# Documentation/Calc Functions/CHIINV

CHIINV

## Category:

Statistical Analysis

## Summary:

Returns the inverse of the one-tailed(right) probability of the chi-square distribution.

## Syntax:

CHIINV(Number; DegreesFreedom)

## Returns:

Returns a non-negative real number which is the inverse of the right-tailed probability of the chi-square distribution. If p = CHIDIST(x;n), then CHIINV(p,n) = x.

## Arguments:

Number is a real number from 0 to 1 or a reference to the cell containing that number which is the value of the error probability.

DegreesFreedom is a positive integer or a reference to a cell containing that number which is the degrees of freedom of the experiment.

• If Number is greater than 1 or less than equal to 0, then the function returns an error value.
• If DegreesFreedom is less than 1, the function returns an error value.
• If DegreesFreedom is a non-integer numeric value, then the function uses its floor value,i.e. it is truncated to an integer.

For more details on the inverse chi-square distribution, visit Wikipedia

## Examples:

A die is thrown 1020 times. The numbers on the die 1 through 6 come up 195, 151, 148, 189, 183 and 154 times (observation values). The hypothesis that the die is not fixed is to be tested.

The Chi square distribution of the random sample is determined by the formula given above. Since the expected value for a given number on the die for n throws is n times 1/6, thus 1020/6 = 170, the formula returns a Chi square value of 13.27.

If the (observed) Chi square is greater than or equal to the (theoretical) Chi square CHIINV, the hypothesis will be discarded, since the deviation between theory and experiment is too great. If the observed Chi square is less that CHIINV, the hypothesis is confirmed with the indicated probability of error.

=CHIINV(0.05;5) returns 11.07.

=CHIINV(0.02;5) returns 13.39.

If the probability of error is 5%, the die is not true. If the probability of error is 2%, there is no reason to believe it is fixed.

For more examples:

Formula Description Returns
=CHIINV(0.75;5) Inverse of the one-tailed(right) probability of the chi-square distribution. =CHIINV(CHIDIST(0.020975769403022;5);5) returns 0.020975769403022. 0.020975769403022
=CHIINV(1.2;5) Number greater than 1 so the function returns an error value Err:502
=CHIINV(0.2;0.9) DegreesFreedom less than 1 so the function returns an error value Err:502

CHIINV