Meta.Numerics Library

## ContingencyTableR, CPearsonChiSquaredTest Method |

Performs a Pearson χ^{2} test for correlation in the table.

Syntax

The result of the test. The test statistic is χ

Remarks

The Pearson Pearson χ^{2} test tests for correlation between the row and column values. If
row and column values are uncorrelated, then the expected number of counts in a table entry is simply proportional to the
totals for its row and column. If that number is large for all entries, then the central limit theorem suggests that the
actual number of counts will be distributed normally with mean equal to the expected value and standard deviation equal
to its square root. The χ^{2} statistic measures the departure of the actual table from this expectation
in the uncorrelated case, and under this null hypothesis its distribution is known. Having calculated χ^{2},
then, we can compute just how unlikely it was to obtain a value as large or larger than the one obtained.

In cases where either the actual or expected counts for some entries are small or zero, the assumptions of the
Pearson χ^{2} test are violated and it should not be used. For 2 X 2 experiments, the
FisherExactTest is a viable alternative in these cases.

See Also