Editing Prediction interval (section)

=== Contrast with confidence intervals ===
{{main article|Confidence interval}}
In the formula for the predictive confidence interval ''no mention'' is made of the unobservable parameters ''μ'' and ''σ'' of population mean and standard deviation – the observed ''sample'' statistics <math>\overline{X}_n</math> and <math>S_n</math> of sample mean and standard deviation are used, and what is estimated is the outcome of ''future'' samples.

When considering prediction intervals, rather than using sample statistics as estimators of population parameters and applying confidence intervals to these estimates, one considers "the next sample" <math>X_{n+1}</math> as ''itself'' a statistic, and computes its [[sampling distribution]].

In parameter confidence intervals, one estimates population parameters; if one wishes to interpret this as prediction of the next sample, one models "the next sample" as a draw from this estimated population, using the (estimated) ''population'' distribution. By contrast, in predictive confidence intervals, one uses the ''sampling'' distribution of (a statistic of) a sample of ''n'' or ''n''&nbsp;+&nbsp;1 observations from such a population, and the population distribution is not directly used, though the assumption about its form (though not the values of its parameters) is used in computing the sampling distribution.