CHITEST

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.

Syntax

CHITEST(actual_range,expected_range)

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.

Remarks

• 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:

  

  where:

  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 χ² is an indicator of independence. As can be seen from the formula, χ² is always positive or 0, and is 0 only if A_ij = E_ij 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 E_ij's are not too small. Some statisticians suggest that each E_ij should be greater than or equal to 5.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

   Note Do not select the row or column headers.

   Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See also:

• CHIDIST
• CHIINV
• Statistical functions