Find Critical Value of t for Two Tailed t-Test

Student's t-distribution table & how to use instructions to quickly find the table or critical (rejection region) value of t at a stated level of significance (α) to check if the test of hypothesis (H₀) for two tailed t-test is accepted or rejected in statistics & probability experiments to analyze the small samples. The degrees of freedom is used to refer the t-table values at a specified level of significance such as 1%, 2%, 3%, 4%, 5%, 10%, 25%, 50% etc. It's generally represented by t_e. In two tailed Student's t-test, the calculated value of t or t-statistic (t₀) is compared with the table or critical value of t from table for the test of significance. This students's t-table for two tailed t-test is also available in pdf format too, users may download this table in pdf format to refer it later offline.

In two tailed t-tests, the critical value of t from t-distribution table represents the rejection area of distribution in both left & right side of the mean. The critical value of t at a specified level of significance (α) is calculated for both left & right side of the mean of t-distribution but the α value is divided by 2 and corresponding critical value of t is derived from the t-distribution table for both halves. For example, t_0.5 of single tailed test equals to t_(0.25) of two tailed test. In other words, a single tailed t-test at 10% significance level have the rejection area either in left or right side of the mean, while for two tailed t-test at 10% significance level have 5% rejection area on the left side & remaining 5% rejection area on the right side of the mean.

How to Find Critical Region in Student's t-Test

Users may use this below two tailed t-table calculator or refer the rows & columns value of t-distribution table to find the critical region of t-distribution.
by Using Calculator
Supply or select the values of type of t-test (two tailed) such as degrees of freedom (df) and significance level (α) directly to the two tailed t-table calculator and hit on "LOCATE" to address the corresponding critical value of t.

by Using t-Distribution Table
Refer the significance level α value in the row & degrees of freedom df in the column. The point where the row & column meets for the corresponding value is the critical value of t or the rejection area of two tailed t-distribution.

Inference

The below statements show when to accept or reject null hypothesis H₀ in two tailed t-test

For null hypothesis H₀ :
If t₀ < t_e then the null hypothesis H₀ is accepted.
It states that there is no significance difference between t-statistic & expected value of t.

If t₀ > t_e then the null hypothesis H₀ is rejected.
It states that there is significance difference between t-statistic & expected value of t.