NUMBAT OER - Open Educational Resources

First, use the Critical Significance Level (α) chosen in Step 2 and degrees of freedom (df) calculated in Step 3 (df = the total sample size minus two) to find the Critical Value of t (tcritical) using a Critical Value Table such as the one below (e.g. if α = 0.05 and df = 5, then Χ2critical = 2.571).

Second, compare tcritical with the value for the t statistic calculated in Step 3.

Reject your Null Hypothesis if your calculated value is greater than or equal to the Critical value; t ≥ tcritical (significant result).

Accept your Null Hypothesis if your calculated value is less than the Critical value; t < tcritical (non-significant result).

For example, if t = 2.981 and tcritical = 2.571 then reject the Null Hypothesis.

Table of Critical Values for Critical Significance Levels (α) of 0.1, 0.05 and 0.01 for the t statistic where degrees of freedom (df) is the total sample size minus two for the independent t-test.

df α = 0.10 α = 0.05 α = 0.01
1 6.314 12.706 63.656
2 2.920 4.303 9.925
3 2.353 3.182 5.841
4 2.132 2.776 4.604
5 2.015 2.571 4.032
6 1.943 2.447 3.707
7 1.895 2.365 3.499
8 1.860 2.306 3.355
9 1.833 2.262 3.250
10 1.812 2.228 3.169
11 1.796 2.201 3.106
12 1.782 2.179 3.055
13 1.771 2.160 3.012
14 1.761 2.145 2.977
15 1.753 2.131 2.947
16 1.746 2.120 2.921
17 1.740 2.110 2.898
18 1.734 2.101 2.878
19 1.729 2.093 2.861
20 1.725 2.086 2.845
21 1.721 2.080 2.831
22 1.717 2.074 2.819
23 1.714 2.069 2.807
24 1.711 2.064 2.797
25 1.708 2.060 2.787
26 1.706 2.056 2.779
27 1.703 2.052 2.771
28 1.701 2.048 2.763
29 1.699 2.045 2.756
30 1.697 2.042 2.750
31 1.696 2.040 2.744
32 1.694 2.037 2.738
33 1.692 2.035 2.733
34 1.691 2.032 2.728
35 1.690 2.030 2.724
36 1.688 2.028 2.719
37 1.687 2.026 2.715
38 1.686 2.024 2.712
39 1.685 2.023 2.708
40 1.684 2.021 2.704

Critical values of the two-tailed t distribution generated using the TINV() function in Microsoft Excel, which returns the inverse of the Student's t-distribution. Table generated by Toby Carter.