Calculators & Converters

    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.

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