What confidence intervals really mean

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If you're unsure what a confidence interval is, you're not alone, Tom Siegfried writes; a lot of scientists have the same problem: "In actual statistical fact, a confidence interval tells you not how confident to be in the answer, but how confident to be in your sampling. In other words, if you repeated the experiment (on different samples from your population) a gazillion times, your confidence interval will reliably contain the true value in 95 percent of the trials."