Editing Pearson correlation coefficient (section)

===Using a permutation test===
[[Permutation test]]s provide a direct approach to performing hypothesis tests and constructing confidence intervals. A permutation test for Pearson's correlation coefficient involves the following two steps: 
# Using the original paired data (''x''<sub>''i''</sub>,&nbsp;''y''<sub>''i''</sub>), randomly redefine the pairs to create a new data set (''x''<sub>''i''</sub>,&nbsp;''y''<sub>''{{prime|i}}''</sub>), where the ''{{prime|i}}'' are a [[permutation]] of the set {1,...,''n''}.  The permutation ''{{prime|i}}'' is selected randomly, with equal probabilities placed on all ''n''! possible permutations.  This is equivalent to drawing the ''{{prime|i}}'' randomly without replacement from the set {1, ..., ''n''}.  In [[Bootstrapping (statistics)|bootstrapping]], a closely related approach, the ''i'' and the ''{{prime|i}}'' are equal and drawn with replacement from {1, ..., ''n''};
# Construct a correlation coefficient ''r'' from the randomized data.
To perform the permutation test, repeat steps&nbsp;(1) and (2) a large number of times.  The [[p-value]] for the permutation test is the proportion of the ''r'' values generated in step&nbsp;(2) that are larger than the Pearson correlation coefficient that was calculated from the original data.  Here "larger" can mean either that the value is larger in magnitude, or larger in signed value, depending on whether a [[two-tailed test|two-sided]] or [[one-sided test|one-sided]] test is desired.