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WorksheetFunction.ChiSq_Test Method (Excel)

Returns the test for independence.

Version Added: Excel 2010

expression .ChiSq_Test(Arg1, Arg2)

expression A variable that represents a WorksheetFunction object.




Data Type





The range of data that contains observations to test against expected values.




The range of data that contains the ratio of the product of row totals and column totals to the grand total.

Return Value


ChiSq_Test returns the value from the chi-squared (χ 2 ) distribution for the statistic and the appropriate degrees of freedom. You can use χ 2 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 a χ2 statistic using the formula: Ff839732.awfchtst_ZA06051120(en-us,office.14).gifwhere: A ij = actual frequency in the i-th row, j-th column E ij = expected frequency in the i-th row, j-th column r = number or rows c = number of columns

  • A low value of χ 2 is an indicator of independence. As can be seen from the formula, χ 2 is always positive or 0, and is 0 only if A ij = E ij for every i,j.

  • ChiSq_Test returns the probability that a value of the χ 2 statistic at least as high as the value calculated by the above formula could have happened by chance under the assumption of independence. In computing this probability, ChiSq_Test uses the χ 2 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 or 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 E ij ’s are not too small. Some statisticians suggest that each E ij should be greater than or equal to 5.