Note
In Excel 2010, the CHIINV() function was replaced with the CHISQ.INV.RT() function, and the CHISQ.INV() function was added to increase the accuracy of the results. To ensure the backward compatibility of CHISQ.INV.RT(), the CHIINV() function is still available.
Syntax. CHISQ.INV.RT(probability,degrees_freedom)
Definition. This function returns the inverse of the right-tailed probability of the chi-square distribution. If probability = CHISQ.DIST.RT(x,...) then CHI.INV(probability,...) = x. Use this function to compare the observed results with the expected results in order to decide whether your original hypothesis is valid.
Arguments
probability (required). A probability associated with the χ2-distribution
degrees_freedom (required). The number of degrees of freedom
Note
If one of the arguments isn’t a numeric value, the CHISQ.INV.RT() function returns the #VALUE! error.
If probability is less than 0 or greater than 1, the CHISQ.INV.RT() function returns the #NUM! error. If degrees_freedom isn’t an integer, the decimal places are truncated. If degrees_freedom is less than 1 or greater than or equal to 1010, the function returns the #NUM! error.
If probability has a value, CHISQ.INV.RT() looks for the value x so that CHISQ.DIST.RT(x, degrees_freedom) = probability. Therefore, the accuracy of CHISQ.INV.RT() depends on the accuracy of CHISQ.DIST.RT(). CHISQ.INV.RT() uses an iterative search technique. If the search has not converged after 100 iterations, the function returns the #N/A error.
Background. The CHISQ.INV.RT() function returns the test statistic c for the confidence interval of a chi-square distributed random variable. The test statistic c is also called a critical value.
See Also
You will find more information about chi-squared distributions in the discussion of the CHISQ.TEST() function.
For a given probability, this function finds the value x such that CHISQ.DIST.RT(x,degrees_freedom) = probability. The degrees_freedom argument in the χ2 test is based on the number of trials decreased by 1. A statistical test is possible only if at least one degree of freedom exists. The CHISQ.DIST.RT() function is the inverse function of CHISQ.INV.RT().
Example. Assume that you are a manufacturer of vitamins and want to prove that the regular use of Vitamin C reduces the risk of catching colds. You took two samples from the same population where 22 of the 936 participants had a cold.
The first sample contains the expected values, and the second sample contains the observed values. The goal is to prove that your assumption that Vitamin C protects against colds (the null hypothesis) is correct.
Therefore, you calculate the critical value for the random variable with a given probability of 2.5 percent (see Figure 12-20).
The critical value calculated by the CHISQ.INV.RT() function is 5.0239 with a significance level of 2.5 percent and 1 degree of freedom.
If v (the measure for the total variance) falls below this statistic, the null hypothesis is assumed and your statement that Vitamin C protects against colds is confirmed.
To calculate v, the differences between the observed and expected frequencies are squared and divided by the expected frequency (see Figure 12-21).
Because v is above the critical value, the null hypothesis cannot be assumed. This means that your statement that Vitamin C protects against colds cannot be confirmed.