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Physical Measurement Laboratory

NIST TN 1297: Guidelines - Appendix B, Table B.1

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Table B.1 - Value of tp(ν) from the t-distribution for degrees of freedom ν that defines an interval - tp(ν) to + tp(ν) that encompasses the fraction p of the distribution

Degrees of
freedom
ν		 Fraction p in percent
68.27 (a)   90 95 95.45 (a)   99 99.73 (a)  
1 1.84 6.31 12.71 13.97 63.66 235.80
2 1.32 2.92 4.30 4.53 9.92 19.21
3 1.20 2.35 3.18 3.31 5.84 9.22
4 1.14 2.13 2.78 2.87 4.60 6.62
5 1.11 2.02 2.57 2.65 4.03 5.51
6 1.09 1.94 2.45 2.52 3.71 4.90
7 1.08 1.89 2.36 2.43 3.50 4.53
8 1.07 1.86 2.31 2.37 3.36 4.28
9 1.06 1.83 2.26 2.32 3.25 4.09
10 1.05 1.81 2.23 2.28 3.17 3.96
11 1.05 1.80 2.20 2.25 3.11 3.85
12 1.04 1.78 2.18 2.23 3.05 3.76
13 1.04 1.77 2.16 2.21 3.01 3.69
14 1.04 1.76 2.14 2.20 2.98 3.64
15 1.03 1.75 2.13 2.18 2.95 3.59
16 1.03 1.75 2.12 2.17 2.92 3.54
17 1.03 1.74 2.11 2.16 2.90 3.51
18 1.03 1.73 2.10 2.15 2.88 3.48
19 1.03 1.73 2.09 2.14 2.86 3.45
20 1.03 1.72 2.09 2.13 2.85 3.42
25 1.02 1.71 2.06 2.11 2.79 3.33
30 1.02 1.70 2.04 2.09 2.75 3.27
35 1.01 1.70 2.03 2.07 2.72 3.23
40 1.01 1.68 2.02 2.06 2.70 3.20
45 1.01 1.68 2.01 2.06 2.69 3.18
50 1.01 1.68 2.01 2.05 2.68 3.16
100 1.005 1.660 1.984 2.025 2.626 3.077
∞ 1.000 1.645 1.960 2.000 2.576 3.000
(a)For a quantity z described by a normal distribution with expectation µz and standard deviation σ, the interval µz ± kσ encompasses p = 68.27, 95.45, and 99.73 percent of the distribution for k = 1, 2, and 3, respectively.

Back to Appendix B

Metrology and Physics
Created November 6, 2015, Updated June 2, 2021
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