How to Read a T Table Statistics

This t-distribution table provides the critical t-values for both ane-tailed and ii-tailed t-tests, and confidence intervals. Larn how to use this t-table with the data, examples, and illustrations below the table.

one-tailed α	0.10	0.05	0.025	0.01	0.005	0.0005
ii-tailed α	0.20	0.x	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	iv.303	6.965	9.925	31.599
3	1.638	2.353	iii.182	4.541	5.841	12.924
four	ane.533	two.132	2.776	3.747	4.604	8.610
5	1.476	2.015	2.571	3.365	4.032	6.869
six	1.440	1.943	2.447	three.143	3.707	5.959
7	1.415	i.895	two.365	two.998	3.499	5.408
8	1.397	1.860	2.306	two.896	3.355	five.041
9	1.383	1.833	2.262	2.821	three.250	4.781
10	1.372	i.812	2.228	2.764	iii.169	4.587
eleven	i.363	1.796	ii.201	2.718	3.106	4.437
12	one.356	1.782	2.179	ii.681	3.055	4.318
xiii	one.350	one.771	2.160	2.650	three.012	4.221
fourteen	1.345	i.761	2.145	2.624	2.977	4.140
xv	1.341	1.753	2.131	2.602	two.947	iv.073
16	1.337	1.746	ii.120	two.583	ii.921	iv.015
17	ane.333	i.740	2.110	2.567	2.898	3.965
18	i.330	ane.734	2.101	2.552	2.878	iii.922
19	1.328	1.729	2.093	ii.539	ii.861	iii.883
20	ane.325	1.725	2.086	ii.528	2.845	iii.850
21	1.323	1.721	2.080	2.518	2.831	3.819
22	one.321	one.717	2.074	two.508	2.819	3.792
23	i.319	ane.714	ii.069	two.500	2.807	3.768
24	1.318	1.711	2.064	2.492	2.797	three.745
25	1.316	i.708	2.060	2.485	2.787	3.725
26	1.315	1.706	2.056	2.479	2.779	3.707
27	ane.314	1.703	ii.052	2.473	two.771	3.690
28	one.313	1.701	2.048	two.467	2.763	iii.674
29	1.311	1.699	2.045	2.462	ii.756	3.659
30	1.310	1.697	2.042	ii.457	2.750	3.646
40	1.303	i.684	2.021	2.423	2.704	3.551
60	1.296	1.671	2.000	ii.390	2.660	3.460
80	1.292	1.664	1.990	2.374	ii.639	3.416
100	one.290	ane.660	1.984	2.364	ii.626	iii.390
1000	1.282	ane.646	one.962	2.330	2.581	3.300
z	1.282	1.645	i.960	2.326	2.576	3.291

How to Use the T-Distribution Table

Utilise the t-distribution tabular array past 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.

Significance Level (Alpha α): Cull the column in the t-distribution table that contains the significance level for your test. Be sure to choose the blastoff for a 1- or two-tailed t-test based on your t-examination's methodology. Larn more almost 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 tabular array lists the z-distribution'due south disquisitional values for comparison. Learn more than nigh Degrees of Freedom.

Disquisitional Values: In the t-distribution tabular array, observe the cell at the column and row intersection. When you are performing a:

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

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

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

Examples of Using the T-Distribution Table of Critical Values

Two-sided t-exam

Suppose you perform a ii-tailed t-test with a significance level of 0.05 and 20 degrees of freedom, and you need to notice the disquisitional values.

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

The t-tabular array indicates that the critical values for our test are -2.086 and +2.086. Apply 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 beneath illustrates these results.

One-sided t-examination

Now, suppose you perform a 1-sided t-exam with a significance level of 0.05 and 20 df.

In the t-distribution table, detect 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.

The row and column intersection in the t-distribution table indicates that the critical t-value is ane.725. Apply either the positive or negative critical value depending on the direction of your t-test. The graphs below illustrate both i-sided tests. Your results are statistically significant if your t-value falls in the scarlet critical region.

Using Disquisitional T-values to Calculate Confidence Intervals

To summate a two-sided conviction interval for a t-test, take the positive critical value from the t-distribution tabular array and multiply it past your sample'southward standard error of the mean. So 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 conviction level is one – α.

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Source: https://statisticsbyjim.com/hypothesis-testing/t-distribution-table/

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