What is a confidence interval, and how should you read one?
A range of values, calculated from a sample, that is intended to capture the true population value — and it conveys both the estimate and its precision, which a single number cannot.
The technical definition, which is strange and worth stating properly. A 95% confidence interval means that if the study were repeated many times, 95% of the intervals constructed this way would contain the true value.
It does not mean there is a 95% probability that this particular interval contains the true value. In the frequentist framework, the true value is fixed and the interval is random, so a specific interval either contains it or does not. This distinction is technically important and, for practical reading, the common interpretation rarely leads people astray — but the precise meaning is a credible interval, which belongs to Bayesian statistics.
How to read one usefully:
The width tells you the precision. A narrow interval means a precise estimate; a very wide one means the study cannot distinguish between quite different possibilities, however impressive the headline figure.
Where it sits matters more than whether it excludes zero. An interval from 0.1 to 40 technically excludes no effect, and tells you almost nothing useful.
Check whether clinically or practically important values lie inside it. An interval including both a trivial effect and a substantial one has not answered the question.
Why it is more informative than a p-value. Both use the same underlying arithmetic, but a confidence interval reports magnitude and uncertainty together, while a p-value reduces everything to whether a threshold was crossed. This is why reporting guidelines and statistical bodies recommend intervals.
What widens or narrows it:
Sample size, which is the main lever — precision improves with the square root of sample size, so quadrupling the sample halves the interval width.
Variability in the underlying data.
The confidence level chosen — a 99% interval is wider than a 95% one, because greater confidence requires a wider net.
Overlapping intervals between two groups do not automatically mean no significant difference, which is a common misreading.