Returns the test for independence. CHITEST returns the value from the chi-squared (χ2) distribution for the statistic and the appropriate degrees of freedom. You can use χ2 tests to determine whether hypothesized results are verified by an experiment.



Actual_range     is the range of data that contains observations to test against expected values.

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


  • If actual_range and expected_range have a different number of data points, CHITEST returns the #N/A error value.
  • The χ2 test first calculates a χ2 statistic using the formula:



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

  • 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.
  • CHITEST returns the probability that a value of the χ2 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, CHITEST 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 or if r > 1 and c = 1, then df = r - 1. r = c= 1 is not allowed and #N/A is returned.
  • Use of CHITEST 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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Men (Actual) Women (Actual) Description
58 35 Agree
11 25 Neutral
10 23 Disagree
Men (Expected) Women (Expected) Description
45.35 47.65 Agree
17.56 18.44 Neutral
16.09 16.91 Disagree
Formula Description (Result)
=CHITEST(A2:B4,A6:B8) The χ2 statistic for the data above is 16.16957 with 2 degrees of freedom (0.000308)
Applies to:
Excel 2003