# Documentation/Calc Functions/CHITEST

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CHITEST

## Category:

Statistical Analysis

## Summary:

Returns the probability of a deviance from a random distribution of two test series based on the chi-square test for independence. CHITEST returns the chi-square distribution of the data.

## Syntax:

CHITEST(DataB; DataE)

## Returns:

Returns a real number which is the chi-square distribution of the data. It is a probability and hence it ranges from 0 to 1, i.e. [0,1].

## Arguments:

DataB is a range of references to the cells containing the array of the observations.

DataE is a range of references to the cells containing the range of the expected values.

• If DataB and DataE have different number of data points then the function returns an error value.
• If any of the cell whose reference is passed contains non-numeric value then the function returns an error value.

## Additional details:

• The probability determined by CHITEST can also be determined with CHIDIST, in which case the chi-square of the random sample must be passed as a parameter instead of the data row.
• The χ2 test first calculates a χ2 statistic using the formula:

where:

Aij = element of actual data which is DataB in our case

Eij = element of expected values which is DataE in our case

r = number or rows

c = number of columns

Then CHIDIST is called with chi-square value and a degree of freedom (df). If r>1 and c>1: df = (r-1)(c-1) else df = r*c-1 and CHITEST = CHIDIST(χ2;df).

## Examples:

Data_B (observed) Data_E (expected)
1 195 170
2 151 170
3 148 170
4 189 170
5 183 170
6 154 170
Formula Description Returns
=CHITEST(A1:A6;B1:B6) This is the probability that suffices the observed data of the theoretical Chi-square distribution. 0.020975769403022
=CHITEST(A1:A5;B1:B6) DataB size not equal to that of DataE so the function will return an error value. Err:502

CHITEST