Editing Test statistic (section)

{{Short description|Statistic used in statistical hypothesis testing}}
[[File:Common_Test_Statistics_Chart.png|thumb|The above image shows a table with some of the most common test statistics and their corresponding [[statistical test]]s or models.]]
'''Test [[statistic]]''' is a quantity derived from the [[Sample (statistics)|sample]] for [[statistical hypothesis testing]].<ref name="CasellaBerger">Berger, R. L.; Casella, G. (2001). ''Statistical Inference'', Duxbury Press, Second Edition (p.374)</ref> A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test.  In general, a test statistic is selected or defined in such a way as to quantify, within observed data, behaviours that would distinguish the [[null hypothesis|null]] from the [[alternative hypothesis]], where such an alternative is prescribed, or that would characterize the null hypothesis if there is no explicitly stated alternative hypothesis.

An important property of a test statistic is that its [[sampling distribution]] under the null hypothesis must be calculable, either exactly or approximately, which allows [[p-value|''p''-values]] to be calculated. A ''test statistic'' shares some of the same qualities of a [[descriptive statistics|descriptive statistic]], and many statistics can be used as both test statistics and descriptive statistics. However, a test statistic is specifically intended for use in statistical testing, whereas the main quality of a descriptive statistic is that it is easily interpretable. Some informative descriptive statistics, such as the [[range (statistics)|sample range]], do not make good test statistics since it is difficult to determine their sampling distribution.

Two widely used test statistics are the [[t-statistic]] and the [[F-test|F-statistic]].