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:
Related (or similar) Excel functions:
CHIDIST