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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…

    …a confidence interval of:

    90%

    95%

    98%

    99%

    …an α value of:

    0.10

    0.05

    0.02

    0.01

    Degrees of Freedom

    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.