After calculating the t-test statistic, the next step is finding a t-critical value to help you decide whether or not to reject the null hypothesis. If the absolute t-statistic value is greater than the absolute t-critical value, we reject the null hypothesis. Otherwise, you fail to reject the null hypothesis. Now, you might be asking, “How do I find a t-critical value?” The good news is that you can find this value either using a t-distribution table, an online t-critical value calculator, or using Excel. In this guide, we’ll show you how to find the t-critical value for a left-sided test, right-sided test, and two-sided test, step-by-step.
Key Takeaways
To find the t-critical value in Excel, first identify your significance level (α), degrees of freedom (df), and the type of t-test.
- For a left-tailed test, use
=T.INV(α, df). - For a right-tailed test, use
=T.INV(1−α, df). - For a two-tailed test, use
=T.INV.2T(α, df).
Excel instantly returns the correct t-critical value once you enter the appropriate formula.
Finding T Critical Value using Excel: Step-by-Step
Before finding the t-critical value in Excel, you need two key inputs: the significance level (α) and the degrees of freedom (df). In addition, you must first identify the type of hypothesis test you are performing, since Excel uses different formulas for different test directions.
In this section, we walk you through exactly how to find the t-critical value in Excel for a left-tailed test, right-tailed test, and two-tailed test, using the appropriate Excel functions and clear examples.
1. Left-Tailed Test (<)
If you’re conducting a left-sided t-test (e.g., finding whether the mean score of students is less than a hypothesized value), then you need to find a left-sided t-critical value. You can easily find this value using the =T.INV(α, df) function in Excel. You only need to follow these 4 simple steps:
- Step 1: Identify your significance level (α).
- Step 2: Find your degrees of freedom (df) for your t-test.
- Step 3: Enter the formula
=T.INV(α, df)in a cell where you want the critical value to appear. - Step 4: Click the Enter button to find the left-tailed t-critical value.
Example 1: Suppose you are running a left-tailed test with α = 0.05 and df = 18. To find the left-sided t-critical value in Excel, enter the formula =T.INV(0.05, 18) and hit the Enter button. Excel will provide you with a left-tailed critical value of t as -1.73406 (See Figure 1).
2. Right-Tailed Test (>)
If you’re performing a right-sided t-test, you need to compare the t-statistic value with a right-sided t-critical value. You can easily find this value in Excel using the =T.INV(1 − α, df) function. You only need to follow these simple steps:
- Step 1. Identify your significance level (α).
- Step 2. Find your degrees of freedom (df).
- Step 3. Enter the formula,
=T.INV(1 − α, df)in Excel. - Step 4. Click the Enter button to find the right-sided t-critical value.
Example 2: Suppose you’re performing a right-tailed t-test with α = 0.05 and 20 degrees of freedom (df = 20). To find the correct critical value in Excel, simply type the formula =T.INV(0.95, 20) in a cell where you want the value to appear and press the Enter key
Excel will return the right-tailed t critical value for your test as 1.7247 (See Figure 2).
3. Two-Tailed Test (≠)
If you’re conducting a hypothesis test for a two-sided t-test to determine whether the mean is significantly different, you need to find a two-sided t-critical value. To find this value in Excel, we use the T.INV.2T() function that automatically splits the significance level between the two tails. This means, you don’t have to divide the significance level (α) by 2 to find the two-tailed t-critical value using this function.
Therefore, to find the t critical value for a two-tailed test in Excel, follow these steps:
- Step 1. Identify your total significance level (α).
- Step 2. Find your degrees of freedom (df).
- Step 3. Enter the formula
=T.INV.2T(α, df)in a cell where you want the critical value to appear. - Step 4. Click Enter key to find the two-tailed t-critical value
Example: Suppose you are running a two-tailed test with α = 0.05 and df = 15. To find a two-sided t-critical value for the test using Excel, enter the formula =T.INV.2T(0.05, 15) in any cell and hit the Enter key.
Excel will return the two-tailed critical value for your test as 2.1315 (See Figure 3).
Want to learn how to find t-critical value manually? Check out our complete guide on finding the t-critical values from the t-distribution table.
