Confidence Interval Estimation

The statistical process of calculating a range of plausible values for an unknown parameter based on sample data and a specified confidence level.

Source: Neyman 1937

Confidence interval estimation calculates a range of plausible values for an unknown quantity from sample data, rather than reporting only a single best guess. It is preferred to a lone point estimate because it shows how much uncertainty surrounds that guess: a point estimate of a treatment effect means little without knowing whether the data narrow it tightly or barely constrain it. Unlike a significance test that yields only a yes or no, it displays the whole range of effects the data support. Pairing an estimate with its uncertainty is its value. Kirkwood and Sterne (2003) describe this.

Source: Kirkwood & Sterne 2003

Confidence interval estimation is carried out by computing the point estimate and its standard error, choosing a confidence level, and forming the interval using an appropriate multiplier from the relevant distribution, typically as the estimate plus and minus the multiplier times the standard error. The method depends on the parameter and the sampling distribution. So confidence interval estimation is carried out by combining the estimate with a margin based on its uncertainty and the confidence level, using exact or approximate methods according to the situation, which yields an interval whose width reflects the precision of the estimate and whose construction achieves the specified coverage over repeated sampling.

Source: Neyman 1937

Confidence interval estimation produces a range of plausible values for a parameter together with a confidence level, conveying uncertainty, while point estimation produces a single best estimate without directly expressing how precise it is. The interval adds information about the precision that the point estimate alone lacks. So confidence interval estimation differs from point estimation in giving a range rather than a single value, which communicates the uncertainty in the estimate, and the two are complementary, since a point estimate provides the best single guess and the confidence interval shows the range of values compatible with the data, giving a fuller picture of what the study establishes.

Source: Neyman 1937

Confidence interval estimation is often preferred over significance testing alone because it conveys the size and precision of an effect, not merely whether it is statistically significant, showing the range of plausible values and thus both statistical and practical importance. A significance test gives only a yes-or-no verdict against a null hypothesis. So confidence interval estimation is preferred for providing richer information than a p-value, since it reveals how large and how precisely estimated an effect is, allowing judgement about clinical importance and about the compatibility of the data with various values, which a bare significance test does not support.

Source: Neyman 1937

The precision of confidence interval estimation, reflected in the width of the interval, is determined chiefly by the sample size and the variability of the data, with larger samples and lower variability giving narrower, more precise intervals, and by the confidence level chosen, with higher levels giving wider intervals. So the precision of confidence interval estimation depends on how much and how variable the data are and on the confidence level, which is why studies are designed with adequate sample sizes to achieve the desired precision, since an imprecise, wide interval limits the usefulness of the estimate for drawing firm conclusions.

Source: Neyman 1937