Critical Values of the t Distribution The probability density function of the t-distribution The t-distribution is a symmetric distribution and its shape depends on the degrees of freedom (df). The t-distribution has thicker tails than the normal distribution but, as the df increases, the t-distribution approximates the normal distribution. The area under the pdf to the right of t is equal to /2. d.f.   = .10   = .05 1 6.314 12.706 2 2.920 4.303 3 2.353 3.182 4 2.132 2.776 5 2.015 2.571 6 1.943 2.447 7 1.895 2.365 8 1.860 2.306 9 1.833 2.262 10 1.812 2.228 11 1.796 2.201 12 1.782 2.179 13 1.771 2.160 14 1.761 2.145 15 1.753 2.131 16 1.746 2.120 17 1.740 2.110 18 1.734 2.101 19 1.729 2.093 20 1.725 2.086 21 1.721 2.080 22 1.717 2.074 23 1.714 2.069 24 1.711 2.064 25 1.708 2.060 26 1.706 2.056 27 1.703 2.052 28 1.701 2.048 29 1.699 2.045 30 1.697 2.042 35 1.690 2.030 40 1.684 2.021 45 1.680 2.014 50 1.676 2.009 60 1.671 2.000 70 1.667 1.994 80 1.664 1.990 90 1.662 1.987 100 1.660 1.984 120 1.658 1.980 1.645 1.960 Note: When the df exceeds 30 critical values are not tabulated for every case. For degrees of freedom that are not tabulated, the SHAZAM CONFID command rounds up. For example, with 31 degrees of freedom the critical value for 35 df is used. Some releases of SHAZAM use critical values that are less accurate for df > 30. [SHAZAM Guide home]