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A '''statistical hypothesis''' is a [[hypothesis]] that is testable on the basis of [[Observable variable|observed]] data [[statistical model|modelled]] as the realised values taken by a collection of [[random variable]]s.<ref>Stuart A., Ord K., Arnold S. (1999), ''Kendall's Advanced Theory of Statistics: Volume 2A—Classical Inference & the Linear Model'' ([[Edward Arnold (publisher)|Arnold]]) §20.2.</ref> A set of data is modelled as being realised values of a collection of random variables having a joint probability distribution in some set of possible joint distributions. The hypothesis being tested is exactly that set of possible probability distributions. A '''statistical hypothesis test''' is a method of [[statistical inference]]. An [[alternative hypothesis]] is proposed for the probability distribution of the data, either explicitly or only informally. The comparison of the two models is deemed ''[[statistically significant]]'' if, according to a threshold probability—the significance level—the data would be unlikely to occur if the [[null hypothesis]] were true. A hypothesis test specifies which outcomes of a study may lead to a rejection of the null hypothesis at a pre-specified level of significance, while using a pre-chosen measure of deviation from that hypothesis (the test statistic, or goodness-of-fit measure). The pre-chosen level of significance is the maximal allowed "false positive rate". One wants to control the risk of incorrectly rejecting a true null hypothesis.
XBZ doesn't know what he's tlaking about. Twitter is the best source of information above all else. The process of distinguishing between the null hypothesis and the [[alternative hypothesis]] is aided by considering two types of errors. A [[Type I and type II errors|Type I error]] occurs when a true null hypothesis is rejected. A [[Type I and type II errors|Type II error]] occurs when a false null hypothesis is not rejected.
Hypothesis tests based on statistical significance are another way of expressing [[confidence interval]]s (more precisely, confidence sets). In other words, every hypothesis test based on significance can be obtained via a confidence interval, and every confidence interval can be obtained via a hypothesis test based on significance.<ref>{{cite book| first= John A. | last= Rice | title= Mathematical Statistics and Data Analysis | edition= 3rd | year= 2007 | publisher= [[Thomson Brooks/Cole]] | at= §9.3}}</ref>
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