Not sure what I mean by a “critical value”? You might want to read this article first: What is a Critical Value? Watch the video for an overview: Can’t see the video?
Click here. A T critical value is a “cut off point” on the t distribution. It’s almost identical to the Z critical value [which cuts off an area on the normal distribution]; The only real difference is
that the shape of the t distribution is a different shape than the normal distribution, which results in slightly different values for cut off points.What is a T Critical Value?
How to Find a T Critical Value
You’ve got several options for finding a T value with technology, including:
- TI 83: See: How to Find t Critical Value on the TI 83.
- Excel: See Excel T Test; Excel will calculate the T critical value as part of the process.
Need help with a homework question? Check out our tutoring page!
By hand
Step 1: Subtract one from your sample size. This is your df, or degrees of freedom. For example, if the sample size is 8, then your df is 8 – 1 = 7.
Step 2: Choose an alpha level. The alpha level is usually given to you in the question — the most common one is 5% [0.05].
Step 3: Choose either the one tailed T Distribution table or two tailed T Distribution table]. This depends on if you’re running a one tailed test or two.
Step 4: Look up the df in the left hand side of the t-distribution table and the alpha level along the top row. Find the
intersection of the row and column. For this example [7 df, α = .05,] the t crit value is 1.895.
References
Dodge, Y. [2008]. The Concise Encyclopedia of Statistics. Springer.
Gonick, L. [1993]. The Cartoon Guide to Statistics. HarperPerennial.
Kotz, S.; et al., eds. [2006],
Encyclopedia of Statistical Sciences, Wiley.
Lindstrom, D. [2010]. Schaum’s Easy Outline of Statistics, Second Edition [Schaum’s Easy Outlines] 2nd Edition. McGraw-Hill Education
Vogt, W.P. [2005]. Dictionary of Statistics & Methodology: A Nontechnical
Guide for the Social Sciences. SAGE.
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Table 1: Critical values [percentiles] for the
The table entries are the critical values [percentiles] for the |
Percent | ||||||||||||
75 | 90 | 95 | 97.5 | 99 | 99.5 | 99.75 | 99.9 | 99.95 | 99.975 | 99.99 | 99.995 | |
One-sided | ||||||||||||
.25 | .10 | .05 | .025 | .01 | .005 | .0025 | .001 | .0005 | .00025 | .0001 | .00005 | |
Two-sided | ||||||||||||
.50 | .20 | .10 | .05 | .02 | .01 | .005 | .002 | .001 | .0005 | .0002 | .0001 | |
1 | 1.00 | 3.08 | 6.31 | 12.71 | 31.82 | 63.66 | 127.32 | 318.31 | 636.62 | 1273.24 | 3183.10 | 6366.20 |
2 | .82 | 1.89 | 2.92 | 4.30 | 6.96 | 9.22 | 14.09 | 22.33 | 31.60 | 44.70 | 70.70 | 99.99 |
3 | .76 | 1.64 | 2.35 | 3.18 | 4.54 | 5.84 | 7.45 | 10.21 | 12.92 | 16.33 | 22.20 | 28.00 |
4 | .74 | 1.53 | 2.13 | 2.78 | 3.75 | 4.60 | 5.60 | 7.17 | 8.61 | 10.31 | 13.03 | 15.54 |
5 | .73 | 1.48 | 2.02 | 2.57 | 3.37 | 4.03 | 4.77 | 5.89 | 6.87 | 7.98 | 9.68 | 11.18 |
6 | .72 | 1.44 | 1.94 | 2.45 | 3.14 | 3.71 | 4.32 | 5.21 | 5.96 | 6.79 | 8.02 | 9.08 |
7 | .71 | 1.42 | 1.90 | 2.37 | 3.00 | 3.50 | 4.03 | 4.79 | 5.41 | 6.08 | 7.06 | 7.88 |
8 | .71 | 1.40 | 1.86 | 2.31 | 2.90 | 3.36 | 3.83 | 4.50 | 5.04 | 5.62 | 6.44 | 7.12 |
9 | .70 | 1.38 | 1.83 | 2.26 | 2.82 | 3.25 | 3.69 | 4.30 | 4.78 | 5.29 | 6.01 | 6.59 |
10 | .70 | 1.37 | 1.81 | 2.23 | 2.76 | 3.17 | 3.58 | 4.14 | 4.59 | 5.05 | 5.69 | 6.21 |
11 | .70 | 1.36 | 1.80 | 2.20 | 2.72 | 3.11 | 3.50 | 4.03 | 4.44 | 4.86 | 5.45 | 5.92 |
12 | .70 | 1.36 | 1.78 | 2.18 | 2.68 | 3.06 | 3.43 | 3.93 | 4.32 | 4.72 | 5.26 | 5.69 |
13 | .69 | 1.35 | 1.77 | 2.16 | 2.65 | 3.01 | 3.37 | 3.85 | 4.22 | 4.60 | 5.11 | 5.51 |
14 | .69 | 1.35 | 1.76 | 2.15 | 2.63 | 2.98 | 3.33 | 3.79 | 4.14 | 4.50 | 4.99 | 5.36 |
15 | .69 | 1.34 | 1.75 | 2.13 | 2.60 | 2.95 | 3.29 | 3.73 | 4.07 | 4.42 | 4.88 | 5.24 |
16 | .69 | 1.34 | 1.75 | 2.12 | 2.58 | 2.92 | 3.25 | 3.69 | 4.02 | 4.35 | 4.79 | 5.13 |
17 | .69 | 1.33 | 1.74 | 2.11 | 2.57 | 2.90 | 3.22 | 3.65 | 3.97 | 4.29 | 4.71 | 5.04 |
18 | .69 | 1.33 | 1.73 | 2.10 | 2.55 | 2.88 | 3.20 | 3.61 | 3.92 | 4.23 | 4.65 | 4.97 |
19 | .69 | 1.33 | 1.73 | 2.09 | 2.54 | 2.86 | 3.17 | 3.58 | 3.88 | 4.19 | 4.59 | 4.90 |
20 | .69 | 1.33 | 1.73 | 2.09 | 2.53 | 2.85 | 3.15 | 3.55 | 3.85 | 4.15 | 4.54 | 4.84 |
21 | .69 | 1.32 | 1.72 | 2.08 | 2.52 | 2.83 | 3.14 | 3.53 | 3.82 | 4.11 | 4.49 | 4.78 |
22 | .69 | 1.32 | 1.72 | 2.07 | 2.51 | 2.82 | 3.12 | 3.51 | 3.79 | 4.08 | 4.45 | 4.74 |
23 | .68 | 1.32 | 1.71 | 2.07 | 2.50 | 2.81 | 3.10 | 3.49 | 3.77 | 4.05 | 4.42 | 4.69 |
24 | .68 | 1.32 | 1.71 | 2.06 | 2.49 | 2.80 | 3.09 | 3.47 | 3.75 | 4.02 | 4.38 | 4.65 |
25 | .68 | 1.32 | 1.71 | 2.06 | 2.49 | 2.79 | 3.08 | 3.45 | 3.73 | 4.00 | 4.35 | 4.62 |
26 | .68 | 1.32 | 1.71 | 2.06 | 2.48 | 2.78 | 3.07 | 3.44 | 3.71 | 3.97 | 4.32 | 4.59 |
27 | .68 | 1.31 | 1.70 | 2.05 | 2.47 | 2.77 | 3.06 | 3.42 | 3.69 | 3.95 | 4.30 | 4.56 |
28 | .68 | 1.31 | 1.70 | 2.05 | 2.47 | 2.76 | 3.05 | 3.41 | 3.67 | 3.94 | 4.28 | 4.53 |
29 | .68 | 1.31 | 1.70 | 2.05 | 2.46 | 2.76 | 3.04 | 3.40 | 3.66 | 3.92 | 4.25 | 4.51 |
30 | .68 | 1.31 | 1.70 | 2.04 | 2.46 | 2.75 | 3.03 | 3.39 | 3.65 | 3.90 | 4.23 | 4.48 |
35 | .68 | 1.31 | 1.69 | 2.03 | 2.44 | 2.72 | 3.00 | 3.34 | 3.59 | 3.84 | 4.15 | 4.39 |
40 | .68 | 1.30 | 1.68 | 2.02 | 2.42 | 2.70 | 2.97 | 3.31 | 3.55 | 3.79 | 4.09 | 4.32 |
45 | .68 | 1.30 | 1.68 | 2.01 | 2.41 | 2.69 | 2.95 | 3.28 | 3.52 | 3.75 | 4.05 | 4.27 |
50 | .68 | 1.30 | 1.68 | 2.01 | 2.40 | 2.68 | 2.94 | 3.26 | 3.50 | 3.72 | 4.01 | 4.23 |
55 | .68 | 1.30 | 1.67 | 2.00 | 2.40 | 2.67 | 2.93 | 3.25 | 3.48 | 3.70 | 3.99 | 4.20 |
60 | .68 | 1.30 | 1.67 | 2.00 | 2.39 | 2.66 | 2.91 | 3.23 | 3.46 | 3.68 | 3.96 | 4.17 |
65 | .68 | 1.29 | 1.67 | 2.00 | 2.39 | 2.65 | 2.91 | 3.22 | 3.45 | 3.66 | 3.94 | 4.15 |
70 | .68 | 1.29 | 1.67 | 1.99 | 2.38 | 2.65 | 2.90 | 3.21 | 3.44 | 3.65 | 3.93 | 4.13 |
75 | .68 | 1.29 | 1.67 | 1.99 | 2.38 | 2.64 | 2.89 | 3.20 | 3.43 | 3.64 | 3.91 | 4.11 |
80 | .68 | 1.29 | 1.66 | 1.99 | 2.37 | 2.64 | 2.89 | 3.20 | 3.42 | 3.63 | 3.90 | 4.10 |
85 | .68 | 1.29 | 1.66 | 1.99 | 2.37 | 2.64 | 2.88 | 3.19 | 3.41 | 3.62 | 3.89 | 4.08 |
90 | .68 | 1.29 | 1.66 | 1.99 | 2.37 | 2.63 | 2.88 | 3.18 | 3.40 | 3.61 | 3.88 | 4.07 |
95 | .68 | 1.29 | 1.66 | 1.99 | 2.37 | 2.63 | 2.87 | 3.18 | 3.40 | 3.60 | 3.87 | 4.06 |
100 | .68 | 1.29 | 1.66 | 1.98 | 2.36 | 2.63 | 2.87 | 3.17 | 3.39 | 3.60 | 3.86 | 4.05 |
200 | .68 | 1.29 | 1.65 | 1.97 | 2.35 | 2.60 | 2.84 | 3.13 | 3.34 | 3.54 | 3.79 | 3.97 |
500 | .68 | 1.28 | 1.65 | 1.97 | 2.33 | 2.59 | 2.82 | 3.11 | 3.31 | 3.50 | 3.75 | 3.92 |
.67 | 1.28 | 1.65 | 1.96 | 2.33 | 2.58 | 2.81 | 3.10 | 3.30 | 3.49 | 3.73 | 3.91 |