to many samples, would produce intervals containing the true value 95% of the time. It is a property of the procedure across hypothetical repetitions.
The specific interval in front of a reader either contains the true value or does not. Saying there is a 95% chance it does is the most common misstatement in applied statistics, and it changes what a reader concludes.
Ninety-five per cent is a convention, not a natural constant. Some fields use stricter levels because the cost of a false positive is higher, and the choice should follow the consequences rather than the habit.
A 99% interval is wider than a 95% one from identical data. The wider interval is not a worse result; it reflects a higher standard for coverage, and comparing intervals computed at different levels is meaningless.
Coverage holds if the statistical assumptions behind the calculation hold. Where they do not — dependent observations, selected samples — the stated level overstates the real coverage, often substantially.
Computing an interval repeatedly as data accumulate, and stopping when it looks convincing, destroys the stated coverage. This is the same problem that affects p-values under interim analysis and it is less widely recognised.
A confidence interval covers a parameter; a prediction interval covers the next observation and is considerably wider. Quoting one when a reader needs the other understates uncertainty in a way that matters for any individual decision.
Treat the interval as the range of values the data do not rule out, note the level, and remember that the guarantee is about the method rather than about this particular answer.
Nothing prevents a paper publishing 90, 95 and 99 per cent intervals side by side, and seeing all three makes the shape of the uncertainty obvious in a way one interval does not. It is almost never done, partly through convention and partly because a single interval reads as a more definite answer. Where a paper does report more than one, it is signalling a comfort with uncertainty that is itself informative.
Published intervals assume the analysis was specified in advance and the model is correct. In fields where analytic choices are made after seeing data, the real-world coverage of nominal 95 per cent intervals has been estimated well below 95 per cent. The number on the page is an upper bound on how reliable the range is, not a guarantee.