Scientific experiments often require comparing two (or more) sets of data. In some cases, the data sets are paired, meaning there is an obvious and meaningful one-to-one correspondence between the data in the first set and the data in the second set, compare
Blocking (statistics)
In the statistical theory of the design of experiments, blocking is the arranging of experimental units that are similar to one another in groups (blocks) based on one or more variables. These variables are chosen carefully to minimize the effect ...
.
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 administering a medicine. In this case, the "before" and "after" data sets are paired, as each patient has a "before" measurement and an "after" measurement, that are likely 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, making it important to use the correct test to prevent erroneous results. Tests for paired data include
McNemar's test
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 frequencies are eq ...
and the paired
permutation test
A permutation test (also called re-randomization test or shuffle test) is an exact statistical hypothesis test.
A permutation test involves two or more samples. The (possibly counterfactual) null hypothesis is that all samples come from the same ...
. Tests for unpaired data include
Pearson's chi-squared test
Pearson's chi-squared test or Pearson's \chi^2 test 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-squa ...
and
Fisher's exact test
Fisher's exact test (also Fisher-Irwin 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. The test assumes that a ...
.
See also
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Paired difference test
A paired difference test, better known as a paired comparison, is a type of location test that is used when comparing two sets of paired sample, paired measurements to assess whether their expected value, population means differ. A paired differen ...
*
Variance reduction
In mathematics, more specifically in the theory of Monte Carlo methods, variance reduction is a procedure used to increase the precision of the estimates obtained for a given simulation or computational effort. Every output random variable fr ...
Notes
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Statistical data types