T-Distribution Table Of Critical Values - Statistics By Jim

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This t-distribution table provides the critical t-values for both one-tailed and two-tailed t-tests, and confidence intervals. Learn how to use this t-table with the information, examples, and illustrations below the table.

one-tailed α 0.10 0.05 0.025 0.01 0.005 0.0005
two-tailed α 0.20 0.10 0.05 0.02 0.01 0.001
df
1 3.078 6.314 12.71 31.82 63.66 636.62
2 1.886 2.920 4.303 6.965 9.925 31.599
3 1.638 2.353 3.182 4.541 5.841 12.924
4 1.533 2.132 2.776 3.747 4.604 8.610
5 1.476 2.015 2.571 3.365 4.032 6.869
6 1.440 1.943 2.447 3.143 3.707 5.959
7 1.415 1.895 2.365 2.998 3.499 5.408
8 1.397 1.860 2.306 2.896 3.355 5.041
9 1.383 1.833 2.262 2.821 3.250 4.781
10 1.372 1.812 2.228 2.764 3.169 4.587
11 1.363 1.796 2.201 2.718 3.106 4.437
12 1.356 1.782 2.179 2.681 3.055 4.318
13 1.350 1.771 2.160 2.650 3.012 4.221
14 1.345 1.761 2.145 2.624 2.977 4.140
15 1.341 1.753 2.131 2.602 2.947 4.073
16 1.337 1.746 2.120 2.583 2.921 4.015
17 1.333 1.740 2.110 2.567 2.898 3.965
18 1.330 1.734 2.101 2.552 2.878 3.922
19 1.328 1.729 2.093 2.539 2.861 3.883
20 1.325 1.725 2.086 2.528 2.845 3.850
21 1.323 1.721 2.080 2.518 2.831 3.819
22 1.321 1.717 2.074 2.508 2.819 3.792
23 1.319 1.714 2.069 2.500 2.807 3.768
24 1.318 1.711 2.064 2.492 2.797 3.745
25 1.316 1.708 2.060 2.485 2.787 3.725
26 1.315 1.706 2.056 2.479 2.779 3.707
27 1.314 1.703 2.052 2.473 2.771 3.690
28 1.313 1.701 2.048 2.467 2.763 3.674
29 1.311 1.699 2.045 2.462 2.756 3.659
30 1.310 1.697 2.042 2.457 2.750 3.646
40 1.303 1.684 2.021 2.423 2.704 3.551
60 1.296 1.671 2.000 2.390 2.660 3.460
80 1.292 1.664 1.990 2.374 2.639 3.416
100 1.290 1.660 1.984 2.364 2.626 3.390
1000 1.282 1.646 1.962 2.330 2.581 3.300
z 1.282 1.645 1.960 2.326 2.576 3.291

How to Use the T-Distribution Table

Use the t-distribution table by finding the intersection of your significance level and degrees of freedom. The t-distribution is the sampling distribution of t-values when the null hypothesis is true. Learn more about the T Distribution: Definition and Uses.

Significance Level (Alpha α): Choose the column in the t-distribution table that contains the significance level for your test. Be sure to choose the alpha for a one- or two-tailed t-test based on your t-test’s methodology. Learn more about the Significance Level and One- and Two-Tailed Tests.

Degrees of freedom (df): Choose the row of the t-table that corresponds to the degrees of freedom in your t-test. The final row in the table lists the z-distribution’s critical values for comparison. Learn more about Degrees of Freedom.

Critical Values: In the t-distribution table, find the cell at the column and row intersection. When you are performing a:

  • Two-tailed t-test: Use the positive critical value AND the negative form to cover both tails of the distribution.
  • One-tailed t-test: Use the positive critical value OR the negative value depending on whether you’re using an upper (+) or lower (-) sided test.

Learn more about: How T-tests Work, test statistics, critical values, and How to do T-Tests in Excel

Tables for other statistics include the z-table, chi-square table, and F-table.

Examples of Using the T-Distribution Table of Critical Values

Two-sided t-test

Suppose you perform a two-tailed t-test with a significance level of 0.05 and 20 degrees of freedom, and you need to find the critical values.

In the t-distribution table, find the column which contains alpha = 0.05 for the two-tailed test. Then, find the row corresponding to 20 degrees of freedom. The truncated t-table below shows the critical t-value.

T-distribution table showing the critical t-value for a two-sided t-test.

The t-table indicates that the critical values for our test are -2.086 and +2.086. Use both the positive and negative values for a two-sided test. Your results are statistically significant if your t-value is less than the negative value or greater than the positive value. The graph below illustrates these results.

Plot that displays the critical regions in the two tails of the distribution for our t-table results.

One-sided t-test

Now, suppose you perform a one-sided t-test with a significance level of 0.05 and 20 df.

In the t-distribution table, find the column which contains alpha = 0.05 for the one-tailed test. Then, find the row corresponding to 20 degrees of freedom. The truncated t-table below shows the critical t-value.

T-distribution table that show the critical t-value for a one-sided t-test.

The row and column intersection in the t-distribution table indicates that the critical t-value is 1.725. Use either the positive or negative critical value depending on the direction of your t-test. The graphs below illustrate both one-sided tests. Your results are statistically significant if your t-value falls in the red critical region.

Plot that displays a single critical region for a one-tailed test for our t-table results.

Plot that displays a single critical region in the left tail for a one-tailed test.

Using Critical T-values to Calculate Confidence Intervals

To calculate a two-sided confidence interval for a t-test, take the positive critical value from the t-distribution table and multiply it by your sample’s standard error of the mean. Then take the sample mean and add and subtract the product from it to calculate the upper and lower interval limits, respectively.

For a one-sided confidence interval, either add or subtract the product from the mean to calculate the upper or lower bound, respectively.

The confidence level is 1 – α.

I have several related online statistical calculators you use for free:

  • Critical Value Calculator: Find the exact critical values for your test.
  • Confidence Interval Calculator: Construct CIs using your critical Z and t-values.

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