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Appendix 04: Critical Values for t-Test

Last updated

Nov 3, 2020
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- Appendix 03: Single-Sided Normal Distribution
- Appendix 05: Critical Values for the F-Test

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Assuming you have calculated t_exp, 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 t_exp>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 t_exp=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%
Degrees of Freedom	…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.

Contributors and Attributions

David Harvey (DePauw University)

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Contributors and Attributions

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