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What does a 95% confidence interval actually mean, and...
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See plansA confidence interval is a range, computed from your sample, built by a procedure guaranteed to contain the true population parameter a specified percentage of the time across repeated sampling — a 95% CI means that if you repeated your sampling and estimation procedure many times, about 95% of the intervals you’d construct would contain the true value.
The near-universal misreading is treating it as “there’s a 95% probability the true value lies in this specific interval.” That doesn’t make sense in frequentist terms, because the true parameter is a fixed (if unknown) number, not a random variable, and any single interval either does or doesn’t contain it — the randomness is in the interval’s construction across hypothetical repeated samples, not in the parameter itself. This distinction matters practically: a narrow CI reflects a precise estimate (usually from more data or lower variance), not a more “confident” claim about probability. In ML reporting, confidence intervals around a metric — say, a model’s AUROC on a held-out set — tell you how much that estimate would likely wobble if you’d drawn a different test set, which is exactly the information you need before declaring model A better than model B on a difference that might just be sampling noise.