Student t Distribution Table

This table below is a compilation of data from the Student t distribution. Anytime that a t-distribution is being used, a table such as this one can be consulted to perform calculations. This distribution is similar to the standard normal distribution, or bell curve, however the table is arranged differently than the table for the bell curve. The table below provides critical t-values for a particular area of one tail (listed along the top of the table) and degrees of freedom (listed along the side of the table).

Degrees of freedom range from 1 to 30, with the bottom row of "Large" referring to several thousand degrees of freedom.

Example of Using the Table

A brief example will illustrate the use of the table below.  Suppose that we have a simple random sample of size 11.  This means that we will consult the row with 11 - 1 = 10 degrees of freedom.  Along the top of the table we have various levels of significance.  Suppose that we have a level of significance of 1%.  This corresponds to 0.01.  This column in the row with 10 degrees of freedom gives us a critical value of 2.76377.

This means that in order to reject the null hypothesis, we need a t-statistic that exceeds this value of 2.76377.  Otherwise we will fail to reject the null hypothesis.

Table of Critical Values for t Distribution

 t 0.4 0.25 0.1 0.05 0.025 0.01 0.005 0.0005 1 0.32492 1 3.07768 6.31375 12.7062 31.8205 63.6567 636.619 2 0.288675 0.816497 1.88562 2.91999 4.30265 6.96456 9.92484 31.5991 3 0.276671 0.764892 1.63774 2.35336 3.18245 4.5407 5.84091 12.924 4 0.270722 0.740697 1.53321 2.13185 2.77645 3.74695 4.60409 8.6103 5 0.267181 0.726687 1.47588 2.01505 2.57058 3.36493 4.03214 6.8688 6 0.264835 0.717558 1.43976 1.94318 2.44691 3.14267 3.70743 5.9588 7 0.263167 0.711142 1.41492 1.89458 2.36462 2.99795 3.49948 5.4079 8 0.261921 0.706387 1.39681 1.85955 2.306 2.89646 3.35539 5.0413 9 0.260955 0.702722 1.38303 1.83311 2.26216 2.82144 3.24984 4.7809 10 0.260185 0.699812 1.37218 1.81246 2.22814 2.76377 3.16927 4.5869 11 0.259556 0.697445 1.36343 1.79588 2.20099 2.71808 3.10581 4.437 12 0.259033 0.695483 1.35622 1.78229 2.17881 2.681 3.05454 4.3178 13 0.258591 0.693829 1.35017 1.77093 2.16037 2.65031 3.01228 4.2208 14 0.258213 0.692417 1.34503 1.76131 2.14479 2.62449 2.97684 4.1405 15 0.257885 0.691197 1.34061 1.75305 2.13145 2.60248 2.94671 4.0728 16 0.257599 0.690132 1.33676 1.74588 2.11991 2.58349 2.92078 4.015 17 0.257347 0.689195 1.33338 1.73961 2.10982 2.56693 2.89823 3.9651 18 0.257123 0.688364 1.33039 1.73406 2.10092 2.55238 2.87844 3.9216 19 0.256923 0.687621 1.32773 1.72913 2.09302 2.53948 2.86093 3.8834 20 0.256743 0.686954 1.32534 1.72472 2.08596 2.52798 2.84534 3.8495 21 0.25658 0.686352 1.32319 1.72074 2.07961 2.51765 2.83136 3.8193 22 0.256432 0.685805 1.32124 1.71714 2.07387 2.50832 2.81876 3.7921 23 0.256297 0.685306 1.31946 1.71387 2.06866 2.49987 2.80734 3.7676 24 0.256173 0.68485 1.31784 1.71088 2.0639 2.49216 2.79694 3.7454 25 0.25606 0.68443 1.31635 1.70814 2.05954 2.48511 2.78744 3.7251 26 0.255955 0.684043 1.31497 1.70562 2.05553 2.47863 2.77871 3.7066 27 0.255858 0.683685 1.3137 1.70329 2.05183 2.47266 2.77068 3.6896 28 0.255768 0.683353 1.31253 1.70113 2.04841 2.46714 2.76326 3.6739 29 0.255684 0.683044 1.31143 1.69913 2.04523 2.46202 2.75639 3.6594 30 0.255605 0.682756 1.31042 1.69726 2.04227 2.45726 2.75 3.646 Large 0.253347 0.67449 1.28155 1.64485 1.95996 2.32635 2.57583 3.2905