Scientific experiments often require comparing two (or more) sets of data. In some cases, the data sets are paired, in that there is an obvious and meaningful one-to-one correspondence between the data in the first set and the data in the second set.
For example, paired data can arise from measuring a single set of individuals at different points in time.
A clinical trial might record the blood pressure in a set of ''n'' patients before and after giving them a medicine. In this case the "before" and "after" data sets are paired, in that each patient has a "before" measurement and an "after" measurement, which are probably related. In contrast, another clinical trial might measure ''n'' patients before treatment and a different set of ''m'' patients after treatment; in that case, the "before" and "after" data are unpaired.
Statistical tests used to compare sets of data have been designed for data sets that are either paired or unpaired, and it is important to use the correct test to prevent erroneous results. Tests for paired data include
McNemar's test
In statistics, McNemar's test is a statistical test used on paired nominal data. It is applied to 2 × 2 contingency tables with a dichotomous trait, with matched pairs of subjects, to determine whether the row and column marginal fre ...
and the paired
permutation test
A permutation test (also called re-randomization test) is an exact statistical hypothesis test making use of the proof by contradiction.
A permutation test involves two or more samples. The null hypothesis is that all samples come from the same dis ...
. Tests for unpaired data include
Pearson's chi-squared test
Pearson's chi-squared test (\chi^2) is a statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance. It is the most widely used of many chi-squared tests (e.g., ...
and
Fisher's exact test
Fisher's exact test is a statistical significance test used in the analysis of contingency tables. Although in practice it is employed when sample sizes are small, it is valid for all sample sizes. It is named after its inventor, Ronald Fisher, ...
.
See also
*
Paired difference test In statistics, a paired difference test is a type of location test that is used when comparing two sets of measurements to assess whether their expected value, population means differ. A paired difference test uses additional information about the ...
Notes
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Statistical tests