# Documentation/Calc Functions/CHIDIST

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## Function name:

CHIDIST

## Category:

Statistical Analysis

## Summary:

Calculates a right-tail probability value for the chi-square ([math]\displaystyle{ \chi }[/math]^{2}) distribution with a given number of degrees of freedom. The calculated value represents the area under the probability density function curve to the right of the specified chi-square statistic value.

Chi-square distributions are a family of continuous probability distributions on the interval [0, +∞), with the shape of each distribution dependent on the number of degrees of freedom. Although few real-world observations follow a chi-square distribution, they are widely used in statistical hypothesis testing.

## Syntax:

CHIDIST(**Number**; **Degrees freedom**)

## Returns:

Returns a real number in the range [0, 1], which is the right-tail probability from the chi-square distribution for the given arguments.

## Arguments:

**Number** is a non-negative real number, or a reference to a cell containing that number, which is the value to be used to determine the right-tail probability. In a hypothesis test, this could be the value of the chi-square statistic calculated using the expression [math]\displaystyle{ \sum_{}^{}\:\frac{(O\:-\:E)^2}{E} }[/math] for each pair of observed (*O*) and expected (*E*) values.

**Degrees freedom** is a positive integer, or a reference to a cell containing that number, which is the number of degrees of freedom of the chi-square distribution.

- If either
**Number**or**Degrees freedom**is non-numeric, then CHIDIST reports a #VALUE! error. - If
**Degrees freedom**is less than 1, then CHIDIST reports an invalid argument error (Err:502). - If
**Degrees freedom**is a non-integer value, then CHIDIST truncates it to an integer value. - If
**Degrees freedom**is greater than or equal to 1 and**Number**is less than 0.0, then CHIDIST returns the value 1. However, this behavior is a requirement of ODF 1.2 and negative values of**Number**are not expected.

## Additional details:

- Calc's CHIDIST function meets the requirements of the LEGACY.CHIDIST function in ODF 1.2.

- Calc's CHITEST and CHISQ.TEST functions are able to take arrays of expected and observed data, calculate the chi-square statistic, and then calculate the right tail probability for a chi-square goodness of fit test.

- The formula for CHIDIST is:

- [math]\displaystyle{ \text{CHIDIST}(x;\:k)~=~\int_{x}^{\infty }\frac{t^{\frac{k}{2}-1}\:e^{-\frac{t}{2}}}{2^\frac{k}{2}\:\Gamma(\frac{k}{2})}~dt }[/math]

- where k is the number of degrees of freedom (k ≥ 1), x is the value of the chi-square statistic (x ≥ 0), and [math]\displaystyle{ \Gamma }[/math] is the gamma function.

- The following figure shows right-tail probability plots for five sample chi-square distributions.

- For more information about chi-square distributions, visit Wikipedia's Chi-squared distribution page.

## Examples:

Formula | Description | Returns |
---|---|---|

=CHIDIST(A1; A2) where cells A1 and A2 contain the values 13.27 and 5 respectively. | Here the function returns a value of approximately 0.02 or 2%. To interpret this result, you might be carrying out a hypothesis test and working to a significance level of 0.05 or 5%. In this case, the value of 2% provides evidence that you should reject the null hypothesis because there is a statistically significant association between the variables of the experiment. Since the formula `=CHIDIST(11.07; 5)` returns approximately 0.05, it can be inferred that any chi-square statistic value greater than 11.07 implies that the null hypothesis should be rejected for an experiment with five degrees of freedom. |
0.0209757694030221 |

=CHIDIST(5; 3) | Here the function returns a value of approximately 0.17 or 17%, which does not provide evidence to reject the null hypothesis when performing a hypothesis test with a 5% significance level. The formulas `=CHISQ.DIST.RT(5; 3)` and `=1-CHISQ.DIST(5; 3; 1)` provide the same result. |
0.171797144296733 |

=CHIDIST(3.45; 1.95) | Here the function returns a value of approximately 0.06 or 6%. The non-integer value for the second argument is truncated to 1 and the formula `=CHIDIST(3.45; 1)` returns the same result. |
0.0632517697927173 |

## Related LibreOffice functions:

## ODF standard:

## Equivalent Excel functions:

CHIDIST