Editing Student's t-test (section)

====Paired samples====
{{Main|Paired difference test}}

[[Paired sample]]s ''t''-tests typically consist of a sample of matched pairs of similar [[unit (statistics)|units]], or one group of units that has been tested twice (a "repeated measures" ''t''-test).

A typical example of the repeated measures ''t''-test would be where subjects are tested prior to a treatment, say for high blood pressure, and the same subjects are tested again after treatment with a blood-pressure-lowering medication. By comparing the same patient's numbers before and after treatment, we are effectively using each patient as their own control. That way the correct rejection of the null hypothesis (here: of no difference made by the treatment) can become much more likely, with statistical power increasing simply because the random interpatient variation has now been eliminated. However, an increase of statistical power comes at a price: more tests are required, each subject having to be tested twice. Because half of the sample now depends on the other half, the paired version of Student's ''t''-test has only {{math|{{sfrac|''n''|2}} − 1}} degrees of freedom (with {{math|''n''}} being the total number of observations). Pairs become individual test units, and the sample has to be doubled to achieve the same number of degrees of freedom. Normally, there are {{math|''n'' − 1}} degrees of freedom (with {{math|''n''}} being the total number of observations).<ref>{{cite web|last1=Weisstein|first1=Eric|title=Student's ''t''-Distribution|url=http://mathworld.wolfram.com/Studentst-Distribution.html|website=mathworld.wolfram.com}}</ref>

A paired samples ''t''-test based on a "matched-pairs sample" results from an unpaired sample that is subsequently used to form a paired sample, by using additional variables that were measured along with the variable of interest.<ref>{{cite journal |last1=David |first1=H.&nbsp;A. |last2=Gunnink |first2=Jason L. |year=1997 |title=The Paired ''t'' Test Under Artificial Pairing |journal=The American Statistician |volume=51 |pages=9–12 |jstor=2684684 |doi=10.2307/2684684 |issue=1}}</ref> The matching is carried out by identifying pairs of values consisting of one observation from each of the two samples, where the pair is similar in terms of other measured variables. This approach is sometimes used in observational studies to reduce or eliminate the effects of confounding factors.

Paired samples ''t''-tests are often referred to as "dependent samples ''t''-tests".