Confidence interval

The width of the interval is the message. A narrow 95 percent CI signals a precise estimate, while a wide one signals uncertainty, often from a small sample. An interval that comfortably excludes the null value (zero for a difference, one for a ratio) conveys the same information as p below 0.05, but adds the range of effect sizes the data are compatible with.

The correct interpretation is subtle. A 95 percent CI does not mean there is a 95 percent probability the true value lies inside this particular interval. It means the procedure captures the truth 95 percent of the time across repetitions. In practice, reporting an estimate with its interval is far more informative than a bare significant or non-significant label.

For reviewers, intervals that straddle the null while the text still claims an effect, or extremely wide intervals presented as if precise, are red flags. When a paper reports only p-values, asking for confidence intervals almost always sharpens the interpretation.