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, we fail to reject the null hypothesis. Now, you might be asking, “How do I find a t-critical value?” There are various methods you can use to find the t-critical value, which include using a t-distribution table, an online t-critical value calculator, or using technology such as 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 using Excel formulas. The article also provides clear examples to help you grasp the concept.
1. T Critical Value for 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. To find the t-critical value for a left-sided test using Excel, follow these 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 get 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. T Critical Value for the 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 the t-critical value for a right-sided test using Excel by following these 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. T Critical Value for the 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 the t critical value for a two-sided 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 3: 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).
Key Takeaways
- A t-critical value is a cutoff point used to determine whether or not to reject the null hypothesis for t-tests.
- Excel provides a quick way to calculate t-critical values for the left-sided, right-sided, and two-tailed tests, without manual lookup from tables.
- To find the t-critical value for a left-tailed test, we use the
=T.INV(α, df)formula - To find the t-critical value for a right-tailed test, we use the
=T.INV(1-α, df)formula - To find the t-critical value for a two-tailed test, we use the
=T.INV.2T(α, df)formula
