Returns the inverse of the one-tailed probability of the chi-squared distribution.
Number is the value of the error probability.
DegreesFreedom is the degrees of freedom of the experiment.
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.