Note
In Excel 2010 the TINV() function was replaced with the T.INV.2T() function, and the T.INV() function was added to increase the accuracy of the results. To ensure the backward compatibility of T.INV.2T(), the TINV() function is still available.
Syntax. T.INV.2T(probability,degrees_freedom)
Definition. This function returns the t-value of the t-distribution as a probability and degrees of freedom.
Arguments
probability (required). The probability associated with the two-tailed Student’s t-distribution
degrees_freedom (required). The number of degrees of freedom with which to characterize the distribution
Note
If one of the arguments isn’t a numeric expression, the T.INV.2T() function returns the #VALUE! error.
If probability is less than 0 or greater than 1, the T.INV.2T() function returns the #NUM! error.
If degrees_freedom isn’t an integer, the decimal places are truncated. If degrees_freedom is less than 1, the function returns the #NUM! error.
T.INV.2T returns the value t, such that P(|X| > t) = probability where X is a random variable that follows the t-distribution and P(|X| > t) = P(X < –t or X > t).
A quantile of the t-distribution can be interpreted as the t-value of a one-tailed confidence interval. Because of the symmetry of the t-distribution, the t-value for a one-tailed confidence interval can be calculated by replacing the probability argument with 2*probability.
For a probability of 0.05 and 10 degrees of freedom, the t-value for a two-tailed confidence interval is calculated with =T.INV.2T()(0.05,10). The result is 2.28139.
The t-value for a one-tailed confidence interval for the same probability and the same number of degrees is calculated with =T.INV.2T() (2*0.05,10). The result is 1.812462.
If probability has a value, T.INV.2T() looks for the value x such that T.DIST.2T(x,degrees_ freedom,2) = probability. Therefore, the accuracy of T.INV.2T() depends on the accuracy of T.DIST.2T(). T.INV.2T() uses an iterative search technique. If the search has not converged after 100 iterations, the function returns the #N/A error.
Background. The t-value returned by the T.INV.2T() function is also called the critical value and is used as a statistic for the prepared hypotheses.
Based on this statistic, you can run additional tests to evaluate the validity of the null hypothesis.
The arguments for this function are the probability and the degrees of freedom. The probability argument indicates the significance level you can calculate with the T.DIST.2T() function. For a one-tailed t-test, the significance level is doubled. The degrees of freedom are calculated based on the sum of the two samples minus 2.
Example. The compatibility of a drug is examined in a clinical study. One test group takes the normal daily dosage, and the other test group takes an increased dosage at the beginning of the study. One person has to cancel the test early for private reasons. The goal is to determine whether the increased dosage accelerates the healing process. The duration of treatment is calculated in days.
The null hypothesis indicates that there is no difference in the two test groups regarding the success of treatment. The alternative hypothesis indicates that the second group recovered faster because the method of treatment is more efficient than the usual treatment.
You use a one-tailed t-test type 2: You compare the mean of two independent samples, and use a significance level of 0.05. Now you want to calculate the critical value of the sample with the T.INV.2T() function. Figure 12-140 shows the calculation of T.INV.2T().
The t-value for the evaluated samples based on a probability is 1.7396. This critical value is a statistic and can be used to evaluate the null hypothesis.