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WorksheetFunction.ChiSq_Test method (Excel)

  • Article

Returns the test for independence.

Syntax

expression.ChiSq_Test (Arg1, Arg2)

expression A variable that represents a WorksheetFunction object.

Parameters

Name Required/Optional Data type Description
Arg1 Required Variant The range of data that contains observations to test against expected values.
Arg2 Required Variant The range of data that contains the ratio of the product of row totals and column totals to the grand total.

Return value

Double

Remarks

ChiSq_Test returns the value from the chi-squared (χ2) distribution for the statistic and the appropriate degrees of freedom. Use χ2 tests to determine whether hypothesized results are verified by an experiment.

If actual_range and expected_range have a different number of data points, ChiSq_Test returns the #N/A error value.

The χ2 test first calculates an χ2 statistic by using the following formula, where:

  • Aij = actual frequency in the i-th row, j-th column
  • Eij = expected frequency in the i-th row, j-th column
  • r = number or rows
  • c = number of columns

Formula

A low value of χ2 is an indicator of independence. As can be seen from the formula, χ2 is always positive or 0, and is 0 only if Aij = Eij for every i,j.

ChiSq_Test returns the probability that a value of the χ2 statistic at least as high as the value calculated by the preceding formula could have happened by chance under the assumption of independence. In computing this probability, ChiSq_Test uses the χ2 distribution with an appropriate number of degrees of freedom, df.

  • If r > 1 and c > 1, then df = (r - 1)(c - 1).
  • If r = 1 and c > 1, then df = c - 1.
  • If r > 1 and c = 1, then df = r - 1.
  • r = c = 1 is not allowed and generates an error.

Use of ChiSq_Test is most appropriate when Eij's are not too small. Some statisticians suggest that each Eij should be greater than or equal to 5.

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