Statistics

=====Interval estimation=====
{{main|Interval estimation}}

[[File:NYW-confidence-interval.svg|thumb|right|[[Confidence intervals]]: the red line is true value for the mean in this example, the blue lines are random confidence intervals for 100 realizations.]]

Most studies only sample part of a population, so results do not fully represent the whole population. Any estimates obtained from the sample only approximate the population value. [[Confidence intervals]] allow statisticians to express how closely the sample estimate matches the true value in the whole population. Often they are expressed as 95% confidence intervals. Formally, a 95% confidence interval for a value is a range where, if the sampling and analysis were repeated under the same conditions (yielding a different dataset), the interval would include the true (population) value in 95% of all possible cases. This does ''not'' imply that the probability that the true value is in the confidence interval is 95%. From the [[frequentist inference|frequentist]] perspective, such a claim does not even make sense, as the true value is not a [[random variable]].  Either the true value is or is not within the given interval. However, it is true that, before any data are sampled and given a plan for how to construct the confidence interval, the probability is 95% that the yet-to-be-calculated interval will cover the true value: at this point, the limits of the interval are yet-to-be-observed [[random variable]]s. One approach that does yield an interval that can be interpreted as having a given probability of containing the true value is to use a [[credible interval]] from [[Bayesian statistics]]: this approach depends on a different way of [[Probability interpretations|interpreting what is meant by "probability"]], that is as a [[Bayesian probability]].

In principle confidence intervals can be symmetrical or asymmetrical. An interval can be asymmetrical because it works as lower or upper bound for a parameter (left-sided interval or right sided interval), but it can also be asymmetrical because the two sided interval is built violating symmetry around the estimate. Sometimes the bounds for a confidence interval are reached asymptotically and these are used to approximate the true bounds.