# 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 te. 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, t0.5 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.

Two Tailed Student's t-Distribution Table
αdf 0.010.030.050.10.20.250.5
1  63.66   31.82   12.71   6.31   3.08   2.41   1.00
2  9.92   6.96   4.30   2.92   1.89   1.60   0.82
3  5.84   4.54   3.18   2.35   1.64   1.42   0.76
4  4.60   3.75   2.78   2.13   1.53   1.34   0.74
5  4.03   3.36   2.57   2.02   1.48   1.30   0.73

6  3.71   3.14   2.45   1.94   1.44   1.27   0.72
7  3.50   3.00   2.36   1.89   1.41   1.25   0.71
8  3.36   2.90   2.31   1.86   1.40   1.24   0.71
9  3.25   2.82   2.26   1.83   1.38   1.23   0.70
10  3.17   2.76   2.23   1.81   1.37   1.22   0.70

11  3.11   2.72   2.20   1.80   1.36   1.21   0.70
12  3.05   2.68   2.18   1.78   1.36   1.21   0.70
13  3.01   2.65   2.16   1.77   1.35   1.20   0.69
14  2.98   2.62   2.14   1.76   1.35   1.20   0.69
15  2.95   2.60   2.13   1.75   1.34   1.20   0.69

16  2.92   2.58   2.12   1.75   1.34   1.19   0.69
17  2.90   2.57   2.11   1.74   1.33   1.19   0.69
18  2.88   2.55   2.10   1.73   1.33   1.19   0.69
19  2.86   2.54   2.09   1.73   1.33   1.19   0.69
20  2.85   2.53   2.09   1.72   1.33   1.18   0.69

21  2.83   2.52   2.08   1.72   1.32   1.18   0.69
22  2.82   2.51   2.07   1.72   1.32   1.18   0.69
23  2.81   2.50   2.07   1.71   1.32   1.18   0.69
24  2.80   2.49   2.06   1.71   1.32   1.18   0.68
25  2.79   2.49   2.06   1.71   1.32   1.18   0.68

26  2.78   2.48   2.06   1.71   1.31   1.18   0.68
27  2.77   2.47   2.05   1.70   1.31   1.18   0.68
28  2.76   2.47   2.05   1.70   1.31   1.17   0.68
29  2.76   2.46   2.05   1.70   1.31   1.17   0.68
30  2.75   2.46   2.04   1.70   1.31   1.17   0.68

31  2.74   2.45   2.04   1.70   1.31   1.17   0.68
32  2.74   2.45   2.04   1.69   1.31   1.17   0.68
33  2.73   2.44   2.03   1.69   1.31   1.17   0.68
34  2.73   2.44   2.03   1.69   1.31   1.17   0.68
35  2.72   2.44   2.03   1.69   1.31   1.17   0.68

36  2.72   2.43   2.03   1.69   1.31   1.17   0.68
37  2.72   2.43   2.03   1.69   1.30   1.17   0.68
38  2.71   2.43   2.02   1.69   1.30   1.17   0.68
39  2.71   2.43   2.02   1.68   1.30   1.17   0.68
40  2.70   2.42   2.02   1.68   1.30   1.17   0.68

41  2.70   2.42   2.02   1.68   1.30   1.17   0.68
42  2.70   2.42   2.02   1.68   1.30   1.17   0.68
43  2.70   2.42   2.02   1.68   1.30   1.17   0.68
44  2.69   2.41   2.02   1.68   1.30   1.17   0.68
45  2.69   2.41   2.01   1.68   1.30   1.17   0.68

46  2.69   2.41   2.01   1.68   1.30   1.17   0.68
47  2.68   2.41   2.01   1.68   1.30   1.16   0.68
48  2.68   2.41   2.01   1.68   1.30   1.16   0.68
49  2.68   2.40   2.01   1.68   1.30   1.16   0.68
50  2.68   2.40   2.01   1.68   1.30   1.16   0.68

51  2.68   2.40   2.01   1.68   1.30   1.16   0.68
52  2.67   2.40   2.01   1.67   1.30   1.16   0.68
53  2.67   2.40   2.01   1.67   1.30   1.16   0.68
54  2.67   2.40   2.00   1.67   1.30   1.16   0.68
55  2.67   2.40   2.00   1.67   1.30   1.16   0.68

56  2.67   2.39   2.00   1.67   1.30   1.16   0.68
57  2.66   2.39   2.00   1.67   1.30   1.16   0.68
58  2.66   2.39   2.00   1.67   1.30   1.16   0.68
59  2.66   2.39   2.00   1.67   1.30   1.16   0.68
60  2.66   2.39   2.00   1.67   1.30   1.16   0.68

61  2.66   2.39   2.00   1.67   1.30   1.16   0.68
62  2.66   2.39   2.00   1.67   1.30   1.16   0.68
63  2.66   2.39   2.00   1.67   1.30   1.16   0.68
64  2.65   2.39   2.00   1.67   1.29   1.16   0.68
65  2.65   2.39   2.00   1.67   1.29   1.16   0.68

66  2.65   2.38   2.00   1.67   1.29   1.16   0.68
67  2.65   2.38   2.00   1.67   1.29   1.16   0.68
68  2.65   2.38   2.00   1.67   1.29   1.16   0.68
69  2.65   2.38   1.99   1.67   1.29   1.16   0.68
70  2.65   2.38   1.99   1.67   1.29   1.16   0.68

71  2.65   2.38   1.99   1.67   1.29   1.16   0.68
72  2.65   2.38   1.99   1.67   1.29   1.16   0.68
73  2.64   2.38   1.99   1.67   1.29   1.16   0.68
74  2.64   2.38   1.99   1.67   1.29   1.16   0.68
75  2.64   2.38   1.99   1.67   1.29   1.16   0.68

76  2.64   2.38   1.99   1.67   1.29   1.16   0.68
77  2.64   2.38   1.99   1.66   1.29   1.16   0.68
78  2.64   2.38   1.99   1.66   1.29   1.16   0.68
79  2.64   2.37   1.99   1.66   1.29   1.16   0.68
80  2.64   2.37   1.99   1.66   1.29   1.16   0.68

81  2.64   2.37   1.99   1.66   1.29   1.16   0.68
82  2.64   2.37   1.99   1.66   1.29   1.16   0.68
83  2.64   2.37   1.99   1.66   1.29   1.16   0.68
84  2.64   2.37   1.99   1.66   1.29   1.16   0.68
85  2.63   2.37   1.99   1.66   1.29   1.16   0.68

86  2.63   2.37   1.99   1.66   1.29   1.16   0.68
87  2.63   2.37   1.99   1.66   1.29   1.16   0.68
88  2.63   2.37   1.99   1.66   1.29   1.16   0.68
89  2.63   2.37   1.99   1.66   1.29   1.16   0.68
90  2.63   2.37   1.99   1.66   1.29   1.16   0.68

91  2.63   2.37   1.99   1.66   1.29   1.16   0.68
92  2.63   2.37   1.99   1.66   1.29   1.16   0.68
93  2.63   2.37   1.99   1.66   1.29   1.16   0.68
94  2.63   2.37   1.99   1.66   1.29   1.16   0.68
95  2.63   2.37   1.99   1.66   1.29   1.16   0.68

96  2.63   2.37   1.98   1.66   1.29   1.16   0.68
97  2.63   2.37   1.98   1.66   1.29   1.16   0.68
98  2.63   2.37   1.98   1.66   1.29   1.16   0.68
99  2.63   2.36   1.98   1.66   1.29   1.16   0.68
100  2.63   2.36   1.98   1.66   1.29   1.16   0.68

## 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 < te then the null hypothesis H0 is accepted.
It states that there is no significance difference between t-statistic & expected value of t.

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