# Documentation/Calc Functions/CHISQ.INV.RT

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CHISQ.INV.RT

## Category:

Statistical Analysis

## Summary:

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

## Syntax:

CHISQ.INV.RT(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 = CHISQ.DIST.RT(x;n), then CHISQ.INV.RT(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 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 truncates it to an integer.

## Additional details:

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.

=CHISQ.INV.RT(0.05;5) returns 11.0704976935.

=CHISQ.INV.RT(0.02;5) returns 13.388222599.

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
=CHISQ.INV.RT(0.75;5) Inverse of the one-tailed(right) probability of the chi-square distribution. Here we can check that =CHISQ.INV.RT(CHISQ.DIST.RT(0.020975769403022;5);5) returns 0.020975769403022. 0.020975769403022
=CHISQ.INV.RT(1.2;5) Number greater than 1 so the function returns an error value Err:502
=CHISQ.INV.RT(1.2;0.9) DegreesFreedom less than 1 so the function returns an error value Err:502

None

CHISQ.INV.RT