8.1.2 Performing a two-tailed one-sample T-test

For a two-tailed one-sample t-test, Excel also provides a specific function: T.INV.2T.

The syntax is: =T.INV.2T(probability, degrees_freedom)

Figure 25 T.INV.2T Function

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The image shows the Excel function T.INV.2T, which calculates the two-tailed inverse of the Student’s t-distribution. It requires two inputs: the probability for the two-tailed distribution and the degrees of freedom (deg_freedom) that define the specific t-distribution. This function is typically used in two-tailed hypothesis testing, where both extremes of the distribution are considered in the analysis.

Figure 25 T.INV.2T Function

Where:

• probability: This value represents the cumulative probability for which you want to find the corresponding t-value. It determines the boundary of the t-distribution.
• degrees_freedom: This equals N-1, where N is the sample size. It defines the specific shape of the t-distribution.

Using our previous example of a two-tailed one-sample t-test with α = 5% and 10 degrees of freedom, we would enter: =T.INV.2T(0.05, 10) which returns 2.228

Remember that the T.INV.2T function returns the two-tailed t critical value, which is the absolute value for the positive side of the t-distribution. For a two-tailed test, the t-distribution has both positive and negative critical values. Therefore, when reporting the t critical value, it is necessary to use the ± sign to show both the upper and lower bounds of the critical region.

Thus, the t critical value for two tailed test = ± 2.228

This boundary is crucial because:

• If your calculated t-statistic falls beyond this boundary, you reject the null hypothesis.
• If your t-statistic falls within these boundaries, you fail to reject the null hypothesis.

We can still use T.INV(probability, degrees_freedom) to find t critical value for two-tailed one-sample t-test. You need to modify the probability by dividing the desired significance level by 2 to account for both tails.

For instance, for a two-tailed test with α = 5%:

• =T.INV(0.025, 10) for lower tail
• =T.INV(0.975, 10) for upper tail