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What is a Confidence Interval?

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University Course Reader · STEM

Average recovery time fell by 2.1 days (95% confidence interval: 0.4 to 3.8), a wide range for a study this size.

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Overview

A confidence interval is the range around a study's result that shows how precise that result is. The headline number is only the best guess, and the interval shows the whole span of values the data support. A narrow range means the answer is pinned down; a wide one means it is not.
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Overview

A confidence interval is the study's own margin of uncertainty. The headline hands you the middle number, and the range tells you how much they really pinned down. Tight range, they nailed it; huge range, they are shrugging in public. 😎

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Detail

Researchers rarely measure everyone, so they study a sample and estimate from it. Every sample comes out a little different, so the estimate always carries uncertainty, and the interval is how that uncertainty gets reported. Say a trial reports recovery 2.1 days faster, with an interval of 0.4 to 3.8 days. The best guess is 2.1, but the data support anything inside that span. Width is the main takeaway: a narrow range means the effect was measured precisely, while a wide one means the study found something but cannot say how big it is. What sits inside the range matters just as much, because a range running from below zero to well above it means no effect at all is still consistent with the data. The 95% does not mean a 95% chance the truth sits in this particular range. It means that if the study were repeated many times, about 95% of the ranges produced would contain it.
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Detail

Every study looks at a sample, so the headline number is a best guess wearing a confident face. An app that saves you 15 minutes a day, range 2 to 28 minutes? Then 15 is not magic, and the truth could be barely worth installing or genuinely great. Width tells you nearly everything: tight means they pinned it down, wide means they know something is happening but not how much. Then look at what is inside the range, because if it runs from slightly worse to much better, zero is sitting in there and doing nothing at all is still on the table. That is what researchers mean when a result is not statistically significant. And the 95% is not a 95% chance the truth is in this particular range; run the study over and over, and about 95% of the ranges you get would catch it. 😎

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Analogy

Two forecasts for tomorrow's high temperature. One says 74 to 76 degrees, the other says 60 to 90, and both centre on 75. Only the first tells you whether to wear shorts or carry a jacket. The midpoint is the estimate, and the width is how much the forecaster actually knows.
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Analogy

Two contractors quote your renovation. One says 4,800 to 5,100 dollars. The other says somewhere between 1,000 and 20,000. The second might be perfectly honest, and you still cannot plan a thing with it, because that is the gap between a weekend job and a new kitchen.
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Formal definition — The same term, explained the usual way

A confidence interval is a range of values, computed from sample data, that would contain the true population parameter in a specified proportion of repeated samples, conventionally 95%. Interval width reflects sample size and variability and conveys the precision of the estimate; intervals including the null value indicate results compatible with no effect, and overlapping intervals across studies do not by themselves indicate disagreement.

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