Calculators & Converters

    Find Critical Value of t for One 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 one (right or left) 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 one (right or left) tailed Student's t-test, the calculated value of t or t-statistic (t0) is compared with the table or critical value of t to check if the null hypothesis is accepted or rejected in the statistical experiments include small sample size. This students's t-table for one tailed t-test is also available in pdf format too, users may download this table in pdf format to refer it later offline.

    In one tailed t-tests, the critical value of t from t-distribution table represents the rejection area of distribution either left or right of the mean. In single tailed t-test, the critical value of t at a specified level of significance (α) is calculated either left side or right side of the mean of t-distribution. Whereas, in two tailed t-test, 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.
     



    One Tailed Student's t-Distribution Table
    αdf 0.010.030.050.10.20.250.5
     1  127.32   63.66   21.20   12.71   6.31   5.03   2.41  
     2  14.09   9.92   5.64   4.30   2.92   2.56   1.60  
     3  7.45   5.84   3.90   3.18   2.35   2.11   1.42  
     4  5.60   4.60   3.30   2.78   2.13   1.94   1.34  
     5  4.77   4.03   3.00   2.57   2.02   1.84   1.30  
     
     6  4.32   3.71   2.83   2.45   1.94   1.78   1.27  
     7  4.03   3.50   2.71   2.36   1.89   1.74   1.25  
     8  3.83   3.36   2.63   2.31   1.86   1.71   1.24  
     9  3.69   3.25   2.57   2.26   1.83   1.69   1.23  
     10  3.58   3.17   2.53   2.23   1.81   1.67   1.22  
     
     11  3.50   3.11   2.49   2.20   1.80   1.66   1.21  
     12  3.43   3.05   2.46   2.18   1.78   1.65   1.21  
     13  3.37   3.01   2.44   2.16   1.77   1.64   1.20  
     14  3.33   2.98   2.41   2.14   1.76   1.63   1.20  
     15  3.29   2.95   2.40   2.13   1.75   1.62   1.20  
     
     16  3.25   2.92   2.38   2.12   1.75   1.62   1.19  
     17  3.22   2.90   2.37   2.11   1.74   1.61   1.19  
     18  3.20   2.88   2.36   2.10   1.73   1.61   1.19  
     19  3.17   2.86   2.35   2.09   1.73   1.60   1.19  
     20  3.15   2.85   2.34   2.09   1.72   1.60   1.18  
     
     21  3.14   2.83   2.33   2.08   1.72   1.60   1.18  
     22  3.12   2.82   2.32   2.07   1.72   1.59   1.18  
     23  3.10   2.81   2.31   2.07   1.71   1.59   1.18  
     24  3.09   2.80   2.31   2.06   1.71   1.59   1.18  
     25  3.08   2.79   2.30   2.06   1.71   1.59   1.18  
     
     26  3.07   2.78   2.30   2.06   1.71   1.59   1.18  
     27  3.06   2.77   2.29   2.05   1.70   1.58   1.18  
     28  3.05   2.76   2.29   2.05   1.70   1.58   1.17  
     29  3.04   2.76   2.28   2.05   1.70   1.58   1.17  
     30  3.03   2.75   2.28   2.04   1.70   1.58   1.17  
     
     31  3.02   2.74   2.27   2.04   1.70   1.58   1.17  
     32  3.01   2.74   2.27   2.04   1.69   1.58   1.17  
     33  3.01   2.73   2.27   2.03   1.69   1.57   1.17  
     34  3.00   2.73   2.27   2.03   1.69   1.57   1.17  
     35  3.00   2.72   2.26   2.03   1.69   1.57   1.17  
     
     36  2.99   2.72   2.26   2.03   1.69   1.57   1.17  
     37  2.99   2.72   2.26   2.03   1.69   1.57   1.17  
     38  2.98   2.71   2.25   2.02   1.69   1.57   1.17  
     39  2.98   2.71   2.25   2.02   1.68   1.57   1.17  
     40  2.97   2.70   2.25   2.02   1.68   1.57   1.17  
     
     41  2.97   2.70   2.25   2.02   1.68   1.57   1.17  
     42  2.96   2.70   2.25   2.02   1.68   1.57   1.17  
     43  2.96   2.70   2.24   2.02   1.68   1.56   1.17  
     44  2.96   2.69   2.24   2.02   1.68   1.56   1.17  
     45  2.95   2.69   2.24   2.01   1.68   1.56   1.17  
     
     46  2.95   2.69   2.24   2.01   1.68   1.56   1.17  
     47  2.95   2.68   2.24   2.01   1.68   1.56   1.16  
     48  2.94   2.68   2.24   2.01   1.68   1.56   1.16  
     49  2.94   2.68   2.24   2.01   1.68   1.56   1.16  
     50  2.94   2.68   2.23   2.01   1.68   1.56   1.16  
     
     51  2.93   2.68   2.23   2.01   1.68   1.56   1.16  
     52  2.93   2.67   2.23   2.01   1.67   1.56   1.16  
     53  2.93   2.67   2.23   2.01   1.67   1.56   1.16  
     54  2.93   2.67   2.23   2.00   1.67   1.56   1.16  
     55  2.92   2.67   2.23   2.00   1.67   1.56   1.16  
     
     56  2.92   2.67   2.23   2.00   1.67   1.56   1.16  
     57  2.92   2.66   2.23   2.00   1.67   1.56   1.16  
     58  2.92   2.66   2.22   2.00   1.67   1.56   1.16  
     59  2.92   2.66   2.22   2.00   1.67   1.56   1.16  
     60  2.91   2.66   2.22   2.00   1.67   1.56   1.16  
     
     61  2.91   2.66   2.22   2.00   1.67   1.56   1.16  
     62  2.91   2.66   2.22   2.00   1.67   1.56   1.16  
     63  2.91   2.66   2.22   2.00   1.67   1.55   1.16  
     64  2.91   2.65   2.22   2.00   1.67   1.55   1.16  
     65  2.91   2.65   2.22   2.00   1.67   1.55   1.16  
     
     66  2.90   2.65   2.22   2.00   1.67   1.55   1.16  
     67  2.90   2.65   2.22   2.00   1.67   1.55   1.16  
     68  2.90   2.65   2.22   2.00   1.67   1.55   1.16  
     69  2.90   2.65   2.22   1.99   1.67   1.55   1.16  
     70  2.90   2.65   2.22   1.99   1.67   1.55   1.16  
     
     71  2.90   2.65   2.21   1.99   1.67   1.55   1.16  
     72  2.90   2.65   2.21   1.99   1.67   1.55   1.16  
     73  2.89   2.64   2.21   1.99   1.67   1.55   1.16  
     74  2.89   2.64   2.21   1.99   1.67   1.55   1.16  
     75  2.89   2.64   2.21   1.99   1.67   1.55   1.16  
     
     76  2.89   2.64   2.21   1.99   1.67   1.55   1.16  
     77  2.89   2.64   2.21   1.99   1.66   1.55   1.16  
     78  2.89   2.64   2.21   1.99   1.66   1.55   1.16  
     79  2.89   2.64   2.21   1.99   1.66   1.55   1.16  
     80  2.89   2.64   2.21   1.99   1.66   1.55   1.16  
     
     81  2.89   2.64   2.21   1.99   1.66   1.55   1.16  
     82  2.88   2.64   2.21   1.99   1.66   1.55   1.16  
     83  2.88   2.64   2.21   1.99   1.66   1.55   1.16  
     84  2.88   2.64   2.21   1.99   1.66   1.55   1.16  
     85  2.88   2.63   2.21   1.99   1.66   1.55   1.16  
     
     86  2.88   2.63   2.21   1.99   1.66   1.55   1.16  
     87  2.88   2.63   2.21   1.99   1.66   1.55   1.16  
     88  2.88   2.63   2.21   1.99   1.66   1.55   1.16  
     89  2.88   2.63   2.21   1.99   1.66   1.55   1.16  
     90  2.88   2.63   2.21   1.99   1.66   1.55   1.16  
     
     91  2.88   2.63   2.20   1.99   1.66   1.55   1.16  
     92  2.88   2.63   2.20   1.99   1.66   1.55   1.16  
     93  2.88   2.63   2.20   1.99   1.66   1.55   1.16  
     94  2.87   2.63   2.20   1.99   1.66   1.55   1.16  
     95  2.87   2.63   2.20   1.99   1.66   1.55   1.16  
     
     96  2.87   2.63   2.20   1.98   1.66   1.55   1.16  
     97  2.87   2.63   2.20   1.98   1.66   1.55   1.16  
     98  2.87   2.63   2.20   1.98   1.66   1.55   1.16  
     99  2.87   2.63   2.20   1.98   1.66   1.55   1.16  
     100  2.87   2.63   2.20   1.98   1.66   1.55   1.16  


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

    Users may use this below single 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 (one tailed) such as degrees of freedom (df) and significance level (α) directly to the single tailed t-table calculator and hit on "LOCATE" to locate 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 one (left or right tailed) t-distribution.

    Inference

    The below statements show when to accept or reject null hypothesis H0 in one (right or left) 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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