93 crit valuetables_4th

© 4th ed. 2006 Dr. Rick Yount Tables
Critical Value Tables
z-Distribution Table
Critical Value Table
for the z-Test
Chapters 17-19
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
z
0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359
0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753
0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141
0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517
0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879
0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224
0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549
0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852
0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133
0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389
1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621
1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830
1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319
1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441
1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545
1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633
1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706
1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767
2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817
2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857
2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890
2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916
2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936
2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952
2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964
2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974
2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981
2.9 0.4981 0.4982 0.4982 0.4983 0.4983 0.4984 0.4985 0.4985 0.4986 0.4986
3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4988 0.4989 0.4989 0.4990 0.4990
3.1 0.49903
3.2 0.49931
3.3 0.49952
3.4 0.49962
3.5 0.49977
3.6 0.49984
3.7 0.49989
3.8 0.49993
3.9 0.49995
4.0 0.50000
A3-1
Example
The horizontal shading above represents z = 1.9
The vertical shading above represents z = +.06
Where they meet represents z = 1.96
The area between the
mean and z = 1.96 equals 0.4750.
Adapted from Robert Johnson, Elementary Statistics, 6th ed. (Boston: PWS-KENT Publishing Company, 1992), F-8

Research Design and Statistical Analysis in Christian Ministry © 4th ed. 2006 Dr. Rick Yount
for the t-Tests
Chapters 19-20
A3-2
t-Distribution Table
df 0.05 0.025 0.01 0.005
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 3.355
9 1.833 2.262 2.821 3.250
10 1.812 2.228 2.764 3.169
11 1.796 2.201 2.718 3.106
12 1.782 2.179 2.681 3.055
13 1.771 2.160 2.650 3.012
14 1.761 2.145 2.624 2.977
15 1.753 2.131 2.602 2.947
16 1.746 2.120 2.583 2.921
17 1.740 2.110 2.567 2.898
18 1.734 2.101 2.552 2.878
19 1.729 2.093 2.539 2.861
20 1.725 2.086 2.528 2.845
21 1.721 2.080 2.518 2.831
22 1.717 2.074 2.508 2.819
23 1.714 2.069 2.500 2.807
24 1.711 2.064 2.492 2.797
25 1.708 2.060 2.485 2.787
26 1.706 2.056 2.479 2.779
27 1.703 2.052 2.473 2.771
28 1.701 2.048 2.467 2.763
29 1.699 2.045 2.462 2.756
30 1.697 2.042 2.457 2.750
40 1.684 2.021 2.423 2.704
50 1.676 2.009 2.403 2.678
100 1.660 1.984 2.364 2.626
∞∞∞∞ 1.645 1.960 2.326 2.576
Adapted from David Howell, Statistical Methods for Psychology (Boston: Duxbury Press, 1982), 521
one sample t
df = n-1
independent samples t
df = nx + ny - 2
matched samples t
df = n-2 pairs

χ2 Distribution Table
df 0.05 0.025 0.01 0.005
1 3.84 5.02 6.63 7.88
2 5.99 7.38 9.21 10.60
3 7.82 9.35 11.35 12.84
4 9.49 11.14 13.28 14.86
5 11.07 12.83 15.09 16.75
6 12.59 14.45 16.81 18.55
7 14.07 16.01 18.48 20.28
8 15.51 17.54 20.09 21.96
9 16.92 19.02 21.66 23.59
10 18.31 20.48 23.21 25.19
11 19.68 21.92 24.72 26.75
12 21.03 23.34 26.21 28.30
13 22.36 24.74 27.69 29.82
14 23.69 26.12 29.14 31.31
15 25.00 27.49 30.58 32.80
16 26.30 28.85 32.00 34.27
17 27.59 30.19 33.41 35.72
18 28.87 31.53 34.81 37.15
19 30.14 32.85 36.19 38.58
20 31.41 34.17 37.56 40.00
21 32.67 35.48 38.93 41.40
22 33.93 36.78 40.29 42.80
23 35.17 38.08 41.64 44.18
24 36.42 39.37 42.98 45.56
25 37.65 40.65 44.32 46.93
26 38.89 41.92 45.64 48.29
27 40.11 43.20 46.96 49.64
28 41.34 44.46 48.28 50.99
29 42.56 45.72 49.59 52.34
30 43.77 46.98 50.89 53.67
40 55.75 59.34 63.71 66.80
50 67.50 71.42 76.17 79.52
100 124.34 129.56 135.82 140.19
A3-3
for the Chi-Square Tests
Chapter 23
Goodness of Fit
df = k-1
Test of Independence
df = (r-1)(c-1)

for the Analysis of Variance Test
Chapter 21
A3-4
F-Distribution Table
Degrees of Freedom for the F-Ratio numera-tor
Degrees of Freedom for the F-Ratio denominator
αααα = 0.05
1 2 3 4 5 6 7 8 9 10
1 161.4 199.5 215.8 224.8 230.0 233.8 236.5 238.6 240.1 242.1
2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40
3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79
4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96
5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74
6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06
7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64
8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35
9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14
10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98
11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85
12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75
13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67
14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60
15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54
16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49
17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45
18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41
19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38
20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35
22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30
24 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25
26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22
28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 2.19
30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16
40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08
50 4.03 3.18 2.79 2.56 2.40 2.29 2.20 2.13 2.07 2.03
60 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04 1.99
120 3.92 3.07 2.68 2.45 2.29 2.18 2.09 2.02 1.96 1.91
200 3.89 3.04 2.65 2.42 2.26 2.14 2.06 1.98 1.93 1.88
500 3.86 3.01 2.62 2.39 2.23 2.12 2.03 1.96 1.90 1.85
1000 3.85 3.01 2.61 2.38 2.22 2.11 2.02 1.95 1.89 1.84

F-Distribution Table
A3-5
Degrees of Freedom for the F-Ratio numera-tor
for the Analysis of Variance Test
Chapter 21
Degrees of Freedom for the F-Ratio denominator
αααα = 0.01
1 2 3 4 5 6 7 8 9 10
1 4048 4993 5377 5577 5668 5924 5992 6096 6132 6168
2 98.50 99.01 99.15 99.23 99.30 99.33 99.35 99.39 99.40 99.43
3 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.34 27.23
4 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66 14.55
5 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16 10.05
6 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.10 7.98 7.87
7 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72 6.62
8 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91 5.81
9 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35 5.26
10 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94 4.85
11 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54
12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39 4.30
13 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10
14 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4.03 3.94
15 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89 3.80
16 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78 3.69
17 8.40 6.11 5.18 4.67 4.34 4.10 3.93 3.79 3.68 3.59
18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60 3.51
19 8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52 3.43
20 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37
22 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35 3.26
24 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17
26 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18 3.09
28 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12 3.03
30 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.98
40 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89 2.80
50 7.17 5.06 4.20 3.72 3.41 3.19 3.02 2.89 2.78 2.70
60 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72 2.63
120 6.85 4.79 3.95 3.48 3.17 2.96 2.79 2.66 2.56 2.47
200 6.76 4.71 3.88 3.41 3.11 2.89 2.73 2.60 2.50 2.41
500 6.69 4.65 3.82 3.36 3.05 2.84 2.68 2.55 2.44 2.36
1000 6.67 4.63 3.80 3.34 3.04 2.82 2.66 2.53 2.43 2.34

for the Wilcoxin Rank-Sum Ordinal Test
Chapter 24
A3-6
Wilcoxin Ws Distribution Table
N1 = 5 N1 = 6
N2 0.5 1.0 2.5 5.0% 0.5 1.0 2.5 5.0%
5 15 16 17 19 . . . .
6 16 17 18 20 23 24 26 28
7 16 16 18 21 24 25 27 29
8 17 19 21 23 25 27 29 31
9 18 20 22 24 26 28 31 33
10 19 21 23 26 27 29 32 35
11 20 22 24 27 28 30 34 37
12 21 23 26 28 30 32 35 38
13 22 24 27 30 31 33 37 40
14 22 25 28 31 32 34 38 42
15 23 26 29 33 33 36 40 44
16 24 27 30 34 34 37 42 46
17 25 28 32 35 36 39 43 47
18 26 29 33 37 37 40 45 49
19 27 30 34 38 38 41 46 51
20 28 31 35 40 39 43 48 53
21 29 32 37 41 40 44 50 55
22 29 33 38 43 42 45 51 57
23 30 34 39 44 43 47 53 59
24 31 35 40 45 44 48 54 60
25 32 36 42 47 45 50 56 62
N1 = 7 N1 = 8
N2 0.5 1.0 2.5 5.0% 0.5 1.0 2.5 5.0%
7 32 34 36 39
8 34 35 38 41 43 45 49 51
9 35 37 40 43 45 47 51 54
10 37 39 42 45 47 49 53 56
11 38 40 44 47 49 51 55 59
12 40 42 46 49 51 53 58 62
13 41 44 48 52 53 56 60 64
14 43 45 50 54 54 58 62 67
15 44 47 52 56 56 60 65 69
16 46 49 54 58 58 62 67 72
17 47 51 56 61 60 64 70 75
18 49 52 58 63 62 66 72 77
19 50 54 60 65 64 68 74 80
20 52 56 62 67 66 70 77 83
21 53 58 64 69 68 72 79 85
22 55 59 66 72 70 74 81 88
23 57 61 68 74 71 76 84 90
24 58 63 70 76 73 78 86 93
25 60 64 72 78 75 81 89 96
.....continued in Howell to N1 = 25
Adapted from David Howell, Statistical Methods for Psychology (Boston: Duxbury Press, 1982), 537-538

Wilcoxin T Distribution Table
A3-7
for the Wilcoxin Matched Pairs Ordinal Test
Chapter 24
.05 .025 .01 .005
number
of pairs
N T αααα T αααα T αααα T αααα
5 0 .0313
1 .0625
6 2 .0469 0 .0156
3 .0781 1 .0313
7 3 .0391 2 .0234 0 .0078
4 .0547 3 .0391 1 .0156
8 5 .0391 3 .0195 1 .0078 0 .0039
6 .0547 4 .0273 2 .0117 1 .0078
9 8 .0488 5 .0195 3 .0098 1 .0039
9 .0645 6 .0273 4 .0137 2 .0059
10 10 .0420 8 .0244 5 .0098 3 .0049
11 .0527 9 .0322 6 .0137 4 .0068
11 13 .0415 10 .0210 7 .0093 5 .0049
14 .0508 11 .0269 8 .0122 6 .0068
12 17 .0461 13 .0212 9 .0081 7 .0046
18 .0549 14 .0261 10 .0105 8 .0061
13 21 .0471 17 .0239 12 .0085 9 .0040
22 .0549 18 .0287 13 .0107 10 .0052
14 25 .0453 21 .0247 15 .0083 12 .0043
26 .0520 22 .0290 16 .0101 13 .0054
15 30 .0473 25 .0240 19 .0090 15 .0042
31 .0535 26 .0277 20 .0108 16 .0051
16 35 .0467 29 .0222 23 .0091 19 .0046
36 .0523 30 .0253 24 .0107 20 .0055
17 41 .0492 34 .0224 27 .0087 23 .0047
42 .0544 35 .0253 28 .0101 24 .0055
18 47 .0494 40 .0241 32 .0091 27 .0045
48 .0542 41 .0269 33 .0104 28 .0052
19 53 .0478 46 .0247 37 .0090 32 .0047
54 .0521 47 .0273 38 .0102 33 .0054
20 60 .0487 52 .0242 43 .0096 37 .0047
61 .0527 53 .0266 44 .0107 38 .0053
.....continued in Howell to N = 50

for the Studentized-Range Statistic - Used with
Chapter 24
A3-8
q-Distribution Table
r = Number of Steps Between Ordered Means
2 3 4 5 6 7 8 9 10
1 17.97 26.98 32.82 37.08 40.41 43.12 45.40 47.36 49.07
2 6.08 8.33 9.80 10.88 11.74 12.44 13.03 13.54 13.99
3 4.50 5.91 6.82 7.50 8.04 8.48 8.85 9.18 9.46
4 3.93 5.04 5.76 6.29 6.71 7.05 7.35 7.60 7.33
5 3.64 4.60 5.22 5.67 6.03 6.33 6.58 6.80 7.00
6 3.46 4.34 4.90 5.31 5.63 5.90 6.12 6.32 6.49
7 3.34 4.16 4.68 5.06 5.36 5.61 5.82 6.00 6.16
8 3.26 4.04 4.53 4.89 5.17 5.40 5.60 5.77 5.92
9 3.20 3.95 4.42 4.76 5.02 5.24 5.43 5.60 5.74
10 3.15 3.88 4.33 4.65 4.91 5.12 5.30 5.46 5.60
11 3.11 3.82 4.26 4.57 4.82 5.03 5.20 5.35 5.49
12 3.08 3.77 4.20 4.51 4.75 4.95 5.12 5.26 5.40
13 3.06 3.74 4.15 4.45 4.69 4.88 5.05 5.19 5.32
14 3.03 3.70 4.11 4.41 4.64 4.83 4.99 5.13 5.25
15 3.01 3.67 4.08 4.37 4.60 4.78 4.94 5.08 5.20
16 3.00 3.65 4.05 4.33 4.56 4.74 4.90 5.03 5.15
17 2.98 3.63 4.02 4.30 4.52 4.70 4.86 4.99 5.11
18 2.97 3.61 4.00 4.28 4.50 4.67 4.82 4.96 5.07
19 2.96 3.59 3.98 4.25 4.47 4.64 4.79 4.92 5.04
20 2.95 3.58 3.96 4.23 4.44 4.62 4.77 4.90 5.01
24 2.92 3.53 3.90 4.17 4.37 4.54 4.68 4.81 4.92
30 2.89 3.49 3.84 4.10 4.30 4.46 4.60 4.72 4.82
40 2.86 3.44 3.79 4.04 4.23 4.39 4.52 4.64 4.74
60 2.83 3.40 3.74 3.98 4.16 4.31 4.44 4.55 4.65
120 2.80 3.36 3.69 3.92 4.10 4.24 4.36 4.47 4.56
∞ 2.77 3.31 3.63 3.86 4.03 4.17 4.29 4.39 4.47
.....continued in Howell to r = 15
dfw

U-Distribution Table
A3-9
for the Mann-Whitney U test
Chapter 24
N2
N2
1-tail test at α = 0.025 or 2-tail test at αααα = 0.05
1-tail test at αααα = 0.05 or 2-tail test at α = 0.10
N1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
12
0 0 0 0 1 1 1 1 1 2 2 2 2
3 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8
4 0 1 2 3 4 4 5 6 7 8 9 10 11 11 12 13 13
5 0 1 2 3 5 6 7 8 9 11 12 13 14 15 17 18 19 20
6 1 2 3 5 6 8 10 11 13 14 16 17 19 21 22 24 25 27
7 1 3 5 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34
8 0 2 4 6 8 10 13 15 17 19 22 24 26 29 21 34 36 38 41
9 0 2 4 7 10 12 15 17 20 23 26 28 31 34 37 39 42 45 48
10 0 3 5 8 11 14 17 20 23 26 29 33 36 39 42 45 48 52 55
11 0 3 6 9 13 16 19 23 26 30 33 37 40 44 47 51 55 58 62
12 1 4 7 11 14 18 22 26 29 33 37 41 45 49 53 57 61 65 69
13 1 4 8 12 16 20 24 28 33 37 41 45 50 54 59 63 67 72 76
14 1 5 9 13 17 22 26 31 36 40 45 50 55 59 64 67 74 78 83
15 1 5 10 14 19 24 29 34 39 44 49 54 59 64 70 75 80 85 90
16 1 6 11 15 21 26 31 37 42 47 53 59 64 70 75 81 86 92 98
17 2 6 11 17 22 28 34 39 45 51 57 63 67 75 81 87 93 99 105
18 2 7 12 18 24 30 36 42 48 55 61 67 74 80 86 93 99 106 112
19 2 7 13 19 25 32 38 45 52 58 65 72 78 95 92 99 106 113 119
20 2 8 13 20 27 34 41 48 55 62 69 76 83 90 98 105 112 119 127
N1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
12
0 0 0 1 1 1 1 2 2 2 3 3 3 4 4 4
3 0 0 1 2 2 3 3 4 5 5 6 7 7 8 9 9 10 11
4 0 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18
5 0 1 2 4 5 6 8 9 11 12 13 15 16 18 19 20 22 23 25
6 0 2 3 5 7 8 10 12 14 16 17 19 21 23 25 26 28 30 32
7 0 2 4 6 8 11 13 15 17 19 21 24 26 28 30 33 35 37 39
8 1 3 5 8 10 13 15 18 20 23 26 28 31 33 36 39 41 44 47
9 1 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54
10 1 4 7 11 14 17 20 24 27 31 34 37 41 44 48 51 55 58 62
11 1 5 8 12 16 19 23 27 31 34 38 42 46 50 54 57 61 65 69
12 2 5 9 13 17 21 26 30 34 38 42 47 51 55 60 64 68 72 77
13 2 6 10 15 19 24 28 33 37 42 47 51 56 61 65 70 75 80 84
14 2 7 11 16 21 26 31 36 41 46 51 56 61 66 71 77 82 87 92
15 3 7 12 18 23 28 33 39 44 50 55 61 66 72 77 83 88 94 100
16 3 8 14 19 25 30 36 42 48 54 60 65 71 77 83 89 95 101 107
17 3 9 15 20 26 33 39 45 51 57 64 70 77 83 89 96 102 109 115
18 4 9 16 22 28 35 41 48 55 61 68 75 82 88 95 102 109 116 123
19 0 4 10 17 23 30 37 44 51 58 65 72 80 87 94 101 109 116 123 130
20 0 4 11 18 25 32 39 47 54 62 69 77 84 92 100 107 115 123 130 138
N1 < N2
Adapted from Robert Johnson, Elementary Statistics, 6th ed. (Boston: PWS-Kent Publishing, 1992), Appendix F-20

A3-10

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