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Appendix 805

TABLE 2 Critical Values for Two-Sided and One-Sided Tests Using the Student t Distribution

Significance Level

Degrees 20% (2-Sided) 10% (2-Sided) 5% (2-Sided) 2% (2-Sided) 1% (2-Sided)
of Freedom 10% (1-Sided) 5% (1-Sided) 2.5% (1-Sided) 1% (1-Sided) 0.5% (1-Sided)

1 3.08 6.31 12.71 31.82 63.66
2 1.89 2.92 4.30 6.96 9.92
3 1.64 2.35 3.18 4.54 5.84
4 1.53 2.13 2.78 3.75 4.60
5 1.48 2.02 2.57 3.36 4.03
6 1.44 1.94 2.45 3.14 3.71
7 1.41 1.89 2.36 3.00 3.50
8 1.40 1.86 2.31 2.90 3.36
9 1.38 1.83 2.26 2.82 3.25
10 1.37 1.81 2.23 2.76 3.17
11 1.36 1.80 2.20 2.72 3.11
12 1.36 1.78 2.18 2.68 3.05
13 1.35 1.77 2.16 2.65 3.01
14 1.35 1.76 2.14 2.62 2.98
15 1.34 1.75 2.13 2.60 2.95
16 1.34 1.75 2.12 2.58 2.92
17 1.33 1.74 2.11 2.57 2.90
18 1.33 1.73 2.10 2.55 2.88
19 1.33 1.73 2.09 2.54 2.86
20 1.33 1.72 2.09 2.53 2.85
21 1.32 1.72 2.08 2.52 2.83
22 1.32 1.72 2.07 2.51 2.82
23 1.32 1.71 2.07 2.50 2.81
24 1.32 1.71 2.06 2.49 2.80
25 1.32 1.71 2.06 2.49 2.79
26 1.32 1.71 2.06 2.48 2.78
27 1.31 1.70 2.05 2.47 2.77
28 1.31 1.70 2.05 2.47 2.76
29 1.31 1.70 2.05 2.46 2.76
30 1.31 1.70 2.04 2.46 2.75
60 1.30 1.67 2.00 2.39 2.66

90 1.29 1.66 1.99 2.37 2.63
120 1.29 1.66 1.98 2.36 2.62
1.28 1.64 1.96 2.33 2.58
∞

Values are shown for the critical values for two-sided ( ) and one-sided ( 7 ) alternative hypotheses. The critical value for the
one-sided ( 6 ) test is the negative of the one-sided ( 7 ) critical value shown in the table. For example, 2.13 is the critical value for a
two-sided test with a significance level of 5% using the Student t distribution with 15 degrees of freedom.