t-table (right tail)

For each row (degrees of freedom k ) and column (right tail probability α ), the table
entry e satisfies Pr(t k ≥ e) = α . Note that the t-distribution is symmetric about 0.

degrees right tail probability

of freedom 0.25 0.10 0.05 0.025 0.01
1 1.000 3.078 6.314 12.706 31.821
2 0.816 1.886 2.920 4.303 6.965
3 0.765 1.638 2.353 3.182 4.541
4 0.741 1.533 2.132 2.776 3.747
5 0.727 1.476 2.015 2.571 3.365
6 0.718 1.440 1.943 2.447 3.143
7 0.711 1.415 1.895 2.365 2.998
8 0.706 1.397 1.860 2.306 2.896
9 0.703 1.383 1.833 2.262 2.821
10 0.700 1.372 1.812 2.228 2.764
11 0.697 1.363 1.796 2.201 2.718
12 0.695 1.356 1.782 2.179 2.681
13 0.694 1.350 1.771 2.160 2.650
14 0.692 1.345 1.761 2.145 2.624
15 0.691 1.341 1.753 2.131 2.602
16 0.690 1.337 1.746 2.120 2.583
17 0.689 1.333 1.740 2.110 2.567
18 0.688 1.330 1.734 2.101 2.552
19 0.688 1.328 1.729 2.093 2.539
20 0.687 1.325 1.725 2.086 2.528
21 0.686 1.323 1.721 2.080 2.518
22 0.686 1.321 1.717 2.074 2.508
23 0.685 1.319 1.714 2.069 2.500
24 0.685 1.318 1.711 2.064 2.492
25 0.684 1.316 1.708 2.060 2.485
26 0.684 1.315 1.706 2.056 2.479
27 0.684 1.314 1.703 2.052 2.473
28 0.683 1.313 1.701 2.048 2.467
29 0.683 1.311 1.699 2.045 2.462
30 0.683 1.310 1.697 2.042 2.457
35 0.682 1.306 1.690 2.030 2.438
40 0.681 1.303 1.684 2.021 2.423
45 0.680 1.301 1.679 2.014 2.412
50 0.679 1.299 1.676 2.009 2.403
gaussian 0.675 1.282 1.646 1.962 2.330

University of Waterloo table -1

 F-table (right tail) α = 010
.

For each row (denominator degrees of freedom k) and column (numerator degrees of
freedom j), the table entry e satisfies P( F ( j , k ) ≥ e) = α .

numerator degrees of freedom

1 2 3 4 5 6 7 8 9 10 20 30
1 39.86 49.50 53.59 55.83 57.24 58.20 58.91 59.44 59.86 60.19 61.74 62.26
2 8.53 9.00 9.16 9.24 9.29 9.33 9.35 9.37 9.38 9.39 9.44 9.46
3 5.54 5.46 5.39 5.34 5.31 5.28 5.27 5.25 5.24 5.23 5.18 5.17
4 4.54 4.32 4.19 4.11 4.05 4.01 3.98 3.95 3.94 3.92 3.84 3.82
5 4.06 3.78 3.62 3.52 3.45 3.40 3.37 3.34 3.32 3.30 3.21 3.17
denominator degrees of freedom

6 3.78 3.46 3.29 3.18 3.11 3.05 3.01 2.98 2.96 2.94 2.84 2.80
7 3.59 3.26 3.07 2.96 2.88 2.83 2.78 2.75 2.72 2.70 2.59 2.56
8 3.46 3.11 2.92 2.81 2.73 2.67 2.62 2.59 2.56 2.54 2.42 2.38
9 3.36 3.01 2.81 2.69 2.61 2.55 2.51 2.47 2.44 2.42 2.30 2.25
10 3.29 2.92 2.73 2.61 2.52 2.46 2.41 2.38 2.35 2.32 2.20 2.16
11 3.23 2.86 2.66 2.54 2.45 2.39 2.34 2.30 2.27 2.25 2.12 2.08
12 3.18 2.81 2.61 2.48 2.39 2.33 2.28 2.24 2.21 2.19 2.06 2.01
13 3.14 2.76 2.56 2.43 2.35 2.28 2.23 2.20 2.16 2.14 2.01 1.96
14 3.10 2.73 2.52 2.39 2.31 2.24 2.19 2.15 2.12 2.10 1.96 1.91
15 3.07 2.70 2.49 2.36 2.27 2.21 2.16 2.12 2.09 2.06 1.92 1.87
16 3.05 2.67 2.46 2.33 2.24 2.18 2.13 2.09 2.06 2.03 1.89 1.84
17 3.03 2.64 2.44 2.31 2.22 2.15 2.10 2.06 2.03 2.00 1.86 1.81
18 3.01 2.62 2.42 2.29 2.20 2.13 2.08 2.04 2.00 1.98 1.84 1.78
19 2.99 2.61 2.40 2.27 2.18 2.11 2.06 2.02 1.98 1.96 1.81 1.76
20 2.97 2.59 2.38 2.25 2.16 2.09 2.04 2.00 1.96 1.94 1.79 1.74
21 2.96 2.57 2.36 2.23 2.14 2.08 2.02 1.98 1.95 1.92 1.78 1.72
22 2.95 2.56 2.35 2.22 2.13 2.06 2.01 1.97 1.93 1.90 1.76 1.70
23 2.94 2.55 2.34 2.21 2.11 2.05 1.99 1.95 1.92 1.89 1.74 1.69
24 2.93 2.54 2.33 2.19 2.10 2.04 1.98 1.94 1.91 1.88 1.73 1.67
25 2.92 2.53 2.32 2.18 2.09 2.02 1.97 1.93 1.89 1.87 1.72 1.66
30 2.88 2.49 2.28 2.14 2.05 1.98 1.93 1.88 1.85 1.82 1.67 1.61
40 2.84 2.44 2.23 2.09 2.00 1.93 1.87 1.83 1.79 1.76 1.61 1.54
50 2.81 2.41 2.20 2.06 1.97 1.90 1.84 1.80 1.76 1.73 1.57 1.50
100 2.76 2.36 2.14 2.00 1.91 1.83 1.78 1.73 1.69 1.66 1.49 1.42

University of Waterloo table -2

 F-table (right tail) α = 0.05

For each row (denominator degrees of freedom k) and column (numerator degrees of
freedom j), the table entry e satisfies P( F ( j , k ) ≥ e) = α .

numerator degrees of freedom

1 2 3 4 5 6 7 8 9 10 20 30
1 161.45 199.50 215.71 224.58 230.16 233.99 236.77 238.88 240.54 241.88 248.02 250.10
2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40 19.45 19.46
3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 8.66 8.62
4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96 5.80 5.75
5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 4.56 4.50
denominator degrees of freedom

6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06 3.87 3.81
7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64 3.44 3.38
8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35 3.15 3.08
9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14 2.94 2.86
10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98 2.77 2.70
11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85 2.65 2.57
12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75 2.54 2.47
13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 2.46 2.38
14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60 2.39 2.31
15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 2.33 2.25
16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.28 2.19
17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45 2.23 2.15
18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 2.19 2.11
19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 2.16 2.07
20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 2.12 2.04
21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 2.32 2.10 2.01
22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30 2.07 1.98
23 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32 2.27 2.05 1.96
24 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25 2.03 1.94
25 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28 2.24 2.01 1.92
30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16 1.93 1.84
40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08 1.84 1.74
50 4.03 3.18 2.79 2.56 2.40 2.29 2.20 2.13 2.07 2.03 1.78 1.69
100 3.94 3.09 2.70 2.46 2.31 2.19 2.10 2.03 1.97 1.93 1.68 1.57

University of Waterloo table -3

 F-table (right tail) α = 0.01

For each row (denominator degrees of freedom k) and column (numerator degrees of
freedom j), the table entry e satisfies P( F ( j , k ) ≥ e) = α .

numerator degrees of freedom

1 2 3 4 5 6 7 8 9 10 20 30
1 4052 4999 5404 5624 5764 5859 5928 5981 6022 6056 6209 6260
2 98.50 99.00 99.16 99.25 99.30 99.33 99.36 99.38 99.39 99.40 99.45 99.47
3 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.34 27.23 26.69 26.50
4 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66 14.55 14.02 13.84
5 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16 10.05 9.55 9.38
denominator degrees of freedom

6 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.10 7.98 7.87 7.40 7.23
7 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72 6.62 6.16 5.99
8 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91 5.81 5.36 5.20
9 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35 5.26 4.81 4.65
10 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94 4.85 4.41 4.25
11 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54 4.10 3.94
12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39 4.30 3.86 3.70
13 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10 3.66 3.51
14 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4.03 3.94 3.51 3.35
15 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89 3.80 3.37 3.21
16 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78 3.69 3.26 3.10
17 8.40 6.11 5.19 4.67 4.34 4.10 3.93 3.79 3.68 3.59 3.16 3.00
18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60 3.51 3.08 2.92
19 8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52 3.43 3.00 2.84
20 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37 2.94 2.78
21 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.40 3.31 2.88 2.72
22 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35 3.26 2.83 2.67
23 7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41 3.30 3.21 2.78 2.62
24 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17 2.74 2.58
25 7.77 5.57 4.68 4.18 3.85 3.63 3.46 3.32 3.22 3.13 2.70 2.54
30 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.98 2.55 2.39
40 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89 2.80 2.37 2.20
50 7.17 5.06 4.20 3.72 3.41 3.19 3.02 2.89 2.78 2.70 2.27 2.10
100 6.90 4.82 3.98 3.51 3.21 2.99 2.82 2.69 2.59 2.50 2.07 1.89

University of Waterloo table -4