Skip to main content
Chemistry LibreTexts

Appendix 04: Critical Values for t-Test

  • Page ID
    6640
  • Assuming you have calculated texp, there are two approaches to interpreting a t-test. In the first approach you choose a value of α for rejecting the null hypothesis and read the value of t(α,ν) from the table shown below. If texp>t(α,ν), you reject the null hypothesis and accept the alternative hypothesis. In the second approach, you find the row in the table below corresponding to your degrees of freedom and move across the row to find (or estimate) the α corresponding to texp=t(α,ν); this establishes largest value of α for which you can retain the null hypothesis. Finding, for example, that α is 0.10 means that you would retain the null hypothesis at the 90% confidence level, but reject it at the 89% confidence level. The examples in this textbook use the first approach.

    Values of t for…
    Degrees of Freedom …a confidence interval of: 90% 95% 98% 99%
    …an α value of: 0.10 0.05 0.02 0.01
    1 6.314 12.706 31.821 63.657
    2 2.920 4.303 6.965 9.925
    3 2.353 3.182 4.541 5.841
    4 2.132 2.776 3.747 4.604
    5 2.015 2.571 3.365 4.032
    6 1.943 2.447 3.143 3.707
    7 1.895 2.365 2.998 3.499
    8 1.860 2.306 2.896 3.255
    9 1.833 2.262 2.821 3.250
    10 1.812 2.228 2.764 3.169
    12 1.782 2.179 2.681 3.055
    14 1.761 2.145 2.624 2.977
    16 1.746 2.120 2.583 2.921
    18 1.734 2.101 2.552 2.878
    20 1.725 2.086 2.528 2.845
    30 1.697 2.042 2.457 2.750
    50 1.676 2.009 2.311 2.678
    1.645 1.960 2.326 2.576

    The values in this table are for a two-tailed t-test. For a one-tail t-test, divide the α values by 2. For example, the last column has an α value of 0.005 and a confidence interval of 99.5% when conducting a one-tailed t-test.