ContingencyTableR, CPearsonChiSquaredTest Method

public virtual TestResult PearsonChiSquaredTest()

Public Overridable Function PearsonChiSquaredTest As TestResult

public:
virtual TestResult^ PearsonChiSquaredTest()

abstract PearsonChiSquaredTest : unit -> TestResult 
override PearsonChiSquaredTest : unit -> TestResult 

Return Value

The Pearson Pearson χ² 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 χ² 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 χ², 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 χ² test are violated and it should not be used. For 2 X 2 experiments, the FisherExactTest is a viable alternative in these cases.

Reference