﻿ CHISQ.TEST function

# CHISQ.TEST function

Returns the test for independence. CHISQ.TEST 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

CHISQ.TEST(actual_range,expected_range)

The CHISQ.TEST function syntax has the following arguments:

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

• Expected_range     Required. 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, CHISQ.TEST returns the #N/A error value.

• The χ2 test first calculates a χ2 statistic using the 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

• 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 above 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 or if r > 1 and c = 1, then df = r - 1. r = c= 1 is not allowed and #N/A is returned.

• 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.

## Example

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

How do I copy an example?

Important   Do not select the row or column headers.

Selecting an example from Help

2. Press CTRL+C.

3. In Excel, create a blank workbook or worksheet.

4. In the worksheet, select cell A1, and press CTRL+V.

Important   For the example to work properly, you must paste it into cell A1 of the worksheet.

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.

After you copy the example to a blank worksheet, you can adapt it to suit your needs.

 1 2 3 4 5 6 7 8 9 10
 A B C 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) =CHISQ.TEST(A2:B4,A6:B8) The χ2 statistic for the data above is 16.16957 with 2 degrees of freedom (0.000308)

Applies To: Excel 2010, Excel Starter, Excel Online, SharePoint Online

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