The Excel CHITEST Function

Related Function:
CHIDIST Function

CHI-SQUARE TEST

The chi-square test uses the chi-square distribution of one or more sets of data, to test whether there is a significant difference between observed frequencies and expected frequencies.

The chi-square distribution is given by the formula :

Chi-Square Distribution Equation

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 of rows
c   =   number of columns

The chi-square test can then be used to determine whether the value of this function is likely to have occurred by chance alone, in independent sets of data.

CHITEST and CHISQ.TEST

In Excel 2010, the Chitest function has been replaced by the Chisq.Test function, which has improved accuracy.

Although it has been replaced, the Chitest function is still available in Excel 2010 (stored in the list of compatibility functions), to allow compatibility with earlier versions of Excel.



Basic Description

The Excel CHITEST function uses the chi-square test to calculate the probability that the differences between two supplied data sets (of observed and expected frequencies), are likely to be simply due to sampling error, or if they are likely to be real.

The syntax of the function is :

CHITEST( actual_range, expected_range )

Where the function arguments are:

actual_range - An array of observed frequencies
expected_range - An array of expected frequencies (must have the same dimension as the actual_range array)

You should bear in mind that the chi-square test is not reliable when the expected values are too small. As a guideline, if any of the expected values are less than 5, or if the total of the expected values is less than 50, you should not rely on the result of the chi-square test.


Chitest Function Example

Cells B3-C5 and F3-G5 of the spreadsheet below show the observed and expected frequencies of responses from men and women to a simple question.

Example Data for the Excel Chitest Function

The chi-square test for independence, for the above data sets, is calculated using the Excel Chitest function as follows:

=CHITEST( B3:C5, F3:G5 )

This gives the result 0.000699103.

Generally, a probability of 0.05 or less is considered to be significant. Therefore, the returned value of 0.000699103 in this example, indicates that there is a significant difference between the observed frequencies and the expected frequencies, which is unlikely to be simply due to sampling error.


Further examples of the Excel Chitest function can be found on the Microsoft Office website.


Chitest Function Errors

If you get an error from the Excel Chitest function this is likely to be one of the following :

Common Errors
#N/A - Occurs if either:
- the two supplied data arrays have different dimensions
or
- the supplied data arrays have width and height 1 (i.e. contain just one value)
#DIV/0! - Occurs if any of the supplied expected_values are zero
#NUM! - Occurs if any of the supplied expected_values are negative
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