Tables
Page T-1
Page T-2
Table entry for z is the area under the standard Normal curve to the left of z.
Table 1.1: TABLE A Standard Normal probabilities
z |
.00 |
.01 |
.02 |
.03 |
.04 |
.05 |
.06 |
.07 |
.08 |
.09 |
−3.4 |
.0003 |
.0003 |
.0003 |
.0003 |
.0003 |
.0003 |
.0003 |
.0003 |
.0003 |
.0002 |
−3.3 |
.0005 |
.0005 |
.0005 |
.0004 |
.0004 |
.0004 |
.0004 |
.0004 |
.0004 |
.0003 |
−3.2 |
.0007 |
.0007 |
.0006 |
.0006 |
.0006 |
.0006 |
.0006 |
.0005 |
.0005 |
.0005 |
−3.1 |
.0010 |
.0009 |
.0009 |
.0009 |
.0008 |
.0008 |
.0008 |
.0008 |
.0007 |
.0007 |
−3.0 |
.0013 |
.0013 |
.0013 |
.0012 |
.0012 |
.0011 |
.0011 |
.0011 |
.0010 |
.0010 |
−2.9 |
.0019 |
.0018 |
.0018 |
.0017 |
.0016 |
.0016 |
.0015 |
.0015 |
.0014 |
.0014 |
−2.8 |
.0026 |
.0025 |
.0024 |
.0023 |
.0023 |
.0022 |
.0021 |
.0021 |
.0020 |
.0019 |
−2.7 |
.0035 |
.0034 |
.0033 |
.0032 |
.0031 |
.0030 |
.0029 |
.0028 |
.0027 |
.0026 |
−2.6 |
.0047 |
.0045 |
.0044 |
.0043 |
.0041 |
.0040 |
.0039 |
.0038 |
.0037 |
.0036 |
−2.5 |
.0062 |
.0060 |
.0059 |
.0057 |
.0055 |
.0054 |
.0052 |
.0051 |
.0049 |
.0048 |
−2.4 |
.0082 |
.0080 |
.0078 |
.0075 |
.0073 |
.0071 |
.0069 |
.0068 |
.0066 |
.0064 |
−2.3 |
.0107 |
.0104 |
.0102 |
.0099 |
.0096 |
.0094 |
.0091 |
.0089 |
.0087 |
.0084 |
−2.2 |
.0139 |
.0136 |
.0132 |
.0129 |
.0125 |
.0122 |
.0119 |
.0116 |
.0113 |
.0110 |
−2.1 |
.0179 |
.0174 |
.0170 |
.0166 |
.0162 |
.0158 |
.0154 |
.0150 |
.0146 |
.0143 |
−2.0 |
.0228 |
.0222 |
.0217 |
.0212 |
.0207 |
.0202 |
.0197 |
.0192 |
.0188 |
.0183 |
−1.9 |
.0287 |
.0281 |
.0274 |
.0268 |
.0262 |
.0256 |
.0250 |
.0244 |
.0239 |
.0233 |
−1.8 |
.0359 |
.0351 |
.0344 |
.0336 |
.0329 |
.0322 |
.0314 |
.0307 |
.0301 |
.0294 |
−1.7 |
.0446 |
.0436 |
.0427 |
.0418 |
.0409 |
.0401 |
.0392 |
.0384 |
.0375 |
.0367 |
−1.6 |
.0548 |
.0537 |
.0526 |
.0516 |
.0505 |
.0495 |
.0485 |
.0475 |
.0465 |
.0455 |
−1.5 |
.0668 |
.0655 |
.0643 |
.0630 |
.0618 |
.0606 |
.0594 |
.0582 |
.0571 |
.0559 |
−1.4 |
.0808 |
.0793 |
.0778 |
.0764 |
.0749 |
.0735 |
.0721 |
.0708 |
.0694 |
.0681 |
−1.3 |
.0968 |
.0951 |
.0934 |
.0918 |
.0901 |
.0885 |
.0869 |
.0853 |
.0838 |
.0823 |
−1.2 |
.1151 |
.1131 |
.1112 |
.1093 |
.1075 |
.1056 |
.1038 |
.1020 |
.1003 |
.0985 |
−1.1 |
.1357 |
.1335 |
.1314 |
.1292 |
.1271 |
.1251 |
.1230 |
.1210 |
.1190 |
.1170 |
−1.0 |
.1587 |
.1562 |
.1539 |
.1515 |
.1492 |
.1469 |
.1446 |
.1423 |
.1401 |
.1379 |
−0.9 |
.1841 |
.1814 |
.1788 |
.1762 |
.1736 |
.1711 |
.1685 |
.1660 |
.1635 |
.1611 |
−0.8 |
.2119 |
.2090 |
.2061 |
.2033 |
.2005 |
.1977 |
.1949 |
.1922 |
.1894 |
.1867 |
−0.7 |
.2420 |
.2389 |
.2358 |
.2327 |
.2296 |
.2266 |
.2236 |
.2206 |
.2177 |
.2148 |
−0.6 |
.2743 |
.2709 |
.2676 |
.2643 |
.2611 |
.2578 |
.2546 |
.2514 |
.2483 |
.2451 |
−0.5 |
.3085 |
.3050 |
.3015 |
.2981 |
.2946 |
.2912 |
.2877 |
.2843 |
.2810 |
.2776 |
−0.4 |
.3446 |
.3409 |
.3372 |
.3336 |
.3300 |
.3264 |
.3228 |
.3192 |
.3156 |
.3121 |
−0.3 |
.3821 |
.3783 |
.3745 |
.3707 |
.3669 |
.3632 |
.3594 |
.3557 |
.3520 |
.3483 |
−0.2 |
.4207 |
.4168 |
.4129 |
.4090 |
.4052 |
.4013 |
.3974 |
.3936 |
.3897 |
.3859 |
−0.1 |
.4602 |
.4562 |
.4522 |
.4483 |
.4443 |
.4404 |
.4364 |
.4325 |
.4286 |
.4247 |
−0.0 |
.5000 |
.4960 |
.4920 |
.4880 |
.4840 |
.4801 |
.4761 |
.4721 |
.4681 |
.4641 |
Page T-3
|
Table entry for z is the area under the standard Normal curve to the left of z.
|
0.0 |
.5000 |
.5040 |
.5080 |
.5120 |
.5160 |
.5199 |
.5239 |
.5279 |
.5319 |
.5359 |
0.1 |
.5398 |
.5438 |
.5478 |
.5517 |
.5557 |
.5596 |
.5636 |
.5675 |
.5714 |
.5753 |
0.2 |
.5793 |
.5832 |
.5871 |
.5910 |
.5948 |
.5987 |
.6026 |
.6064 |
.6103 |
.6141 |
0.3 |
.6179 |
.6217 |
.6255 |
.6293 |
.6331 |
.6368 |
.6406 |
.6443 |
.6480 |
.6517 |
0.4 |
.6554 |
.6591 |
.6628 |
.6664 |
.6700 |
.6736 |
.6772 |
.6808 |
.6844 |
.6879 |
0.5 |
.6915 |
.6950 |
.6985 |
.7019 |
.7054 |
.7088 |
.7123 |
.7157 |
.7190 |
.7224 |
0.6 |
.7257 |
.7291 |
.7324 |
.7357 |
.7389 |
.7422 |
.7454 |
.7486 |
.7517 |
.7549 |
0.7 |
.7580 |
.7611 |
.7642 |
.7673 |
.7704 |
.7734 |
.7764 |
.7794 |
.7823 |
.7852 |
0.8 |
.7881 |
.7910 |
.7939 |
.7967 |
.7995 |
.8023 |
.8051 |
.8078 |
.8106 |
.8133 |
0.9 |
.8159 |
.8186 |
.8212 |
.8238 |
.8264 |
.8289 |
.8315 |
.8340 |
.8365 |
.8389 |
1.0 |
.8413 |
.8438 |
.8461 |
.8485 |
.8508 |
.8531 |
.8554 |
.8577 |
.8599 |
.8621 |
1.1 |
.8643 |
.8665 |
.8686 |
.8708 |
.8729 |
.8749 |
.8770 |
.8790 |
.8810 |
.8830 |
1.2 |
.8849 |
.8869 |
.8888 |
.8907 |
.8925 |
.8944 |
.8962 |
.8980 |
.8997 |
.9015 |
1.3 |
.9032 |
.9049 |
.9066 |
.9082 |
.9099 |
.9115 |
.9131 |
.9147 |
.9162 |
.9177 |
1.4 |
.9192 |
.9207 |
.9222 |
.9236 |
.9251 |
.9265 |
.9279 |
.9292 |
.9306 |
.9319 |
1.5 |
.9332 |
.9345 |
.9357 |
.9370 |
.9382 |
.9394 |
.9406 |
.9418 |
.9429 |
.9441 |
1.6 |
.9452 |
.9463 |
.9474 |
.9484 |
.9495 |
.9505 |
.9515 |
.9525 |
.9535 |
.9545 |
1.7 |
.9554 |
.9564 |
.9573 |
.9582 |
.9591 |
.9599 |
.9608 |
.9616 |
.9625 |
.9633 |
1.8 |
.9641 |
.9649 |
.9656 |
.9664 |
.9671 |
.9678 |
.9686 |
.9693 |
.9699 |
.9706 |
1.9 |
.9713 |
.9719 |
.9726 |
.9732 |
.9738 |
.9744 |
.9750 |
.9756 |
.9761 |
.9767 |
2.0 |
.9772 |
.9778 |
.9783 |
.9788 |
.9793 |
.9798 |
.9803 |
.9808 |
.9812 |
.9817 |
2.1 |
.9821 |
.9826 |
.9830 |
.9834 |
.9838 |
.9842 |
.9846 |
.9850 |
.9854 |
.9857 |
2.2 |
.9861 |
.9864 |
.9868 |
.9871 |
.9875 |
.9878 |
.9881 |
.9884 |
.9887 |
.9890 |
2.3 |
.9893 |
.9896 |
.9898 |
.9901 |
.9904 |
.9906 |
.9909 |
.9911 |
.9913 |
.9916 |
2.4 |
.9918 |
.9920 |
.9922 |
.9925 |
.9927 |
.9929 |
.9931 |
.9932 |
.9934 |
.9936 |
2.5 |
.9938 |
.9940 |
.9941 |
.9943 |
.9945 |
.9946 |
.9948 |
.9949 |
.9951 |
.9952 |
2.6 |
.9953 |
.9955 |
.9956 |
.9957 |
.9959 |
.9960 |
.9961 |
.9962 |
.9963 |
.9964 |
2.7 |
.9965 |
.9966 |
.9967 |
.9968 |
.9969 |
.9970 |
.9971 |
.9972 |
.9973 |
.9974 |
2.8 |
.9974 |
.9975 |
.9976 |
.9977 |
.9977 |
.9978 |
.9979 |
.9979 |
.9980 |
.9981 |
2.9 |
.9981 |
.9982 |
.9982 |
.9983 |
.9984 |
.9984 |
.9985 |
.9985 |
.9986 |
.9986 |
3.0 |
.9987 |
.9987 |
.9987 |
.9988 |
.9988 |
.9989 |
.9989 |
.9989 |
.9990 |
.9990 |
3.1 |
.9990 |
.9991 |
.9991 |
.9991 |
.9992 |
.9992 |
.9992 |
.9992 |
.9993 |
.9993 |
3.2 |
.9993 |
.9993 |
.9994 |
.9994 |
.9994 |
.9994 |
.9994 |
.9995 |
.9995 |
.9995 |
3.3 |
.9995 |
.9995 |
.9995 |
.9996 |
.9996 |
.9996 |
.9996 |
.9996 |
.9996 |
.9997 |
3.4 |
.9997 |
.9997 |
.9997 |
.9997 |
.9997 |
.9997 |
.9997 |
.9997 |
.9997 |
.9998 |
Page T-4
Table 1.2: TABLE B Random digits
Line |
101 |
19223 |
95034 |
05756 |
28713 |
96409 |
12531 |
42544 |
82853 |
102 |
73676 |
47150 |
99400 |
01927 |
27754 |
42648 |
82425 |
36290 |
103 |
45467 |
71709 |
77558 |
00095 |
32863 |
29485 |
82226 |
90056 |
104 |
52711 |
38889 |
93074 |
60227 |
40011 |
85848 |
48767 |
52573 |
105 |
95592 |
94007 |
69971 |
91481 |
60779 |
53791 |
17297 |
59335 |
106 |
68417 |
35013 |
15529 |
72765 |
85089 |
57067 |
50211 |
47487 |
107 |
82739 |
57890 |
20807 |
47511 |
81676 |
55300 |
94383 |
14893 |
108 |
60940 |
72024 |
17868 |
24943 |
61790 |
90656 |
87964 |
18883 |
109 |
36009 |
19365 |
15412 |
39638 |
85453 |
46816 |
83485 |
41979 |
110 |
38448 |
48789 |
18338 |
24697 |
39364 |
42006 |
76688 |
08708 |
111 |
81486 |
69487 |
60513 |
09297 |
00412 |
71238 |
27649 |
39950 |
112 |
59636 |
88804 |
04634 |
71197 |
19352 |
73089 |
84898 |
45785 |
113 |
62568 |
70206 |
40325 |
03699 |
71080 |
22553 |
11486 |
11776 |
114 |
45149 |
32992 |
75730 |
66280 |
03819 |
56202 |
02938 |
70915 |
115 |
61041 |
77684 |
94322 |
24709 |
73698 |
14526 |
31893 |
32592 |
116 |
14459 |
26056 |
31424 |
80371 |
65103 |
62253 |
50490 |
61181 |
117 |
38167 |
98532 |
62183 |
70632 |
23417 |
26185 |
41448 |
75532 |
118 |
73190 |
32533 |
04470 |
29669 |
84407 |
90785 |
65956 |
86382 |
119 |
95857 |
07118 |
87664 |
92099 |
58806 |
66979 |
98624 |
84826 |
120 |
35476 |
55972 |
39421 |
65850 |
04266 |
35435 |
43742 |
11937 |
121 |
71487 |
09984 |
29077 |
14863 |
61683 |
47052 |
62224 |
51025 |
122 |
13873 |
81598 |
95052 |
90908 |
73592 |
75186 |
87136 |
95761 |
123 |
54580 |
81507 |
27102 |
56027 |
55892 |
33063 |
41842 |
81868 |
124 |
71035 |
09001 |
43367 |
49497 |
72719 |
96758 |
27611 |
91596 |
125 |
96746 |
12149 |
37823 |
71868 |
18442 |
35119 |
62103 |
39244 |
126 |
96927 |
19931 |
36089 |
74192 |
77567 |
88741 |
48409 |
41903 |
127 |
43909 |
99477 |
25330 |
64359 |
40085 |
16925 |
85117 |
36071 |
128 |
15689 |
14227 |
06565 |
14374 |
13352 |
49367 |
81982 |
87209 |
129 |
36759 |
58984 |
68288 |
22913 |
18638 |
54303 |
00795 |
08727 |
130 |
69051 |
64817 |
87174 |
09517 |
84534 |
06489 |
87201 |
97245 |
131 |
05007 |
16632 |
81194 |
14873 |
04197 |
85576 |
45195 |
96565 |
132 |
68732 |
55259 |
84292 |
08796 |
43165 |
93739 |
31685 |
97150 |
133 |
45740 |
41807 |
65561 |
33302 |
07051 |
93623 |
18132 |
09547 |
134 |
27816 |
78416 |
18329 |
21337 |
35213 |
37741 |
04312 |
68508 |
135 |
66925 |
55658 |
39100 |
78458 |
11206 |
19876 |
87151 |
31260 |
136 |
08421 |
44753 |
77377 |
28744 |
75592 |
08563 |
79140 |
92454 |
137 |
53645 |
66812 |
61421 |
47836 |
12609 |
15373 |
98481 |
14592 |
138 |
66831 |
68908 |
40772 |
21558 |
47781 |
33586 |
79177 |
06928 |
139 |
55588 |
99404 |
70708 |
41098 |
43563 |
56934 |
48394 |
51719 |
140 |
12975 |
13258 |
13048 |
45144 |
72321 |
81940 |
00360 |
02428 |
141 |
96767 |
35964 |
23822 |
96012 |
94591 |
65194 |
50842 |
53372 |
142 |
72829 |
50232 |
97892 |
63408 |
77919 |
44575 |
24870 |
04178 |
143 |
88565 |
42628 |
17797 |
49376 |
61762 |
16953 |
88604 |
12724 |
144 |
62964 |
88145 |
83083 |
69453 |
46109 |
59505 |
69680 |
00900 |
145 |
19687 |
12633 |
57857 |
95806 |
09931 |
02150 |
43163 |
58636 |
146 |
37609 |
59057 |
66967 |
83401 |
60705 |
02384 |
90597 |
93600 |
147 |
54973 |
86278 |
88737 |
74351 |
47500 |
84552 |
19909 |
67181 |
148 |
00694 |
05977 |
19664 |
65441 |
20903 |
62371 |
22725 |
53340 |
149 |
71546 |
05233 |
53946 |
68743 |
72460 |
27601 |
45403 |
88692 |
150 |
07511 |
88915 |
41267 |
16853 |
84569 |
79367 |
32337 |
03316 |
Page T-5
|
151 |
03802 |
29341 |
29264 |
80198 |
12371 |
13121 |
54969 |
43912 |
152 |
77320 |
35030 |
77519 |
41109 |
98296 |
18984 |
60869 |
12349 |
153 |
07886 |
56866 |
39648 |
69290 |
03600 |
05376 |
58958 |
22720 |
154 |
87065 |
74133 |
21117 |
70595 |
22791 |
67306 |
28420 |
52067 |
155 |
42090 |
09628 |
54035 |
93879 |
98441 |
04606 |
27381 |
82637 |
156 |
55494 |
67690 |
88131 |
81800 |
11188 |
28552 |
25752 |
21953 |
157 |
16698 |
30406 |
96587 |
65985 |
07165 |
50148 |
16201 |
86792 |
158 |
16297 |
07626 |
68683 |
45335 |
34377 |
72941 |
41764 |
77038 |
159 |
22897 |
17467 |
17638 |
70043 |
36243 |
13008 |
83993 |
22869 |
160 |
98163 |
45944 |
34210 |
64158 |
76971 |
27689 |
82926 |
75957 |
161 |
43400 |
25831 |
06283 |
22138 |
16043 |
15706 |
73345 |
26238 |
162 |
97341 |
46254 |
88153 |
62336 |
21112 |
35574 |
99271 |
45297 |
163 |
64578 |
67197 |
28310 |
90341 |
37531 |
63890 |
52630 |
76315 |
164 |
11022 |
79124 |
49525 |
63078 |
17229 |
32165 |
01343 |
21394 |
165 |
81232 |
43939 |
23840 |
05995 |
84589 |
06788 |
76358 |
26622 |
166 |
36843 |
84798 |
51167 |
44728 |
20554 |
55538 |
27647 |
32708 |
167 |
84329 |
80081 |
69516 |
78934 |
14293 |
92478 |
16479 |
26974 |
168 |
27788 |
85789 |
41592 |
74472 |
96773 |
27090 |
24954 |
41474 |
169 |
99224 |
00850 |
43737 |
75202 |
44753 |
63236 |
14260 |
73686 |
170 |
38075 |
73239 |
52555 |
46342 |
13365 |
02182 |
30443 |
53229 |
171 |
87368 |
49451 |
55771 |
48343 |
51236 |
18522 |
73670 |
23212 |
172 |
40512 |
00681 |
44282 |
47178 |
08139 |
78693 |
34715 |
75606 |
173 |
81636 |
57578 |
54286 |
27216 |
58758 |
80358 |
84115 |
84568 |
174 |
26411 |
94292 |
06340 |
97762 |
37033 |
85968 |
94165 |
46514 |
175 |
80011 |
09937 |
57195 |
33906 |
94831 |
10056 |
42211 |
65491 |
176 |
92813 |
87503 |
63494 |
71379 |
76550 |
45984 |
05481 |
50830 |
177 |
70348 |
72871 |
63419 |
57363 |
29685 |
43090 |
18763 |
31714 |
178 |
24005 |
52114 |
26224 |
39078 |
80798 |
15220 |
43186 |
00976 |
179 |
85063 |
55810 |
10470 |
08029 |
30025 |
29734 |
61181 |
72090 |
180 |
11532 |
73186 |
92541 |
06915 |
72954 |
10167 |
12142 |
26492 |
181 |
59618 |
03914 |
05208 |
84088 |
20426 |
39004 |
84582 |
87317 |
182 |
92965 |
50837 |
39921 |
84661 |
82514 |
81899 |
24565 |
60874 |
183 |
85116 |
27684 |
14597 |
85747 |
01596 |
25889 |
41998 |
15635 |
184 |
15106 |
10411 |
90221 |
49377 |
44369 |
28185 |
80959 |
76355 |
185 |
03638 |
31589 |
07871 |
25792 |
85823 |
55400 |
56026 |
12193 |
186 |
97971 |
48932 |
45792 |
63993 |
95635 |
28753 |
46069 |
84635 |
187 |
49345 |
18305 |
76213 |
82390 |
77412 |
97401 |
50650 |
71755 |
188 |
87370 |
88099 |
89695 |
87633 |
76987 |
85503 |
26257 |
51736 |
189 |
88296 |
95670 |
74932 |
65317 |
93848 |
43988 |
47597 |
83044 |
190 |
79485 |
92200 |
99401 |
54473 |
34336 |
82786 |
05457 |
60343 |
191 |
40830 |
24979 |
23333 |
37619 |
56227 |
95941 |
59494 |
86539 |
192 |
32006 |
76302 |
81221 |
00693 |
95197 |
75044 |
46596 |
11628 |
193 |
37569 |
85187 |
44692 |
50706 |
53161 |
69027 |
88389 |
60313 |
194 |
56680 |
79003 |
23361 |
67094 |
15019 |
63261 |
24543 |
52884 |
195 |
05172 |
08100 |
22316 |
54495 |
60005 |
29532 |
18433 |
18057 |
196 |
74782 |
27005 |
03894 |
98038 |
20627 |
40307 |
47317 |
92759 |
197 |
85288 |
93264 |
61409 |
03404 |
09649 |
55937 |
60843 |
66167 |
198 |
68309 |
12060 |
14762 |
58002 |
03716 |
81968 |
57934 |
32624 |
199 |
26461 |
88346 |
52430 |
60906 |
74216 |
96263 |
69296 |
90107 |
200 |
42672 |
67680 |
42376 |
95023 |
82744 |
03971 |
96560 |
55148 |
Page T-6
Table 1.3: TABLE C Binomial probabilities
|
|
Entry is P(X=k)=(nk)pk(1−p)n−k
|
n |
k |
.01 |
.02 |
.03 |
.04 |
.05 |
.06 |
.07 |
.08 |
.09 |
.10 |
.15 |
.20 |
.25 |
.30 |
.35 |
.40 |
.45 |
.50 |
2 |
0 |
.9801 |
.9604 |
.9409 |
.9216 |
.9025 |
.8836 |
.8649 |
.8464 |
.8281 |
.8100 |
.7225 |
.6400 |
.5625 |
.4900 |
.4225 |
.3600 |
.3025 |
.2500 |
|
1 |
.0198 |
.0392 |
.0582 |
.0768 |
.0950 |
.1128 |
.1302 |
.1472 |
.1638 |
.1800 |
.2550 |
.3200 |
.3750 |
.4200 |
.4550 |
.4800 |
.4950 |
.5000 |
|
2 |
.0001 |
.0004 |
.0009 |
.0016 |
.0025 |
.0036 |
.0049 |
.0064 |
.0081 |
.0100 |
.0225 |
.0400 |
.0625 |
.0900 |
.1225 |
.1600 |
.2025 |
.2500 |
3 |
0 |
.9703 |
.9412 |
.9127 |
.8847 |
.8574 |
.8306 |
.8044 |
.7787 |
.7536 |
.7290 |
.6141 |
.5120 |
.4219 |
.3430 |
.2746 |
.2160 |
.1664 |
.1250 |
|
1 |
.0294 |
.0576 |
.0847 |
.1106 |
.1354 |
.1590 |
.1816 |
.2031 |
.2236 |
.2430 |
.3251 |
.3840 |
.4219 |
.4410 |
.4436 |
.4320 |
.4084 |
.3750 |
|
2 |
.0003 |
.0012 |
.0026 |
.0046 |
.0071 |
.0102 |
.0137 |
.0177 |
.0221 |
.0270 |
.0574 |
.0960 |
.1406 |
.1890 |
.2389 |
.2880 |
.3341 |
.3750 |
|
3 |
|
|
|
.0001 |
.0001 |
.0002 |
.0003 |
.0005 |
.0007 |
.0010 |
.0034 |
.0080 |
.0156 |
.0270 |
.0429 |
.0640 |
.0911 |
.1250 |
4 |
0 |
.9606 |
.9224 |
.8853 |
.8493 |
.8145 |
.7807 |
.7481 |
.7164 |
.6857 |
.6561 |
.5220 |
.4096 |
.3164 |
.2401 |
.1785 |
.1296 |
.0915 |
.0625 |
|
1 |
.0388 |
.0753 |
.1095 |
.1416 |
.1715 |
.1993 |
.2252 |
.2492 |
.2713 |
.2916 |
.3685 |
.4096 |
.4219 |
.4116 |
.3845 |
.3456 |
.2995 |
.2500 |
|
2 |
.0006 |
.0023 |
.0051 |
.0088 |
.0135 |
.0191 |
.0254 |
.0325 |
.0402 |
.0486 |
.0975 |
.1536 |
.2109 |
.2646 |
.3105 |
.3456 |
.3675 |
.3750 |
|
3 |
|
|
.0001 |
.0002 |
.0005 |
.0008 |
.0013 |
.0019 |
.0027 |
.0036 |
.0115 |
.0256 |
.0469 |
.0756 |
.1115 |
.1536 |
.2005 |
.2500 |
|
4 |
|
|
|
|
|
|
|
|
.0001 |
.0001 |
.0005 |
.0016 |
.0039 |
.0081 |
.0150 |
.0256 |
.0410 |
.0625 |
5 |
0 |
.9510 |
.9039 |
.8587 |
.8154 |
.7738 |
.7339 |
.6957 |
.6591 |
.6240 |
.5905 |
.4437 |
.3277 |
.2373 |
.1681 |
.1160 |
.0778 |
.0503 |
.0313 |
|
1 |
.0480 |
.0922 |
.1328 |
.1699 |
.2036 |
.2342 |
.2618 |
.2866 |
.3086 |
.3280 |
.3915 |
.4096 |
.3955 |
.3602 |
.3124 |
.2592 |
.2059 |
.1563 |
|
2 |
.0010 |
.0038 |
.0082 |
.0142 |
.0214 |
.0299 |
.0394 |
.0498 |
.0610 |
.0729 |
.1382 |
.2048 |
.2637 |
.3087 |
.3364 |
.3456 |
.3369 |
.3125 |
|
3 |
|
.0001 |
.0003 |
.0006 |
.0011 |
.0019 |
.0030 |
.0043 |
.0060 |
.0081 |
.0244 |
.0512 |
.0879 |
.1323 |
.1811 |
.2304 |
.2757 |
.3125 |
|
4 |
|
|
|
|
|
.0001 |
.0001 |
.0002 |
.0003 |
.0004 |
.0022 |
.0064 |
.0146 |
.0284 |
.0488 |
.0768 |
.1128 |
.1562 |
|
5 |
|
|
|
|
|
|
|
|
|
|
.0001 |
.0003 |
.0010 |
.0024 |
.0053 |
.0102 |
.0185 |
.0312 |
6 |
0 |
.9415 |
.8858 |
.8330 |
.7828 |
.7351 |
.6899 |
.6470 |
.6064 |
.5679 |
.5314 |
.3771 |
.2621 |
.1780 |
.1176 |
.0754 |
.0467 |
.0277 |
.0156 |
|
1 |
.0571 |
.1085 |
.1546 |
.1957 |
.2321 |
.2642 |
.2922 |
.3164 |
.3370 |
.3543 |
.3993 |
.3932 |
.3560 |
.3025 |
.2437 |
.1866 |
.1359 |
.0938 |
|
2 |
.0014 |
.0055 |
.0120 |
.0204 |
.0305 |
.0422 |
.0550 |
.0688 |
.0833 |
.0984 |
.1762 |
.2458 |
.2966 |
.3241 |
.3280 |
.3110 |
.2780 |
.2344 |
|
3 |
|
.0002 |
.0005 |
.0011 |
.0021 |
.0036 |
.0055 |
.0080 |
.0110 |
.0146 |
.0415 |
.0819 |
.1318 |
.1852 |
.2355 |
.2765 |
.3032 |
.3125 |
|
4 |
|
|
|
|
.0001 |
.0002 |
.0003 |
.0005 |
.0008 |
.0012 |
.0055 |
.0154 |
.0330 |
.0595 |
.0951 |
.1382 |
.1861 |
.2344 |
|
5 |
|
|
|
|
|
|
|
|
|
.0001 |
.0004 |
.0015 |
.0044 |
.0102 |
.0205 |
.0369 |
.0609 |
.0937 |
|
6 |
|
|
|
|
|
|
|
|
|
|
|
.0001 |
.0002 |
.0007 |
.0018 |
.0041 |
.0083 |
.0156 |
7 |
0 |
.9321 |
.8681 |
.8080 |
.7514 |
.6983 |
.6485 |
.6017 |
.5578 |
.5168 |
.4783 |
.3206 |
.2097 |
.1335 |
.0824 |
.0490 |
.0280 |
.0152 |
.0078 |
|
1 |
.0659 |
.1240 |
.1749 |
.2192 |
.2573 |
.2897 |
.3170 |
.3396 |
.3578 |
.3720 |
.3960 |
.3670 |
.3115 |
.2471 |
.1848 |
.1306 |
.0872 |
.0547 |
|
2 |
.0020 |
.0076 |
.0162 |
.0274 |
.0406 |
.0555 |
.0716 |
.0886 |
.1061 |
.1240 |
.2097 |
.2753 |
.3115 |
.3177 |
.2985 |
.2613 |
.2140 |
.1641 |
|
3 |
|
.0003 |
.0008 |
.0019 |
.0036 |
.0059 |
.0090 |
.0128 |
.0175 |
.0230 |
.0617 |
.1147 |
.1730 |
.2269 |
.2679 |
.2903 |
.2918 |
.2734 |
|
4 |
|
|
|
.0001 |
.0002 |
.0004 |
.0007 |
.0011 |
.0017 |
.0026 |
.0109 |
.0287 |
.0577 |
.0972 |
.1442 |
.1935 |
.2388 |
.2734 |
|
5 |
|
|
|
|
|
|
|
.0001 |
.0001 |
.0002 |
.0012 |
.0043 |
.0115 |
.0250 |
.0466 |
.0774 |
.1172 |
.1641 |
|
6 |
|
|
|
|
|
|
|
|
|
|
.0001 |
.0004 |
.0013 |
.0036 |
.0084 |
.0172 |
.0320 |
.0547 |
|
7 |
|
|
|
|
|
|
|
|
|
|
|
|
.0001 |
.0002 |
.0006 |
.0016 |
.0037 |
.0078 |
8 |
0 |
.9227 |
.8508 |
.7837 |
.7214 |
.6634 |
.6096 |
.5596 |
.5132 |
.4703 |
.4305 |
.2725 |
.1678 |
.1001 |
.0576 |
.0319 |
.0168 |
.0084 |
.0039 |
|
1 |
.0746 |
.1389 |
.1939 |
.2405 |
.2793 |
.3113 |
.3370 |
.3570 |
.3721 |
.3826 |
.3847 |
.3355 |
.2670 |
.1977 |
.1373 |
.0896 |
.0548 |
.0313 |
|
2 |
.0026 |
.0099 |
.0210 |
.0351 |
.0515 |
.0695 |
.0888 |
.1087 |
.1288 |
.1488 |
.2376 |
.2936 |
.3115 |
.2965 |
.2587 |
.2090 |
.1569 |
.1094 |
|
3 |
.0001 |
.0004 |
.0013 |
.0029 |
.0054 |
.0089 |
.0134 |
.0189 |
.0255 |
.0331 |
.0839 |
.1468 |
.2076 |
.2541 |
.2786 |
.2787 |
.2568 |
.2188 |
|
4 |
|
|
.0001 |
.0002 |
.0004 |
.0007 |
.0013 |
.0021 |
.0031 |
.0046 |
.0185 |
.0459 |
.0865 |
.1361 |
.1875 |
.2322 |
.2627 |
.2734 |
|
5 |
|
|
|
|
|
|
.0001 |
.0001 |
.0002 |
.0004 |
.0026 |
.0092 |
.0231 |
.0467 |
.0808 |
.1239 |
.1719 |
.2188 |
|
6 |
|
|
|
|
|
|
|
|
|
|
.0002 |
.0011 |
.0038 |
.0100 |
.0217 |
.0413 |
.0703 |
.1094 |
|
7 |
|
|
|
|
|
|
|
|
|
|
|
.0001 |
.0004 |
.0012 |
.0033 |
.0079 |
.0164 |
.0312 |
|
8 |
|
|
|
|
|
|
|
|
|
|
|
|
|
.0001 |
.0002 |
.0007 |
.0017 |
.0039 |
9 |
0 |
.9135 |
.8337 |
.7602 |
.6925 |
.6302 |
.5730 |
.5204 |
.4722 |
.4279 |
.3874 |
.2316 |
.1342 |
.0751 |
.0404 |
.0207 |
.0101 |
.0046 |
.0020 |
|
1 |
.0830 |
.1531 |
.2116 |
.2597 |
.2985 |
.3292 |
.3525 |
.3695 |
.3809 |
.3874 |
.3679 |
.3020 |
.2253 |
.1556 |
.1004 |
.0605 |
.0339 |
.0176 |
|
2 |
.0034 |
.0125 |
.0262 |
.0433 |
.0629 |
.0840 |
.1061 |
.1285 |
.1507 |
.1722 |
.2597 |
.3020 |
.3003 |
.2668 |
.2162 |
.1612 |
.1110 |
.0703 |
|
3 |
.0001 |
.0006 |
.0019 |
.0042 |
.0077 |
.0125 |
.0186 |
.0261 |
.0348 |
.0446 |
.1069 |
.1762 |
.2336 |
.2668 |
.2716 |
.2508 |
.2119 |
.1641 |
|
4 |
|
|
.0001 |
.0003 |
.0006 |
.0012 |
.0021 |
.0034 |
.0052 |
.0074 |
.0283 |
.0661 |
.1168 |
.1715 |
.2194 |
.2508 |
.2600 |
.2461 |
|
5 |
|
|
|
|
|
.0001 |
.0002 |
.0003 |
.0005 |
.0008 |
.0050 |
.0165 |
.0389 |
.0735 |
.1181 |
.1672 |
.2128 |
.2461 |
|
6 |
|
|
|
|
|
|
|
|
|
.0001 |
.0006 |
.0028 |
.0087 |
.0210 |
.0424 |
.0743 |
.1160 |
.1641 |
|
7 |
|
|
|
|
|
|
|
|
|
|
|
.0003 |
.0012 |
.0039 |
.0098 |
.0212 |
.0407 |
.0703 |
|
8 |
|
|
|
|
|
|
|
|
|
|
|
|
.0001 |
.0004 |
.0013 |
.0035 |
.0083 |
.0176 |
|
9 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
.0001 |
.0003 |
.0008 |
.0020 |
10 |
0 |
.9044 |
.8171 |
.7374 |
.6648 |
.5987 |
.5386 |
.4840 |
.4344 |
.3894 |
.3487 |
.1969 |
.1074 |
.0563 |
.0282 |
.0135 |
.0060 |
.0025 |
.0010 |
|
1 |
.0914 |
.1667 |
.2281 |
.2770 |
.3151 |
.3438 |
.3643 |
.3777 |
.3851 |
.3874 |
.3474 |
.2684 |
.1877 |
.1211 |
.0725 |
.0403 |
.0207 |
.0098 |
|
2 |
.0042 |
.0153 |
.0317 |
.0519 |
.0746 |
.0988 |
.1234 |
.1478 |
.1714 |
.1937 |
.2759 |
.3020 |
.2816 |
.2335 |
.1757 |
.1209 |
.0763 |
.0439 |
|
3 |
.0001 |
.0008 |
.0026 |
.0058 |
.0105 |
.0168 |
.0248 |
.0343 |
.0452 |
.0574 |
.1298 |
.2013 |
.2503 |
.2668 |
.2522 |
.2150 |
.1665 |
.1172 |
|
4 |
|
|
.0001 |
.0004 |
.0010 |
.0019 |
.0033 |
.0052 |
.0078 |
.0112 |
.0401 |
.0881 |
.1460 |
.2001 |
.2377 |
.2508 |
.2384 |
.2051 |
|
5 |
|
|
|
|
.0001 |
.0001 |
.0003 |
.0005 |
.0009 |
.0015 |
.0085 |
.0264 |
.0584 |
.1029 |
.1536 |
.2007 |
.2340 |
.2461 |
|
6 |
|
|
|
|
|
|
|
|
.0001 |
.0001 |
.0012 |
.0055 |
.0162 |
.0368 |
.0689 |
.1115 |
.1596 |
.2051 |
|
7 |
|
|
|
|
|
|
|
|
|
|
.0001 |
.0008 |
.0031 |
.0090 |
.0212 |
.0425 |
.0746 |
.1172 |
|
8 |
|
|
|
|
|
|
|
|
|
|
|
.0001 |
.0004 |
.0014 |
.0043 |
.0106 |
.0229 |
.0439 |
|
9 |
|
|
|
|
|
|
|
|
|
|
|
|
|
.0001 |
.0005 |
.0016 |
.0042 |
.0098 |
|
10 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
.0001 |
.0003 |
.0010 |
12 |
0 |
.8864 |
.7847 |
.6938 |
.6127 |
.5404 |
.4759 |
.4186 |
.3677 |
.3225 |
.2824 |
.1422 |
.0687 |
.0317 |
.0138 |
.0057 |
.0022 |
.0008 |
.0002 |
|
1 |
.1074 |
.1922 |
.2575 |
.3064 |
.3413 |
.3645 |
.3781 |
.3837 |
.3827 |
.3766 |
.3012 |
.2062 |
.1267 |
.0712 |
.0368 |
.0174 |
.0075 |
.0029 |
|
2 |
.0060 |
.0216 |
.0438 |
.0702 |
.0988 |
.1280 |
.1565 |
.1835 |
.2082 |
.2301 |
.2924 |
.2835 |
.2323 |
.1678 |
.1088 |
.0639 |
.0339 |
.0161 |
|
3 |
.0002 |
.0015 |
.0045 |
.0098 |
.0173 |
.0272 |
.0393 |
.0532 |
.0686 |
.0852 |
.1720 |
.2362 |
.2581 |
.2397 |
.1954 |
.1419 |
.0923 |
.0537 |
|
4 |
|
.0001 |
.0003 |
.0009 |
.0021 |
.0039 |
.0067 |
.0104 |
.0153 |
.0213 |
.0683 |
.1329 |
.1936 |
.2311 |
.2367 |
.2128 |
.1700 |
.1208 |
|
5 |
|
|
|
.0001 |
.0002 |
.0004 |
.0008 |
.0014 |
.0024 |
.0038 |
.0193 |
.0532 |
.1032 |
.1585 |
.2039 |
.2270 |
.2225 |
.1934 |
|
6 |
|
|
|
|
|
|
.0001 |
.0001 |
.0003 |
.0005 |
.0040 |
.0155 |
.0401 |
.0792 |
.1281 |
.1766 |
.2124 |
.2256 |
|
7 |
|
|
|
|
|
|
|
|
|
|
.0006 |
.0033 |
.0115 |
.0291 |
.0591 |
.1009 |
.1489 |
.1934 |
|
8 |
|
|
|
|
|
|
|
|
|
|
.0001 |
.0005 |
.0024 |
.0078 |
.0199 |
.0420 |
.0762 |
.1208 |
|
9 |
|
|
|
|
|
|
|
|
|
|
|
.0001 |
.0004 |
.0015 |
.0048 |
.0125 |
.0277 |
.0537 |
|
10 |
|
|
|
|
|
|
|
|
|
|
|
|
|
.0002 |
.0008 |
.0025 |
.0068 |
.0161 |
|
11 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
.0001 |
.0003 |
.0010 |
.0029 |
|
12 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
.0001 |
.0002 |
15 |
0 |
.8601 |
.7386 |
.6333 |
.5421 |
.4633 |
.3953 |
.3367 |
.2863 |
.2430 |
.2059 |
.0874 |
.0352 |
.0134 |
.0047 |
.0016 |
.0005 |
.0001 |
.0000 |
|
1 |
.1303 |
.2261 |
.2938 |
.3388 |
.3658 |
.3785 |
.3801 |
.3734 |
.3605 |
.3432 |
.2312 |
.1319 |
.0668 |
.0305 |
.0126 |
.0047 |
.0016 |
.0005 |
|
2 |
.0092 |
.0323 |
.0636 |
.0988 |
.1348 |
.1691 |
.2003 |
.2273 |
.2496 |
.2669 |
.2856 |
.2309 |
.1559 |
.0916 |
.0476 |
.0219 |
.0090 |
.0032 |
|
3 |
.0004 |
.0029 |
.0085 |
.0178 |
.0307 |
.0468 |
.0653 |
.0857 |
.1070 |
.1285 |
.2184 |
.2501 |
.2252 |
.1700 |
.1110 |
.0634 |
.0318 |
.0139 |
|
4 |
|
.0002 |
.0008 |
.0022 |
.0049 |
.0090 |
.0148 |
.0223 |
.0317 |
.0428 |
.1156 |
.1876 |
.2252 |
.2186 |
.1792 |
.1268 |
.0780 |
.0417 |
|
5 |
|
|
.0001 |
.0002 |
.0006 |
.0013 |
.0024 |
.0043 |
.0069 |
.0105 |
.0449 |
.1032 |
.1651 |
.2061 |
.2123 |
.1859 |
.1404 |
.0916 |
|
6 |
|
|
|
|
|
.0001 |
.0003 |
.0006 |
.0011 |
.0019 |
.0132 |
.0430 |
.0917 |
.1472 |
.1906 |
.2066 |
.1914 |
.1527 |
|
7 |
|
|
|
|
|
|
|
.0001 |
.0001 |
.0003 |
.0030 |
.0138 |
.0393 |
.0811 |
.1319 |
.1771 |
.2013 |
.1964 |
|
8 |
|
|
|
|
|
|
|
|
|
|
.0005 |
.0035 |
.0131 |
.0348 |
.0710 |
.1181 |
.1647 |
.1964 |
|
9 |
|
|
|
|
|
|
|
|
|
|
.0001 |
.0007 |
.0034 |
.0116 |
.0298 |
.0612 |
.1048 |
.1527 |
|
10 |
|
|
|
|
|
|
|
|
|
|
|
.0001 |
.0007 |
.0030 |
.0096 |
.0245 |
.0515 |
.0916 |
|
11 |
|
|
|
|
|
|
|
|
|
|
|
|
.0001 |
.0006 |
.0024 |
.0074 |
.0191 |
.0417 |
|
12 |
|
|
|
|
|
|
|
|
|
|
|
|
|
.0001 |
.0004 |
.0016 |
.0052 |
.0139 |
|
13 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
.0001 |
.0003 |
.0010 |
.0032 |
|
14 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
.0001 |
.0005 |
|
15 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20 |
0 |
.8179 |
.6676 |
.5438 |
.4420 |
.3585 |
.2901 |
.2342 |
.1887 |
.1516 |
.1216 |
.0388 |
.0115 |
.0032 |
.0008 |
.0002 |
.0000 |
.0000 |
.0000 |
|
1 |
.1652 |
.2725 |
.3364 |
.3683 |
.3774 |
.3703 |
.3526 |
.3282 |
.3000 |
.2702 |
.1368 |
.0576 |
.0211 |
.0068 |
.0020 |
.0005 |
.0001 |
.0000 |
|
2 |
.0159 |
.0528 |
.0988 |
.1458 |
.1887 |
.2246 |
.2521 |
.2711 |
.2818 |
.2852 |
.2293 |
.1369 |
.0669 |
.0278 |
.0100 |
.0031 |
.0008 |
.0002 |
|
3 |
.0010 |
.0065 |
.0183 |
.0364 |
.0596 |
.0860 |
.1139 |
.1414 |
.1672 |
.1901 |
.2428 |
.2054 |
.1339 |
.0716 |
.0323 |
.0123 |
.0040 |
.0011 |
|
4 |
|
.0006 |
.0024 |
.0065 |
.0133 |
.0233 |
.0364 |
.0523 |
.0703 |
.0898 |
.1821 |
.2182 |
.1897 |
.1304 |
.0738 |
.0350 |
.0139 |
.0046 |
|
5 |
|
|
.0002 |
.0009 |
.0022 |
.0048 |
.0088 |
.0145 |
.0222 |
.0319 |
.1028 |
.1746 |
.2023 |
.1789 |
.1272 |
.0746 |
.0365 |
.0148 |
|
6 |
|
|
|
.0001 |
.0003 |
.0008 |
.0017 |
.0032 |
.0055 |
.0089 |
.0454 |
.1091 |
.1686 |
.1916 |
.1712 |
.1244 |
.0746 |
.0370 |
|
7 |
|
|
|
|
|
.0001 |
.0002 |
.0005 |
.0011 |
.0020 |
.0160 |
.0545 |
.1124 |
.1643 |
.1844 |
.1659 |
.1221 |
.0739 |
|
8 |
|
|
|
|
|
|
|
.0001 |
.0002 |
.0004 |
.0046 |
.0222 |
.0609 |
.1144 |
.1614 |
.1797 |
.1623 |
.1201 |
|
9 |
|
|
|
|
|
|
|
|
|
.0001 |
.0011 |
.0074 |
.0271 |
.0654 |
.1158 |
.1597 |
.1771 |
.1602 |
|
10 |
|
|
|
|
|
|
|
|
|
|
.0002 |
.0020 |
.0099 |
.0308 |
.0686 |
.1171 |
.1593 |
.1762 |
|
11 |
|
|
|
|
|
|
|
|
|
|
|
.0005 |
.0030 |
.0120 |
.0336 |
.0710 |
.1185 |
.1602 |
|
12 |
|
|
|
|
|
|
|
|
|
|
|
.0001 |
.0008 |
.0039 |
.0136 |
.0355 |
.0727 |
.1201 |
|
13 |
|
|
|
|
|
|
|
|
|
|
|
|
.0002 |
.0010 |
.0045 |
.0146 |
.0366 |
.0739 |
|
14 |
|
|
|
|
|
|
|
|
|
|
|
|
|
.0002 |
.0012 |
.0049 |
.0150 |
.0370 |
|
15 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
.0003 |
.0013 |
.0049 |
.0148 |
|
16 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
.0003 |
.0013 |
.0046 |
|
17 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
.0002 |
.0011 |
|
18 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
.0002 |
|
19 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Page T-7
Page T-8
Page T-9
Page T-10
Page T-11
Table entry for p and C is the critical value t* with probability p lying to its right and probability C lying between −t* and t*.
Table 1.4: TABLE D t distribution critical values
|
Upper tail probability p
|
df |
.25 |
.20 |
.15 |
.10 |
.05 |
.025 |
.02 |
.01 |
.005 |
.0025 |
.001 |
.0005 |
1 |
1.000 |
1.376 |
1.963 |
3.078 |
6.314 |
12.71 |
15.89 |
31.82 |
63.66 |
127.3 |
318.3 |
636.6 |
2 |
0.816 |
1.061 |
1.386 |
1.886 |
2.920 |
4.303 |
4.849 |
6.965 |
9.925 |
14.09 |
22.33 |
31.60 |
3 |
0.765 |
0.978 |
1.250 |
1.638 |
2.353 |
3.182 |
3.482 |
4.541 |
5.841 |
7.453 |
10.21 |
12.92 |
4 |
0.741 |
0.941 |
1.190 |
1.533 |
2.132 |
2.776 |
2.999 |
3.747 |
4.604 |
5.598 |
7.173 |
8.610 |
5 |
0.727 |
0.920 |
1.156 |
1.476 |
2.015 |
2.571 |
2.757 |
3.365 |
4.032 |
4.773 |
5.893 |
6.869 |
6 |
0.718 |
0.906 |
1.134 |
1.440 |
1.943 |
2.447 |
2.612 |
3.143 |
3.707 |
4.317 |
5.208 |
5.959 |
7 |
0.711 |
0.896 |
1.119 |
1.415 |
1.895 |
2.365 |
2.517 |
2.998 |
3.499 |
4.029 |
4.785 |
5.408 |
8 |
0.706 |
0.889 |
1.108 |
1.397 |
1.860 |
2.306 |
2.449 |
2.896 |
3.355 |
3.833 |
4.501 |
5.041 |
9 |
0.703 |
0.883 |
1.100 |
1.383 |
1.833 |
2.262 |
2.398 |
2.821 |
3.250 |
3.690 |
4.297 |
4.781 |
10 |
0.700 |
0.879 |
1.093 |
1.372 |
1.812 |
2.228 |
2.359 |
2.764 |
3.169 |
3.581 |
4.144 |
4.587 |
11 |
0.697 |
0.876 |
1.088 |
1.363 |
1.796 |
2.201 |
2.328 |
2.718 |
3.106 |
3.497 |
4.025 |
4.437 |
12 |
0.695 |
0.873 |
1.083 |
1.356 |
1.782 |
2.179 |
2.303 |
2.681 |
3.055 |
3.428 |
3.930 |
4.318 |
13 |
0.694 |
0.870 |
1.079 |
1.350 |
1.771 |
2.160 |
2.282 |
2.650 |
3.012 |
3.372 |
3.852 |
4.221 |
14 |
0.692 |
0.868 |
1.076 |
1.345 |
1.761 |
2.145 |
2.264 |
2.624 |
2.977 |
3.326 |
3.787 |
4.140 |
15 |
0.691 |
0.866 |
1.074 |
1.341 |
1.753 |
2.131 |
2.249 |
2.602 |
2.947 |
3.286 |
3.733 |
4.073 |
16 |
0.690 |
0.865 |
1.071 |
1.337 |
1.746 |
2.120 |
2.235 |
2.583 |
2.921 |
3.252 |
3.686 |
4.015 |
17 |
0.689 |
0.863 |
1.069 |
1.333 |
1.740 |
2.110 |
2.224 |
2.567 |
2.898 |
3.222 |
3.646 |
3.965 |
18 |
0.688 |
0.862 |
1.067 |
1.330 |
1.734 |
2.101 |
2.214 |
2.552 |
2.878 |
3.197 |
3.611 |
3.922 |
19 |
0.688 |
0.861 |
1.066 |
1.328 |
1.729 |
2.093 |
2.205 |
2.539 |
2.861 |
3.174 |
3.579 |
3.883 |
20 |
0.687 |
0.860 |
1.064 |
1.325 |
1.725 |
2.086 |
2.197 |
2.528 |
2.845 |
3.153 |
3.552 |
3.850 |
21 |
0.686 |
0.859 |
1.063 |
1.323 |
1.721 |
2.080 |
2.189 |
2.518 |
2.831 |
3.135 |
3.527 |
3.819 |
22 |
0.686 |
0.858 |
1.061 |
1.321 |
1.717 |
2.074 |
2.183 |
2.508 |
2.819 |
3.119 |
3.505 |
3.792 |
23 |
0.685 |
0.858 |
1.060 |
1.319 |
1.714 |
2.069 |
2.177 |
2.500 |
2.807 |
3.104 |
3.485 |
3.768 |
24 |
0.685 |
0.857 |
1.059 |
1.318 |
1.711 |
2.064 |
2.172 |
2.492 |
2.797 |
3.091 |
3.467 |
3.745 |
25 |
0.684 |
0.856 |
1.058 |
1.316 |
1.708 |
2.060 |
2.167 |
2.485 |
2.787 |
3.078 |
3.450 |
3.725 |
26 |
0.684 |
0.856 |
1.058 |
1.315 |
1.706 |
2.056 |
2.162 |
2.479 |
2.779 |
3.067 |
3.435 |
3.707 |
27 |
0.684 |
0.855 |
1.057 |
1.314 |
1.703 |
2.052 |
2.158 |
2.473 |
2.771 |
3.057 |
3.421 |
3.690 |
28 |
0.683 |
0.855 |
1.056 |
1.313 |
1.701 |
2.048 |
2.154 |
2.467 |
2.763 |
3.047 |
3.408 |
3.674 |
29 |
0.683 |
0.854 |
1.055 |
1.311 |
1.699 |
2.045 |
2.150 |
2.462 |
2.756 |
3.038 |
3.396 |
3.659 |
30 |
0.683 |
0.854 |
1.055 |
1.310 |
1.697 |
2.042 |
2.147 |
2.457 |
2.750 |
3.030 |
3.385 |
3.646 |
40 |
0.681 |
0.851 |
1.050 |
1.303 |
1.684 |
2.021 |
2.123 |
2.423 |
2.704 |
2.971 |
3.307 |
3.551 |
50 |
0.679 |
0.849 |
1.047 |
1.299 |
1.676 |
2.009 |
2.109 |
2.403 |
2.678 |
2.937 |
3.261 |
3.496 |
60 |
0.679 |
0.848 |
1.045 |
1.296 |
1.671 |
2.000 |
2.099 |
2.390 |
2.660 |
2.915 |
3.232 |
3.460 |
80 |
0.678 |
0.846 |
1.043 |
1.292 |
1.664 |
1.990 |
2.088 |
2.374 |
2.639 |
2.887 |
3.195 |
3.416 |
100 |
0.677 |
0.845 |
1.042 |
1.290 |
1.660 |
1.984 |
2.081 |
2.364 |
2.626 |
2.871 |
3.174 |
3.390 |
1000 |
0.675 |
0.842 |
1.037 |
1.282 |
1.646 |
1.962 |
2.056 |
2.330 |
2.581 |
2.813 |
3.098 |
3.300 |
z* |
0.674 |
0.841 |
1.036 |
1.282 |
1.645 |
1.960 |
2.054 |
2.326 |
2.576 |
2.807 |
3.091 |
3.291 |
|
50% |
60% |
70% |
80% |
90% |
95% |
96% |
98% |
99% |
99.5% |
99.8% |
99.9% |
Confidence level C |
Page T-12
Table entry for p is the critical value F* with probability p lying to its right.
Table 1.5: TABLE E F critical values
|
|
|
Degrees of freedom in the numerator |
|
|
p |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
12 |
15 |
20 |
25 |
30 |
40 |
50 |
60 |
120 |
1000 |
Degrees of freedom in the denominator |
1 |
.100 |
39.86 |
49.50 |
53.59 |
55.83 |
57.24 |
58.20 |
58.91 |
59.44 |
59.86 |
60.19 |
60.71 |
61.22 |
61.74 |
62.05 |
62.26 |
62.53 |
62.69 |
62.79 |
63.06 |
63.30 |
.050 |
161.45 |
199.50 |
215.71 |
224.58 |
230.16 |
233.99 |
236.77 |
238.88 |
240.54 |
241.88 |
243.91 |
245.95 |
248.01 |
249.26 |
250.10 |
251.14 |
251.77 |
252.20 |
253.25 |
254.19 |
.025 |
647.79 |
799.50 |
864.16 |
899.58 |
921.85 |
937.11 |
948.22 |
956.66 |
963.28 |
968.63 |
976.71 |
984.87 |
993.10 |
998.08 |
1001.4 |
1005.6 |
1008.1 |
1009.8 |
1014.0 |
1017.7 |
.010 |
4052.2 |
4999.5 |
5403.4 |
5624.6 |
5763.6 |
5859.0 |
5928.4 |
5981.1 |
6022.5 |
6055.8 |
6106.3 |
6157.3 |
6208.7 |
6239.8 |
6260.6 |
6286.8 |
6302.5 |
6313.0 |
6339.4 |
6362.7 |
.001 |
405284 |
500000 |
540379 |
562500 |
576405 |
585937 |
592873 |
598144 |
602284 |
605621 |
610668 |
615764 |
620908 |
624017 |
626099 |
628712 |
630285 |
631337 |
633972 |
636301 |
2 |
.100 |
8.53 |
9.00 |
9.16 |
9.24 |
9.29 |
9.33 |
9.35 |
9.37 |
9.38 |
9.39 |
9.41 |
9.42 |
9.44 |
9.45 |
9.46 |
9.47 |
9.47 |
9.47 |
9.48 |
9.49 |
.050 |
18.51 |
19.00 |
19.16 |
19.25 |
19.30 |
19.33 |
19.35 |
19.37 |
19.38 |
19.40 |
19.41 |
19.43 |
19.45 |
19.46 |
19.46 |
19.47 |
19.48 |
19.48 |
19.49 |
19.49 |
.025 |
38.51 |
39.00 |
39.17 |
39.25 |
39.30 |
39.33 |
39.36 |
39.37 |
39.39 |
39.40 |
39.41 |
39.43 |
39.45 |
39.46 |
39.46 |
39.47 |
39.48 |
39.48 |
39.49 |
39.50 |
.010 |
98.50 |
99.00 |
99.17 |
99.25 |
99.30 |
99.33 |
99.36 |
99.37 |
99.39 |
99.40 |
99.42 |
99.43 |
99.45 |
99.46 |
99.47 |
99.47 |
99.48 |
99.48 |
99.49 |
99.50 |
.001 |
998.50 |
999.00 |
999.17 |
999.25 |
999.30 |
999.33 |
999.36 |
999.37 |
999.39 |
999.40 |
999.42 |
999.43 |
999.45 |
999.46 |
999.47 |
999.47 |
999.48 |
999.48 |
999.49 |
999.50 |
3 |
.100 |
5.54 |
5.46 |
5.39 |
5.34 |
5.31 |
5.28 |
5.27 |
5.25 |
5.24 |
5.23 |
5.22 |
5.20 |
5.18 |
5.17 |
5.17 |
5.16 |
5.15 |
5.15 |
5.14 |
5.13 |
.050 |
10.13 |
9.55 |
9.28 |
9.12 |
9.01 |
8.94 |
8.89 |
8.85 |
8.81 |
8.79 |
8.74 |
8.70 |
8.66 |
8.63 |
8.62 |
8.59 |
8.58 |
8.57 |
8.55 |
8.53 |
.025 |
17.44 |
16.04 |
15.44 |
15.10 |
14.88 |
14.73 |
14.62 |
14.54 |
14.47 |
14.42 |
14.34 |
14.25 |
14.17 |
14.12 |
14.08 |
14.04 |
14.01 |
13.99 |
13.95 |
13.91 |
.010 |
34.12 |
30.82 |
29.46 |
28.71 |
28.24 |
27.91 |
27.67 |
27.49 |
27.35 |
27.23 |
27.05 |
26.87 |
26.69 |
26.58 |
26.50 |
26.41 |
26.35 |
26.32 |
26.22 |
26.14 |
.001 |
167.03 |
148.50 |
141.11 |
137.10 |
134.58 |
132.85 |
131.58 |
130.62 |
129.86 |
129.25 |
128.32 |
127.37 |
126.42 |
125.84 |
125.45 |
124.96 |
124.66 |
124.47 |
123.97 |
123.53 |
4 |
.100 |
4.54 |
4.32 |
4.19 |
4.11 |
4.05 |
4.01 |
3.98 |
3.95 |
3.94 |
3.92 |
3.90 |
3.87 |
3.84 |
3.83 |
3.82 |
3.80 |
3.80 |
3.79 |
3.78 |
3.76 |
.050 |
7.71 |
6.94 |
6.59 |
6.39 |
6.26 |
6.16 |
6.09 |
6.04 |
6.00 |
5.96 |
5.91 |
5.86 |
5.80 |
5.77 |
5.75 |
5.72 |
5.70 |
5.69 |
5.66 |
5.63 |
.025 |
12.22 |
10.65 |
9.98 |
9.60 |
9.36 |
9.20 |
9.07 |
8.98 |
8.90 |
8.84 |
8.75 |
8.66 |
8.56 |
8.50 |
8.46 |
8.41 |
8.38 |
8.36 |
8.31 |
8.26 |
.010 |
21.20 |
18.00 |
16.69 |
15.98 |
15.52 |
15.21 |
14.98 |
14.80 |
14.66 |
14.55 |
14.37 |
14.20 |
14.02 |
13.91 |
13.84 |
13.75 |
13.69 |
13.65 |
13.56 |
13.47 |
.001 |
74.14 |
61.25 |
56.18 |
53.44 |
51.71 |
50.53 |
49.66 |
49.00 |
48.47 |
48.05 |
47.41 |
46.76 |
46.10 |
45.70 |
45.43 |
45.09 |
44.88 |
44.75 |
44.40 |
44.09 |
5 |
.100 |
4.06 |
3.78 |
3.62 |
3.52 |
3.45 |
3.40 |
3.37 |
3.34 |
3.32 |
3.30 |
3.27 |
3.24 |
3.21 |
3.19 |
3.17 |
3.16 |
3.15 |
3.14 |
3.12 |
3.11 |
.050 |
6.61 |
5.79 |
5.41 |
5.19 |
5.05 |
4.95 |
4.88 |
4.82 |
4.77 |
4.74 |
4.68 |
4.62 |
4.56 |
4.52 |
4.50 |
4.46 |
4.44 |
4.43 |
4.40 |
4.37 |
.025 |
10.01 |
8.43 |
7.76 |
7.39 |
7.15 |
6.98 |
6.85 |
6.76 |
6.68 |
6.62 |
6.52 |
6.43 |
6.33 |
6.27 |
6.23 |
6.18 |
6.14 |
6.12 |
6.07 |
6.02 |
.010 |
16.26 |
13.27 |
12.06 |
11.39 |
10.97 |
10.67 |
10.46 |
10.29 |
10.16 |
10.05 |
9.89 |
9.72 |
9.55 |
9.45 |
9.38 |
9.29 |
9.24 |
9.20 |
9.11 |
9.03 |
.001 |
47.18 |
37.12 |
33.20 |
31.09 |
29.75 |
28.83 |
28.16 |
27.65 |
27.24 |
26.92 |
26.42 |
25.91 |
25.39 |
25.08 |
24.87 |
24.60 |
24.44 |
24.33 |
24.06 |
23.82 |
6 |
.100 |
3.78 |
3.46 |
3.29 |
3.18 |
3.11 |
3.05 |
3.01 |
2.98 |
2.96 |
2.94 |
2.90 |
2.87 |
2.84 |
2.81 |
2.80 |
2.78 |
2.77 |
2.76 |
2.74 |
2.72 |
.050 |
5.99 |
5.14 |
4.76 |
4.53 |
4.39 |
4.28 |
4.21 |
4.15 |
4.10 |
4.06 |
4.00 |
3.94 |
3.87 |
3.83 |
3.81 |
3.77 |
3.75 |
3.74 |
3.70 |
3.67 |
.025 |
8.81 |
7.26 |
6.60 |
6.23 |
5.99 |
5.82 |
5.70 |
5.60 |
5.52 |
5.46 |
5.37 |
5.27 |
5.17 |
5.11 |
5.07 |
5.01 |
4.98 |
4.96 |
4.90 |
4.86 |
.010 |
13.75 |
10.92 |
9.78 |
9.15 |
8.75 |
8.47 |
8.26 |
8.10 |
7.98 |
7.87 |
7.72 |
7.56 |
7.40 |
7.30 |
7.23 |
7.14 |
7.09 |
7.06 |
6.97 |
6.89 |
.001 |
35.51 |
27.00 |
23.70 |
21.92 |
20.80 |
20.03 |
19.46 |
19.03 |
18.69 |
18.41 |
17.99 |
17.56 |
17.12 |
16.85 |
16.67 |
16.44 |
16.31 |
16.21 |
15.98 |
15.77 |
7 |
.100 |
3.59 |
3.26 |
3.07 |
2.96 |
2.88 |
2.83 |
2.78 |
2.75 |
2.72 |
2.70 |
2.67 |
2.63 |
2.59 |
2.57 |
2.56 |
2.54 |
2.52 |
2.51 |
2.49 |
2.47 |
.050 |
5.59 |
4.74 |
4.35 |
4.12 |
3.97 |
3.87 |
3.79 |
3.73 |
3.68 |
3.64 |
3.57 |
3.51 |
3.44 |
3.40 |
3.38 |
3.34 |
3.32 |
3.30 |
3.27 |
3.23 |
.025 |
8.07 |
6.54 |
5.89 |
5.52 |
5.29 |
5.12 |
4.99 |
4.90 |
4.82 |
4.76 |
4.67 |
4.57 |
4.47 |
4.40 |
4.36 |
4.31 |
4.28 |
4.25 |
4.20 |
4.15 |
.010 |
12.25 |
9.55 |
8.45 |
7.85 |
7.46 |
7.19 |
6.99 |
6.84 |
6.72 |
6.62 |
6.47 |
6.31 |
6.16 |
6.06 |
5.99 |
5.91 |
5.86 |
5.82 |
5.74 |
5.66 |
.001 |
29.25 |
21.69 |
18.77 |
17.20 |
16.21 |
15.52 |
15.02 |
14.63 |
14.33 |
14.08 |
13.71 |
13.32 |
12.93 |
12.69 |
12.53 |
12.33 |
12.20 |
12.12 |
11.91 |
11.72 |
8 |
.100 |
3.46 |
3.11 |
2.92 |
2.81 |
2.73 |
2.67 |
2.62 |
2.59 |
2.56 |
2.54 |
2.50 |
2.46 |
2.42 |
2.40 |
2.38 |
2.36 |
2.35 |
2.34 |
2.32 |
2.30 |
.050 |
5.32 |
4.46 |
4.07 |
3.84 |
3.69 |
3.58 |
3.50 |
3.44 |
3.39 |
3.35 |
3.28 |
3.22 |
3.15 |
3.11 |
3.08 |
3.04 |
3.02 |
3.01 |
2.97 |
2.93 |
.025 |
7.57 |
6.06 |
5.42 |
5.05 |
4.82 |
4.65 |
4.53 |
4.43 |
4.36 |
4.30 |
4.20 |
4.10 |
4.00 |
3.94 |
3.89 |
3.84 |
3.81 |
3.78 |
3.73 |
3.68 |
.010 |
11.26 |
8.65 |
7.59 |
7.01 |
6.63 |
6.37 |
6.18 |
6.03 |
5.91 |
5.81 |
5.67 |
5.52 |
5.36 |
5.26 |
5.20 |
5.12 |
5.07 |
5.03 |
4.95 |
4.87 |
.001 |
25.41 |
18.49 |
15.83 |
14.39 |
13.48 |
12.86 |
12.40 |
12.05 |
11.77 |
11.54 |
11.19 |
10.84 |
10.48 |
10.26 |
10.11 |
9.92 |
9.80 |
9.73 |
9.53 |
9.36 |
9 |
.100 |
3.36 |
3.01 |
2.81 |
2.69 |
2.61 |
2.55 |
2.51 |
2.47 |
2.44 |
2.42 |
2.38 |
2.34 |
2.30 |
2.27 |
2.25 |
2.23 |
2.22 |
2.21 |
2.18 |
2.16 |
.050 |
5.12 |
4.26 |
3.86 |
3.63 |
3.48 |
3.37 |
3.29 |
3.23 |
3.18 |
3.14 |
3.07 |
3.01 |
2.94 |
2.89 |
2.86 |
2.83 |
2.80 |
2.79 |
2.75 |
2.71 |
.025 |
7.21 |
5.71 |
5.08 |
4.72 |
4.48 |
4.32 |
4.20 |
4.10 |
4.03 |
3.96 |
3.87 |
3.77 |
3.67 |
3.60 |
3.56 |
3.51 |
3.47 |
3.45 |
3.39 |
3.34 |
.010 |
10.56 |
8.02 |
6.99 |
6.42 |
6.06 |
5.80 |
5.61 |
5.47 |
5.35 |
5.26 |
5.11 |
4.96 |
4.81 |
4.71 |
4.65 |
4.57 |
4.52 |
4.48 |
4.40 |
4.32 |
.001 |
22.86 |
16.39 |
13.90 |
12.56 |
11.71 |
11.13 |
10.70 |
10.37 |
10.11 |
9.89 |
9.57 |
9.24 |
8.90 |
8.69 |
8.55 |
8.37 |
8.26 |
8.19 |
8.00 |
7.84 |
10 |
.100 |
3.29 |
2.92 |
2.73 |
2.61 |
2.52 |
2.46 |
2.41 |
2.38 |
2.35 |
2.32 |
2.28 |
2.24 |
2.20 |
2.17 |
2.16 |
2.13 |
2.12 |
2.11 |
2.08 |
2.06 |
.050 |
4.96 |
4.10 |
3.71 |
3.48 |
3.33 |
3.22 |
3.14 |
3.07 |
3.02 |
2.98 |
2.91 |
2.85 |
2.77 |
2.73 |
2.70 |
2.66 |
2.64 |
2.62 |
2.58 |
2.54 |
.025 |
6.94 |
5.46 |
4.83 |
4.47 |
4.24 |
4.07 |
3.95 |
3.85 |
3.78 |
3.72 |
3.62 |
3.52 |
3.42 |
3.35 |
3.31 |
3.26 |
3.22 |
3.20 |
3.14 |
3.09 |
.010 |
10.04 |
7.56 |
6.55 |
5.99 |
5.64 |
5.39 |
5.20 |
5.06 |
4.94 |
4.85 |
4.71 |
4.56 |
4.41 |
4.31 |
4.25 |
4.17 |
4.12 |
4.08 |
4.00 |
3.92 |
.001 |
21.04 |
14.91 |
12.55 |
11.28 |
10.48 |
9.93 |
9.52 |
9.20 |
8.96 |
8.75 |
8.45 |
8.13 |
7.80 |
7.60 |
7.47 |
7.30 |
7.19 |
7.12 |
6.94 |
6.78 |
11 |
.100 |
3.23 |
2.86 |
2.66 |
2.54 |
2.45 |
2.39 |
2.34 |
2.30 |
2.27 |
2.25 |
2.21 |
2.17 |
2.12 |
2.10 |
2.08 |
2.05 |
2.04 |
2.03 |
2.00 |
1.98 |
.050 |
4.84 |
3.98 |
3.59 |
3.36 |
3.20 |
3.09 |
3.01 |
2.95 |
2.90 |
2.85 |
2.79 |
2.72 |
2.65 |
2.60 |
2.57 |
2.53 |
2.51 |
2.49 |
2.45 |
2.41 |
.025 |
6.72 |
5.26 |
4.63 |
4.28 |
4.04 |
3.88 |
3.76 |
3.66 |
3.59 |
3.53 |
3.43 |
3.33 |
3.23 |
3.16 |
3.12 |
3.06 |
3.03 |
3.00 |
2.94 |
2.89 |
.010 |
9.65 |
7.21 |
6.22 |
5.67 |
5.32 |
5.07 |
4.89 |
4.74 |
4.63 |
4.54 |
4.40 |
4.25 |
4.10 |
4.01 |
3.94 |
3.86 |
3.81 |
3.78 |
3.69 |
3.61 |
.001 |
19.69 |
13.81 |
11.56 |
10.35 |
9.58 |
9.05 |
8.66 |
8.35 |
8.12 |
7.92 |
7.63 |
7.32 |
7.01 |
6.81 |
6.68 |
6.52 |
6.42 |
6.35 |
6.18 |
6.02 |
12 |
.100 |
3.18 |
2.81 |
2.61 |
2.48 |
2.39 |
2.33 |
2.28 |
2.24 |
2.21 |
2.19 |
2.15 |
2.10 |
2.06 |
2.03 |
2.01 |
1.99 |
1.97 |
1.96 |
1.93 |
1.91 |
.050 |
4.75 |
3.89 |
3.49 |
3.26 |
3.11 |
3.00 |
2.91 |
2.85 |
2.80 |
2.75 |
2.69 |
2.62 |
2.54 |
2.50 |
2.47 |
2.43 |
2.40 |
2.38 |
2.34 |
2.30 |
.025 |
6.55 |
5.10 |
4.47 |
4.12 |
3.89 |
3.73 |
3.61 |
3.51 |
3.44 |
3.37 |
3.28 |
3.18 |
3.07 |
3.01 |
2.96 |
2.91 |
2.87 |
2.85 |
2.79 |
2.73 |
.010 |
9.33 |
6.93 |
5.95 |
5.41 |
5.06 |
4.82 |
4.64 |
4.50 |
4.39 |
4.30 |
4.16 |
4.01 |
3.86 |
3.76 |
3.70 |
3.62 |
3.57 |
3.54 |
3.45 |
3.37 |
.001 |
18.64 |
12.97 |
10.80 |
9.63 |
8.89 |
8.38 |
8.00 |
7.71 |
7.48 |
7.29 |
7.00 |
6.71 |
6.40 |
6.22 |
6.09 |
5.93 |
5.83 |
5.76 |
5.59 |
5.44 |
13 |
.100 |
3.14 |
2.76 |
2.56 |
2.43 |
2.35 |
2.28 |
2.23 |
2.20 |
2.16 |
2.14 |
2.10 |
2.05 |
2.01 |
1.98 |
1.96 |
1.93 |
1.92 |
1.90 |
1.88 |
1.85 |
.050 |
4.67 |
3.81 |
3.41 |
3.18 |
3.03 |
2.92 |
2.83 |
2.77 |
2.71 |
2.67 |
2.60 |
2.53 |
2.46 |
2.41 |
2.38 |
2.34 |
2.31 |
2.30 |
2.25 |
2.21 |
.025 |
6.41 |
4.97 |
4.35 |
4.00 |
3.77 |
3.60 |
3.48 |
3.39 |
3.31 |
3.25 |
3.15 |
3.05 |
2.95 |
2.88 |
2.84 |
2.78 |
2.74 |
2.72 |
2.66 |
2.60 |
.010 |
9.07 |
6.70 |
5.74 |
5.21 |
4.86 |
4.62 |
4.44 |
4.30 |
4.19 |
4.10 |
3.96 |
3.82 |
3.66 |
3.57 |
3.51 |
3.43 |
3.38 |
3.34 |
3.25 |
3.18 |
.001 |
17.82 |
12.31 |
10.21 |
9.07 |
8.35 |
7.86 |
7.49 |
7.21 |
6.98 |
6.80 |
6.52 |
6.23 |
5.93 |
5.75 |
5.63 |
5.47 |
5.37 |
5.30 |
5.14 |
4.99 |
14 |
.100 |
3.10 |
2.73 |
2.52 |
2.39 |
2.31 |
2.24 |
2.19 |
2.15 |
2.12 |
2.10 |
2.05 |
2.01 |
1.96 |
1.93 |
1.91 |
1.89 |
1.87 |
1.86 |
1.83 |
1.80 |
.050 |
4.60 |
3.74 |
3.34 |
3.11 |
2.96 |
2.85 |
2.76 |
2.70 |
2.65 |
2.60 |
2.53 |
2.46 |
2.39 |
2.34 |
2.31 |
2.27 |
2.24 |
2.22 |
2.18 |
2.14 |
.025 |
6.30 |
4.86 |
4.24 |
3.89 |
3.66 |
3.50 |
3.38 |
3.29 |
3.21 |
3.15 |
3.05 |
2.95 |
2.84 |
2.78 |
2.73 |
2.67 |
2.64 |
2.61 |
2.55 |
2.50 |
.010 |
8.86 |
6.51 |
5.56 |
5.04 |
4.69 |
4.46 |
4.28 |
4.14 |
4.03 |
3.94 |
3.80 |
3.66 |
3.51 |
3.41 |
3.35 |
3.27 |
3.22 |
3.18 |
3.09 |
3.02 |
.001 |
17.14 |
11.78 |
9.73 |
8.62 |
7.92 |
7.44 |
7.08 |
6.80 |
6.58 |
6.40 |
6.13 |
5.85 |
5.56 |
5.38 |
5.25 |
5.10 |
5.00 |
4.94 |
4.77 |
4.62 |
15 |
.100 |
3.07 |
2.70 |
2.49 |
2.36 |
2.27 |
2.21 |
2.16 |
2.12 |
2.09 |
2.06 |
2.02 |
1.97 |
1.92 |
1.89 |
1.87 |
1.85 |
1.83 |
1.82 |
1.79 |
1.76 |
.050 |
4.54 |
3.68 |
3.29 |
3.06 |
2.90 |
2.79 |
2.71 |
2.64 |
2.59 |
2.54 |
2.48 |
2.40 |
2.33 |
2.28 |
2.25 |
2.20 |
2.18 |
2.16 |
2.11 |
2.07 |
.025 |
6.20 |
4.77 |
4.15 |
3.80 |
3.58 |
3.41 |
3.29 |
3.20 |
3.12 |
3.06 |
2.96 |
2.86 |
2.76 |
2.69 |
2.64 |
2.59 |
2.55 |
2.52 |
2.46 |
2.40 |
.010 |
8.68 |
6.36 |
5.42 |
4.89 |
4.56 |
4.32 |
4.14 |
4.00 |
3.89 |
3.80 |
3.67 |
3.52 |
3.37 |
3.28 |
3.21 |
3.13 |
3.08 |
3.05 |
2.96 |
2.88 |
.001 |
16.59 |
11.34 |
9.34 |
8.25 |
7.57 |
7.09 |
6.74 |
6.47 |
6.26 |
6.08 |
5.81 |
5.54 |
5.25 |
5.07 |
4.95 |
4.80 |
4.70 |
4.64 |
4.47 |
4.33 |
16 |
.100 |
3.05 |
2.67 |
2.46 |
2.33 |
2.24 |
2.18 |
2.13 |
2.09 |
2.06 |
2.03 |
1.99 |
1.94 |
1.89 |
1.86 |
1.84 |
1.81 |
1.79 |
1.78 |
1.75 |
1.72 |
.050 |
4.49 |
3.63 |
3.24 |
3.01 |
2.85 |
2.74 |
2.66 |
2.59 |
2.54 |
2.49 |
2.42 |
2.35 |
2.28 |
2.23 |
2.19 |
2.15 |
2.12 |
2.11 |
2.06 |
2.02 |
.025 |
6.12 |
4.69 |
4.08 |
3.73 |
3.50 |
3.34 |
3.22 |
3.12 |
3.05 |
2.99 |
2.89 |
2.79 |
2.68 |
2.61 |
2.57 |
2.51 |
2.47 |
2.45 |
2.38 |
2.32 |
.010 |
8.53 |
6.23 |
5.29 |
4.77 |
4.44 |
4.20 |
4.03 |
3.89 |
3.78 |
3.69 |
3.55 |
3.41 |
3.26 |
3.16 |
3.10 |
3.02 |
2.97 |
2.93 |
2.84 |
2.76 |
.001 |
16.12 |
10.97 |
9.01 |
7.94 |
7.27 |
6.80 |
6.46 |
6.19 |
5.98 |
5.81 |
5.55 |
5.27 |
4.99 |
4.82 |
4.70 |
4.54 |
4.45 |
4.39 |
4.23 |
4.08 |
17 |
.100 |
3.03 |
2.64 |
2.44 |
2.31 |
2.22 |
2.15 |
2.10 |
2.06 |
2.03 |
2.00 |
1.96 |
1.91 |
1.86 |
1.83 |
1.81 |
1.78 |
1.76 |
1.75 |
1.72 |
1.69 |
.050 |
4.45 |
3.59 |
3.20 |
2.96 |
2.81 |
2.70 |
2.61 |
2.55 |
2.49 |
2.45 |
2.38 |
2.31 |
2.23 |
2.18 |
2.15 |
2.10 |
2.08 |
2.06 |
2.01 |
1.97 |
.025 |
6.04 |
4.62 |
4.01 |
3.66 |
3.44 |
3.28 |
3.16 |
3.06 |
2.98 |
2.92 |
2.82 |
2.72 |
2.62 |
2.55 |
2.50 |
2.44 |
2.41 |
2.38 |
2.32 |
2.26 |
.010 |
8.40 |
6.11 |
5.19 |
4.67 |
4.34 |
4.10 |
3.93 |
3.79 |
3.68 |
3.59 |
3.46 |
3.31 |
3.16 |
3.07 |
3.00 |
2.92 |
2.87 |
2.83 |
2.75 |
2.66 |
.001 |
15.72 |
10.66 |
8.73 |
7.68 |
7.02 |
6.56 |
6.22 |
5.96 |
5.75 |
5.58 |
5.32 |
5.05 |
4.78 |
4.60 |
4.48 |
4.33 |
4.24 |
4.18 |
4.02 |
3.87 |
18 |
.100 |
3.01 |
2.62 |
2.42 |
2.29 |
2.20 |
2.13 |
2.08 |
2.04 |
2.00 |
1.98 |
1.93 |
1.89 |
1.84 |
1.80 |
1.78 |
1.75 |
1.74 |
1.72 |
1.69 |
1.66 |
.050 |
4.41 |
3.55 |
3.16 |
2.93 |
2.77 |
2.66 |
2.58 |
2.51 |
2.46 |
2.41 |
2.34 |
2.27 |
2.19 |
2.14 |
2.11 |
2.06 |
2.04 |
2.02 |
1.97 |
1.92 |
.025 |
5.98 |
4.56 |
3.95 |
3.61 |
3.38 |
3.22 |
3.10 |
3.01 |
2.93 |
2.87 |
2.77 |
2.67 |
2.56 |
2.49 |
2.44 |
2.38 |
2.35 |
2.32 |
2.26 |
2.20 |
.010 |
8.29 |
6.01 |
5.09 |
4.58 |
4.25 |
4.01 |
3.84 |
3.71 |
3.60 |
3.51 |
3.37 |
3.23 |
3.08 |
2.98 |
2.92 |
2.84 |
2.78 |
2.75 |
2.66 |
2.58 |
.001 |
15.38 |
10.39 |
8.49 |
7.46 |
6.81 |
6.35 |
6.02 |
5.76 |
5.56 |
5.39 |
5.13 |
4.87 |
4.59 |
4.42 |
4.30 |
4.15 |
4.06 |
4.00 |
3.84 |
3.69 |
19 |
.100 |
2.99 |
2.61 |
2.40 |
2.27 |
2.18 |
2.11 |
2.06 |
2.02 |
1.98 |
1.96 |
1.91 |
1.86 |
1.81 |
1.78 |
1.76 |
1.73 |
1.71 |
1.70 |
1.67 |
1.64 |
.050 |
4.38 |
3.52 |
3.13 |
2.90 |
2.74 |
2.63 |
2.54 |
2.48 |
2.42 |
2.38 |
2.31 |
2.23 |
2.16 |
2.11 |
2.07 |
2.03 |
2.00 |
1.98 |
1.93 |
1.88 |
.025 |
5.92 |
4.51 |
3.90 |
3.56 |
3.33 |
3.17 |
3.05 |
2.96 |
2.88 |
2.82 |
2.72 |
2.62 |
2.51 |
2.44 |
2.39 |
2.33 |
2.30 |
2.27 |
2.20 |
2.14 |
.010 |
8.18 |
5.93 |
5.01 |
4.50 |
4.17 |
3.94 |
3.77 |
3.63 |
3.52 |
3.43 |
3.30 |
3.15 |
3.00 |
2.91 |
2.84 |
2.76 |
2.71 |
2.67 |
2.58 |
2.50 |
.001 |
15.08 |
10.16 |
8.28 |
7.27 |
6.62 |
6.18 |
5.85 |
5.59 |
5.39 |
5.22 |
4.97 |
4.70 |
4.43 |
4.26 |
4.14 |
3.99 |
3.90 |
3.84 |
3.68 |
3.53 |
20 |
.100 |
2.97 |
2.59 |
2.38 |
2.25 |
2.16 |
2.09 |
2.04 |
2.00 |
1.96 |
1.94 |
1.89 |
1.84 |
1.79 |
1.76 |
1.74 |
1.71 |
1.69 |
1.68 |
1.64 |
1.61 |
.050 |
4.35 |
3.49 |
3.10 |
2.87 |
2.71 |
2.60 |
2.51 |
2.45 |
2.39 |
2.35 |
2.28 |
2.20 |
2.12 |
2.07 |
2.04 |
1.99 |
1.97 |
1.95 |
1.90 |
1.85 |
.025 |
5.87 |
4.46 |
3.86 |
3.51 |
3.29 |
3.13 |
3.01 |
2.91 |
2.84 |
2.77 |
2.68 |
2.57 |
2.46 |
2.40 |
2.35 |
2.29 |
2.25 |
2.22 |
2.16 |
2.09 |
.010 |
8.10 |
5.85 |
4.94 |
4.43 |
4.10 |
3.87 |
3.70 |
3.56 |
3.46 |
3.37 |
3.23 |
3.09 |
2.94 |
2.84 |
2.78 |
2.69 |
2.64 |
2.61 |
2.52 |
2.43 |
.001 |
14.82 |
9.95 |
8.10 |
7.10 |
6.46 |
6.02 |
5.69 |
5.44 |
5.24 |
5.08 |
4.82 |
4.56 |
4.29 |
4.12 |
4.00 |
3.86 |
3.77 |
3.70 |
3.54 |
3.40 |
21 |
.100 |
2.96 |
2.57 |
2.36 |
2.23 |
2.14 |
2.08 |
2.02 |
1.98 |
1.95 |
1.92 |
1.87 |
1.83 |
1.78 |
1.74 |
1.72 |
1.69 |
1.67 |
1.66 |
1.62 |
1.59 |
.050 |
4.32 |
3.47 |
3.07 |
2.84 |
2.68 |
2.57 |
2.49 |
2.42 |
2.37 |
2.32 |
2.25 |
2.18 |
2.10 |
2.05 |
2.01 |
1.96 |
1.94 |
1.92 |
1.87 |
1.82 |
.025 |
5.83 |
4.42 |
3.82 |
3.48 |
3.25 |
3.09 |
2.97 |
2.87 |
2.80 |
2.73 |
2.64 |
2.53 |
2.42 |
2.36 |
2.31 |
2.25 |
2.21 |
2.18 |
2.11 |
2.05 |
.010 |
8.02 |
5.78 |
4.87 |
4.37 |
4.04 |
3.81 |
3.64 |
3.51 |
3.40 |
3.31 |
3.17 |
3.03 |
2.88 |
2.79 |
2.72 |
2.64 |
2.58 |
2.55 |
2.46 |
2.37 |
.001 |
14.59 |
9.77 |
7.94 |
6.95 |
6.32 |
5.88 |
5.56 |
5.31 |
5.11 |
4.95 |
4.70 |
4.44 |
4.17 |
4.00 |
3.88 |
3.74 |
3.64 |
3.58 |
3.42 |
3.28 |
22 |
.100 |
2.95 |
2.56 |
2.35 |
2.22 |
2.13 |
2.06 |
2.01 |
1.97 |
1.93 |
1.90 |
1.86 |
1.81 |
1.76 |
1.73 |
1.70 |
1.67 |
1.65 |
1.64 |
1.60 |
1.57 |
.050 |
4.30 |
3.44 |
3.05 |
2.82 |
2.66 |
2.55 |
2.46 |
2.40 |
2.34 |
2.30 |
2.23 |
2.15 |
2.07 |
2.02 |
1.98 |
1.94 |
1.91 |
1.89 |
1.84 |
1.79 |
.025 |
5.79 |
4.38 |
3.78 |
3.44 |
3.22 |
3.05 |
2.93 |
2.84 |
2.76 |
2.70 |
2.60 |
2.50 |
2.39 |
2.32 |
2.27 |
2.21 |
2.17 |
2.14 |
2.08 |
2.01 |
.010 |
7.95 |
5.72 |
4.82 |
4.31 |
3.99 |
3.76 |
3.59 |
3.45 |
3.35 |
3.26 |
3.12 |
2.98 |
2.83 |
2.73 |
2.67 |
2.58 |
2.53 |
2.50 |
2.40 |
2.32 |
.001 |
14.38 |
9.61 |
7.80 |
6.81 |
6.19 |
5.76 |
5.44 |
5.19 |
4.99 |
4.83 |
4.58 |
4.33 |
4.06 |
3.89 |
3.78 |
3.63 |
3.54 |
3.48 |
3.32 |
3.17 |
23 |
.100 |
2.94 |
2.55 |
2.34 |
2.21 |
2.11 |
2.05 |
1.99 |
1.95 |
1.92 |
1.89 |
1.84 |
1.80 |
1.74 |
1.71 |
1.69 |
1.66 |
1.64 |
1.62 |
1.59 |
1.55 |
.050 |
4.28 |
3.42 |
3.03 |
2.80 |
2.64 |
2.53 |
2.44 |
2.37 |
2.32 |
2.27 |
2.20 |
2.13 |
2.05 |
2.00 |
1.96 |
1.91 |
1.88 |
1.86 |
1.81 |
1.76 |
.025 |
5.75 |
4.35 |
3.75 |
3.41 |
3.18 |
3.02 |
2.90 |
2.81 |
2.73 |
2.67 |
2.57 |
2.47 |
2.36 |
2.29 |
2.24 |
2.18 |
2.14 |
2.11 |
2.04 |
1.98 |
.010 |
7.88 |
5.66 |
4.76 |
4.26 |
3.94 |
3.71 |
3.54 |
3.41 |
3.30 |
3.21 |
3.07 |
2.93 |
2.78 |
2.69 |
2.62 |
2.54 |
2.48 |
2.45 |
2.35 |
2.27 |
.001 |
14.20 |
9.47 |
7.67 |
6.70 |
6.08 |
5.65 |
5.33 |
5.09 |
4.89 |
4.73 |
4.48 |
4.23 |
3.96 |
3.79 |
3.68 |
3.53 |
3.44 |
3.38 |
3.22 |
3.08 |
24 |
.100 |
2.93 |
2.54 |
2.33 |
2.19 |
2.10 |
2.04 |
1.98 |
1.94 |
1.91 |
1.88 |
1.83 |
1.78 |
1.73 |
1.70 |
1.67 |
1.64 |
1.62 |
1.61 |
1.57 |
1.54 |
.050 |
4.26 |
3.40 |
3.01 |
2.78 |
2.62 |
2.51 |
2.42 |
2.36 |
2.30 |
2.25 |
2.18 |
2.11 |
2.03 |
1.97 |
1.94 |
1.89 |
1.86 |
1.84 |
1.79 |
1.74 |
.025 |
5.72 |
4.32 |
3.72 |
3.38 |
3.15 |
2.99 |
2.87 |
2.78 |
2.70 |
2.64 |
2.54 |
2.44 |
2.33 |
2.26 |
2.21 |
2.15 |
2.11 |
2.08 |
2.01 |
1.94 |
.010 |
7.82 |
5.61 |
4.72 |
4.22 |
3.90 |
3.67 |
3.50 |
3.36 |
3.26 |
3.17 |
3.03 |
2.89 |
2.74 |
2.64 |
2.58 |
2.49 |
2.44 |
2.40 |
2.31 |
2.22 |
.001 |
14.03 |
9.34 |
7.55 |
6.59 |
5.98 |
5.55 |
5.23 |
4.99 |
4.80 |
4.64 |
4.39 |
4.14 |
3.87 |
3.71 |
3.59 |
3.45 |
3.36 |
3.29 |
3.14 |
2.99 |
25 |
.100 |
2.92 |
2.53 |
2.32 |
2.18 |
2.09 |
2.02 |
1.97 |
1.93 |
1.89 |
1.87 |
1.82 |
1.77 |
1.72 |
1.68 |
1.66 |
1.63 |
1.61 |
1.59 |
1.56 |
1.52 |
.050 |
4.24 |
3.39 |
2.99 |
2.76 |
2.60 |
2.49 |
2.40 |
2.34 |
2.28 |
2.24 |
2.16 |
2.09 |
2.01 |
1.96 |
1.92 |
1.87 |
1.84 |
1.82 |
1.77 |
1.72 |
.025 |
5.69 |
4.29 |
3.69 |
3.35 |
3.13 |
2.97 |
2.85 |
2.75 |
2.68 |
2.61 |
2.51 |
2.41 |
2.30 |
2.23 |
2.18 |
2.12 |
2.08 |
2.05 |
1.98 |
1.91 |
.010 |
7.77 |
5.57 |
4.68 |
4.18 |
3.85 |
3.63 |
3.46 |
3.32 |
3.22 |
3.13 |
2.99 |
2.85 |
2.70 |
2.60 |
2.54 |
2.45 |
2.40 |
2.36 |
2.27 |
2.18 |
.001 |
13.88 |
9.22 |
7.45 |
6.49 |
5.89 |
5.46 |
5.15 |
4.91 |
4.71 |
4.56 |
4.31 |
4.06 |
3.79 |
3.63 |
3.52 |
3.37 |
3.28 |
3.22 |
3.06 |
2.91 |
26 |
.100 |
2.91 |
2.52 |
2.31 |
2.17 |
2.08 |
2.01 |
1.96 |
1.92 |
1.88 |
1.86 |
1.81 |
1.76 |
1.71 |
1.67 |
1.65 |
1.61 |
1.59 |
1.58 |
1.54 |
1.51 |
.050 |
4.23 |
3.37 |
2.98 |
2.74 |
2.59 |
2.47 |
2.39 |
2.32 |
2.27 |
2.22 |
2.15 |
2.07 |
1.99 |
1.94 |
1.90 |
1.85 |
1.82 |
1.80 |
1.75 |
1.70 |
.025 |
5.66 |
4.27 |
3.67 |
3.33 |
3.10 |
2.94 |
2.82 |
2.73 |
2.65 |
2.59 |
2.49 |
2.39 |
2.28 |
2.21 |
2.16 |
2.09 |
2.05 |
2.03 |
1.95 |
1.89 |
.010 |
7.72 |
5.53 |
4.64 |
4.14 |
3.82 |
3.59 |
3.42 |
3.29 |
3.18 |
3.09 |
2.96 |
2.81 |
2.66 |
2.57 |
2.50 |
2.42 |
2.36 |
2.33 |
2.23 |
2.14 |
.001 |
13.74 |
9.12 |
7.36 |
6.41 |
5.80 |
5.38 |
5.07 |
4.83 |
4.64 |
4.48 |
4.24 |
3.99 |
3.72 |
3.56 |
3.44 |
3.30 |
3.21 |
3.15 |
2.99 |
2.84 |
27 |
.100 |
2.90 |
2.51 |
2.30 |
2.17 |
2.07 |
2.00 |
1.95 |
1.91 |
1.87 |
1.85 |
1.80 |
1.75 |
1.70 |
1.66 |
1.64 |
1.60 |
1.58 |
1.57 |
1.53 |
1.50 |
.050 |
4.21 |
3.35 |
2.96 |
2.73 |
2.57 |
2.46 |
2.37 |
2.31 |
2.25 |
2.20 |
2.13 |
2.06 |
1.97 |
1.92 |
1.88 |
1.84 |
1.81 |
1.79 |
1.73 |
1.68 |
.025 |
5.63 |
4.24 |
3.65 |
3.31 |
3.08 |
2.92 |
2.80 |
2.71 |
2.63 |
2.57 |
2.47 |
2.36 |
2.25 |
2.18 |
2.13 |
2.07 |
2.03 |
2.00 |
1.93 |
1.86 |
.010 |
7.68 |
5.49 |
4.60 |
4.11 |
3.78 |
3.56 |
3.39 |
3.26 |
3.15 |
3.06 |
2.93 |
2.78 |
2.63 |
2.54 |
2.47 |
2.38 |
2.33 |
2.29 |
2.20 |
2.11 |
.001 |
13.61 |
9.02 |
7.27 |
6.33 |
5.73 |
5.31 |
5.00 |
4.76 |
4.57 |
4.41 |
4.17 |
3.92 |
3.66 |
3.49 |
3.38 |
3.23 |
3.14 |
3.08 |
2.92 |
2.78 |
28 |
.100 |
2.89 |
2.50 |
2.29 |
2.16 |
2.06 |
2.00 |
1.94 |
1.90 |
1.87 |
1.84 |
1.79 |
1.74 |
1.69 |
1.65 |
1.63 |
1.59 |
1.57 |
1.56 |
1.52 |
1.48 |
.050 |
4.20 |
3.34 |
2.95 |
2.71 |
2.56 |
2.45 |
2.36 |
2.29 |
2.24 |
2.19 |
2.12 |
2.04 |
1.96 |
1.91 |
1.87 |
1.82 |
1.79 |
1.77 |
1.71 |
1.66 |
.025 |
5.61 |
4.22 |
3.63 |
3.29 |
3.06 |
2.90 |
2.78 |
2.69 |
2.61 |
2.55 |
2.45 |
2.34 |
2.23 |
2.16 |
2.11 |
2.05 |
2.01 |
1.98 |
1.91 |
1.84 |
.010 |
7.64 |
5.45 |
4.57 |
4.07 |
3.75 |
3.53 |
3.36 |
3.23 |
3.12 |
3.03 |
2.90 |
2.75 |
2.60 |
2.51 |
2.44 |
2.35 |
2.30 |
2.26 |
2.17 |
2.08 |
.001 |
13.50 |
8.93 |
7.19 |
6.25 |
5.66 |
5.24 |
4.93 |
4.69 |
4.50 |
4.35 |
4.11 |
3.86 |
3.60 |
3.43 |
3.32 |
3.18 |
3.09 |
3.02 |
2.86 |
2.72 |
29 |
.100 |
2.89 |
2.50 |
2.28 |
2.15 |
2.06 |
1.99 |
1.93 |
1.89 |
1.86 |
1.83 |
1.78 |
1.73 |
1.68 |
1.64 |
1.62 |
1.58 |
1.56 |
1.55 |
1.51 |
1.47 |
.050 |
4.18 |
3.33 |
2.93 |
2.70 |
2.55 |
2.43 |
2.35 |
2.28 |
2.22 |
2.18 |
2.10 |
2.03 |
1.94 |
1.89 |
1.85 |
1.81 |
1.77 |
1.75 |
1.70 |
1.65 |
.025 |
5.59 |
4.20 |
3.61 |
3.27 |
3.04 |
2.88 |
2.76 |
2.67 |
2.59 |
2.53 |
2.43 |
2.32 |
2.21 |
2.14 |
2.09 |
2.03 |
1.99 |
1.96 |
1.89 |
1.82 |
.010 |
7.60 |
5.42 |
4.54 |
4.04 |
3.73 |
3.50 |
3.33 |
3.20 |
3.09 |
3.00 |
2.87 |
2.73 |
2.57 |
2.48 |
2.41 |
2.33 |
2.27 |
2.23 |
2.14 |
2.05 |
.001 |
13.39 |
8.85 |
7.12 |
6.19 |
5.59 |
5.18 |
4.87 |
4.64 |
4.45 |
4.29 |
4.05 |
3.80 |
3.54 |
3.38 |
3.27 |
3.12 |
3.03 |
2.97 |
2.81 |
2.66 |
30 |
.100 |
2.88 |
2.49 |
2.28 |
2.14 |
2.05 |
1.98 |
1.93 |
1.88 |
1.85 |
1.82 |
1.77 |
1.72 |
1.67 |
1.63 |
1.61 |
1.57 |
1.55 |
1.54 |
1.50 |
1.46 |
.050 |
4.17 |
3.32 |
2.92 |
2.69 |
2.53 |
2.42 |
2.33 |
2.27 |
2.21 |
2.16 |
2.09 |
2.01 |
1.93 |
1.88 |
1.84 |
1.79 |
1.76 |
1.74 |
1.68 |
1.63 |
.025 |
5.57 |
4.18 |
3.59 |
3.25 |
3.03 |
2.87 |
2.75 |
2.65 |
2.57 |
2.51 |
2.41 |
2.31 |
2.20 |
2.12 |
2.07 |
2.01 |
1.97 |
1.94 |
1.87 |
1.80 |
.010 |
7.56 |
5.39 |
4.51 |
4.02 |
3.70 |
3.47 |
3.30 |
3.17 |
3.07 |
2.98 |
2.84 |
2.70 |
2.55 |
2.45 |
2.39 |
2.30 |
2.25 |
2.21 |
2.11 |
2.02 |
.001 |
13.29 |
8.77 |
7.05 |
6.12 |
5.53 |
5.12 |
4.82 |
4.58 |
4.39 |
4.24 |
4.00 |
3.75 |
3.49 |
3.33 |
3.22 |
3.07 |
2.98 |
2.92 |
2.76 |
2.61 |
40 |
.100 |
2.84 |
2.44 |
2.23 |
2.09 |
2.00 |
1.93 |
1.87 |
1.83 |
1.79 |
1.76 |
1.71 |
1.66 |
1.61 |
1.57 |
1.54 |
1.51 |
1.48 |
1.47 |
1.42 |
1.38 |
.050 |
4.08 |
3.23 |
2.84 |
2.61 |
2.45 |
2.34 |
2.25 |
2.18 |
2.12 |
2.08 |
2.00 |
1.92 |
1.84 |
1.78 |
1.74 |
1.69 |
1.66 |
1.64 |
1.58 |
1.52 |
.025 |
5.42 |
4.05 |
3.46 |
3.13 |
2.90 |
2.74 |
2.62 |
2.53 |
2.45 |
2.39 |
2.29 |
2.18 |
2.07 |
1.99 |
1.94 |
1.88 |
1.83 |
1.80 |
1.72 |
1.65 |
.010 |
7.31 |
5.18 |
4.31 |
3.83 |
3.51 |
3.29 |
3.12 |
2.99 |
2.89 |
2.80 |
2.66 |
2.52 |
2.37 |
2.27 |
2.20 |
2.11 |
2.06 |
2.02 |
1.92 |
1.82 |
.001 |
12.61 |
8.25 |
6.59 |
5.70 |
5.13 |
4.73 |
4.44 |
4.21 |
4.02 |
3.87 |
3.64 |
3.40 |
3.14 |
2.98 |
2.87 |
2.73 |
2.64 |
2.57 |
2.41 |
2.25 |
50 |
.100 |
2.81 |
2.41 |
2.20 |
2.06 |
1.97 |
1.90 |
1.84 |
1.80 |
1.76 |
1.73 |
1.68 |
1.63 |
1.57 |
1.53 |
1.50 |
1.46 |
1.44 |
1.42 |
1.38 |
1.33 |
.050 |
4.03 |
3.18 |
2.79 |
2.56 |
2.40 |
2.29 |
2.20 |
2.13 |
2.07 |
2.03 |
1.95 |
1.87 |
1.78 |
1.73 |
1.69 |
1.63 |
1.60 |
1.58 |
1.51 |
1.45 |
.025 |
5.34 |
3.97 |
3.39 |
3.05 |
2.83 |
2.67 |
2.55 |
2.46 |
2.38 |
2.32 |
2.22 |
2.11 |
1.99 |
1.92 |
1.87 |
1.80 |
1.75 |
1.72 |
1.64 |
1.56 |
.010 |
7.17 |
5.06 |
4.20 |
3.72 |
3.41 |
3.19 |
3.02 |
2.89 |
2.78 |
2.70 |
2.56 |
2.42 |
2.27 |
2.17 |
2.10 |
2.01 |
1.95 |
1.91 |
1.80 |
1.70 |
.001 |
12.22 |
7.96 |
6.34 |
5.46 |
4.90 |
4.51 |
4.22 |
4.00 |
3.82 |
3.67 |
3.44 |
3.20 |
2.95 |
2.79 |
2.68 |
2.53 |
2.44 |
2.38 |
2.21 |
2.05 |
60 |
.100 |
2.79 |
2.39 |
2.18 |
2.04 |
1.95 |
1.87 |
1.82 |
1.77 |
1.74 |
1.71 |
1.66 |
1.60 |
1.54 |
1.50 |
1.48 |
1.44 |
1.41 |
1.40 |
1.35 |
1.30 |
.050 |
4.00 |
3.15 |
2.76 |
2.53 |
2.37 |
2.25 |
2.17 |
2.10 |
2.04 |
1.99 |
1.92 |
1.84 |
1.75 |
1.69 |
1.65 |
1.59 |
1.56 |
1.53 |
1.47 |
1.40 |
.025 |
5.29 |
3.93 |
3.34 |
3.01 |
2.79 |
2.63 |
2.51 |
2.41 |
2.33 |
2.27 |
2.17 |
2.06 |
1.94 |
1.87 |
1.82 |
1.74 |
1.70 |
1.67 |
1.58 |
1.49 |
.010 |
7.08 |
4.98 |
4.13 |
3.65 |
3.34 |
3.12 |
2.95 |
2.82 |
2.72 |
2.63 |
2.50 |
2.35 |
2.20 |
2.10 |
2.03 |
1.94 |
1.88 |
1.84 |
1.73 |
1.62 |
.001 |
11.97 |
7.77 |
6.17 |
5.31 |
4.76 |
4.37 |
4.09 |
3.86 |
3.69 |
3.54 |
3.32 |
3.08 |
2.83 |
2.67 |
2.55 |
2.41 |
2.32 |
2.25 |
2.08 |
1.92 |
100 |
.100 |
2.76 |
2.36 |
2.14 |
2.00 |
1.91 |
1.83 |
1.78 |
1.73 |
1.69 |
1.66 |
1.61 |
1.56 |
1.49 |
1.45 |
1.42 |
1.38 |
1.35 |
1.34 |
1.28 |
1.22 |
.050 |
3.94 |
3.09 |
2.70 |
2.46 |
2.31 |
2.19 |
2.10 |
2.03 |
1.97 |
1.93 |
1.85 |
1.77 |
1.68 |
1.62 |
1.57 |
1.52 |
1.48 |
1.45 |
1.38 |
1.30 |
.025 |
5.18 |
3.83 |
3.25 |
2.92 |
2.70 |
2.54 |
2.42 |
2.32 |
2.24 |
2.18 |
2.08 |
1.97 |
1.85 |
1.77 |
1.71 |
1.64 |
1.59 |
1.56 |
1.46 |
1.36 |
.010 |
6.90 |
4.82 |
3.98 |
3.51 |
3.21 |
2.99 |
2.82 |
2.69 |
2.59 |
2.50 |
2.37 |
2.22 |
2.07 |
1.97 |
1.89 |
1.80 |
1.74 |
1.69 |
1.57 |
1.45 |
.001 |
11.50 |
7.41 |
5.86 |
5.02 |
4.48 |
4.11 |
3.83 |
3.61 |
3.44 |
3.30 |
3.07 |
2.84 |
2.59 |
2.43 |
2.32 |
2.17 |
2.08 |
2.01 |
1.83 |
1.64 |
200 |
.100 |
2.73 |
2.33 |
2.11 |
1.97 |
1.88 |
1.80 |
1.75 |
1.70 |
1.66 |
1.63 |
1.58 |
1.52 |
1.46 |
1.41 |
1.38 |
1.34 |
1.31 |
1.29 |
1.23 |
1.16 |
.050 |
3.89 |
3.04 |
2.65 |
2.42 |
2.26 |
2.14 |
2.06 |
1.98 |
1.93 |
1.88 |
1.80 |
1.72 |
1.62 |
1.56 |
1.52 |
1.46 |
1.41 |
1.39 |
1.30 |
1.21 |
.025 |
5.10 |
3.76 |
3.18 |
2.85 |
2.63 |
2.47 |
2.35 |
2.26 |
2.18 |
2.11 |
2.01 |
1.90 |
1.78 |
1.70 |
1.64 |
1.56 |
1.51 |
1.47 |
1.37 |
1.25 |
.010 |
6.76 |
4.71 |
3.88 |
3.41 |
3.11 |
2.89 |
2.73 |
2.60 |
2.50 |
2.41 |
2.27 |
2.13 |
1.97 |
1.87 |
1.79 |
1.69 |
1.63 |
1.58 |
1.45 |
1.30 |
.001 |
11.15 |
7.15 |
5.63 |
4.81 |
4.29 |
3.92 |
3.65 |
3.43 |
3.26 |
3.12 |
2.90 |
2.67 |
2.42 |
2.26 |
2.15 |
2.00 |
1.90 |
1.83 |
1.64 |
1.43 |
1000 |
.100 |
2.71 |
2.31 |
2.09 |
1.95 |
1.85 |
1.78 |
1.72 |
1.68 |
1.64 |
1.61 |
1.55 |
1.49 |
1.43 |
1.38 |
1.35 |
1.30 |
1.27 |
1.25 |
1.18 |
1.08 |
.050 |
3.85 |
3.00 |
2.61 |
2.38 |
2.22 |
2.11 |
2.02 |
1.95 |
1.89 |
1.84 |
1.76 |
1.68 |
1.58 |
1.52 |
1.47 |
1.41 |
1.36 |
1.33 |
1.24 |
1.11 |
.025 |
5.04 |
3.70 |
3.13 |
2.80 |
2.58 |
2.42 |
2.30 |
2.20 |
2.13 |
2.06 |
1.96 |
1.85 |
1.72 |
1.64 |
1.58 |
1.50 |
1.45 |
1.41 |
1.29 |
1.13 |
.010 |
6.66 |
4.63 |
3.80 |
3.34 |
3.04 |
2.82 |
2.66 |
2.53 |
2.43 |
2.34 |
2.20 |
2.06 |
1.90 |
1.79 |
1.72 |
1.61 |
1.54 |
1.50 |
1.35 |
1.16 |
.001 |
10.89 |
6.96 |
5.46 |
4.65 |
4.14 |
3.78 |
3.51 |
3.30 |
3.13 |
2.99 |
2.77 |
2.54 |
2.30 |
2.14 |
2.02 |
1.87 |
1.77 |
1.69 |
1.49 |
1.22 |
Table entry for p is the critical value (χ2)* with probability p lying to its right.
Page T-13
Page T-14
Page T-15
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Page T-20
Table 1.6: TABLE F χ2 distribution critical values
|
Tail probability p
|
df |
.25 |
.20 |
.15 |
.10 |
.05 |
.025 |
.02 |
.01 |
.005 |
.0025 |
.001 |
.0005 |
1 |
1.32 |
1.64 |
2.07 |
2.71 |
3.84 |
5.02 |
5.41 |
6.63 |
7.88 |
9.14 |
10.83 |
12.12 |
2 |
2.77 |
3.22 |
3.79 |
4.61 |
5.99 |
7.38 |
7.82 |
9.21 |
10.60 |
11.98 |
13.82 |
15.20 |
3 |
4.11 |
4.64 |
5.32 |
6.25 |
7.81 |
9.35 |
9.84 |
11.34 |
12.84 |
14.32 |
16.27 |
17.73 |
4 |
5.39 |
5.99 |
6.74 |
7.78 |
9.49 |
11.14 |
11.67 |
13.28 |
14.86 |
16.42 |
18.47 |
20.00 |
5 |
6.63 |
7.29 |
8.12 |
9.24 |
11.07 |
12.83 |
13.39 |
15.09 |
16.75 |
18.39 |
20.51 |
22.11 |
6 |
7.84 |
8.56 |
9.45 |
10.64 |
12.59 |
14.45 |
15.03 |
16.81 |
18.55 |
20.25 |
22.46 |
24.10 |
7 |
9.04 |
9.80 |
10.75 |
12.02 |
14.07 |
16.01 |
16.62 |
18.48 |
20.28 |
22.04 |
24.32 |
26.02 |
8 |
10.22 |
11.03 |
12.03 |
13.36 |
15.51 |
17.53 |
18.17 |
20.09 |
21.95 |
23.77 |
26.12 |
27.87 |
9 |
11.39 |
12.24 |
13.29 |
14.68 |
16.92 |
19.02 |
19.68 |
21.67 |
23.59 |
25.46 |
27.88 |
29.67 |
10 |
12.55 |
13.44 |
14.53 |
15.99 |
18.31 |
20.48 |
21.16 |
23.21 |
25.19 |
27.11 |
29.59 |
31.42 |
11 |
13.70 |
14.63 |
15.77 |
17.28 |
19.68 |
21.92 |
22.62 |
24.72 |
26.76 |
28.73 |
31.26 |
33.14 |
12 |
14.85 |
15.81 |
16.99 |
18.55 |
21.03 |
23.34 |
24.05 |
26.22 |
28.30 |
30.32 |
32.91 |
34.82 |
13 |
15.98 |
16.98 |
18.20 |
19.81 |
22.36 |
24.74 |
25.47 |
27.69 |
29.82 |
31.88 |
34.53 |
36.48 |
14 |
17.12 |
18.15 |
19.41 |
21.06 |
23.68 |
26.12 |
26.87 |
29.14 |
31.32 |
33.43 |
36.12 |
38.11 |
15 |
18.25 |
19.31 |
20.60 |
22.31 |
25.00 |
27.49 |
28.26 |
30.58 |
32.80 |
34.95 |
37.70 |
39.72 |
16 |
19.37 |
20.47 |
21.79 |
23.54 |
26.30 |
28.85 |
29.63 |
32.00 |
34.27 |
36.46 |
39.25 |
41.31 |
17 |
20.49 |
21.61 |
22.98 |
24.77 |
27.59 |
30.19 |
31.00 |
33.41 |
35.72 |
37.95 |
40.79 |
42.88 |
18 |
21.60 |
22.76 |
24.16 |
25.99 |
28.87 |
31.53 |
32.35 |
34.81 |
37.16 |
39.42 |
42.31 |
44.43 |
19 |
22.72 |
23.90 |
25.33 |
27.20 |
30.14 |
32.85 |
33.69 |
36.19 |
38.58 |
40.88 |
43.82 |
45.97 |
20 |
23.83 |
25.04 |
26.50 |
28.41 |
31.41 |
34.17 |
35.02 |
37.57 |
40.00 |
42.34 |
45.31 |
47.50 |
21 |
24.93 |
26.17 |
27.66 |
29.62 |
32.67 |
35.48 |
36.34 |
38.93 |
41.40 |
43.78 |
46.80 |
49.01 |
22 |
26.04 |
27.30 |
28.82 |
30.81 |
33.92 |
36.78 |
37.66 |
40.29 |
42.80 |
45.20 |
48.27 |
50.51 |
23 |
27.14 |
28.43 |
29.98 |
32.01 |
35.17 |
38.08 |
38.97 |
41.64 |
44.18 |
46.62 |
49.73 |
52.00 |
24 |
28.24 |
29.55 |
31.13 |
33.20 |
36.42 |
39.36 |
40.27 |
42.98 |
45.56 |
48.03 |
51.18 |
53.48 |
25 |
29.34 |
30.68 |
32.28 |
34.38 |
37.65 |
40.65 |
41.57 |
44.31 |
46.93 |
49.44 |
52.62 |
54.95 |
26 |
30.43 |
31.79 |
33.43 |
35.56 |
38.89 |
41.92 |
42.86 |
45.64 |
48.29 |
50.83 |
54.05 |
56.41 |
27 |
31.53 |
32.91 |
34.57 |
36.74 |
40.11 |
43.19 |
44.14 |
46.96 |
49.64 |
52.22 |
55.48 |
57.86 |
28 |
32.62 |
34.03 |
35.71 |
37.92 |
41.34 |
44.46 |
45.42 |
48.28 |
50.99 |
53.59 |
56.89 |
59.30 |
29 |
33.71 |
35.14 |
36.85 |
39.09 |
42.56 |
45.72 |
46.69 |
49.59 |
52.34 |
54.97 |
58.30 |
60.73 |
30 |
34.80 |
36.25 |
37.99 |
40.26 |
43.77 |
46.98 |
47.96 |
50.89 |
53.67 |
56.33 |
59.70 |
62.16 |
40 |
45.62 |
47.27 |
49.24 |
51.81 |
55.76 |
59.34 |
60.44 |
63.69 |
66.77 |
69.70 |
73.40 |
76.09 |
50 |
56.33 |
58.16 |
60.35 |
63.17 |
67.50 |
71.42 |
72.61 |
76.15 |
79.49 |
82.66 |
86.66 |
89.56 |
60 |
66.98 |
68.97 |
71.34 |
74.40 |
79.08 |
83.30 |
84.58 |
88.38 |
91.95 |
95.34 |
99.61 |
102.7 |
80 |
88.13 |
90.41 |
93.11 |
96.58 |
101.9 |
106.6 |
108.1 |
112.3 |
116.3 |
120.1 |
124.8 |
128.3 |
100 |
109.1 |
111.7 |
114.7 |
118.5 |
124.3 |
129.6 |
131.1 |
135.8 |
140.2 |
144.3 |
149.4 |
153.2 |
Page T-21
Table entry for p is the value r with probability p lying above it.
Table 1.7: TABLE G Critical values of the correlation r
n |
.20 |
.10 |
.05 |
.025 |
.02 |
.01 |
.005 |
.0025 |
.001 |
.0005 |
3 |
0.8090 |
0.9511 |
0.9877 |
0.9969 |
0.9980 |
0.9995 |
0.9999 |
1.0000 |
1.0000 |
1.0000 |
4 |
0.6000 |
0.8000 |
0.9000 |
0.9500 |
0.9600 |
0.9800 |
0.9900 |
0.9950 |
0.9980 |
0.9990 |
5 |
0.4919 |
0.6870 |
0.8054 |
0.8783 |
0.8953 |
0.9343 |
0.9587 |
0.9740 |
0.9859 |
0.9911 |
6 |
0.4257 |
0.6084 |
0.7293 |
0.8114 |
0.8319 |
0.8822 |
0.9172 |
0.9417 |
0.9633 |
0.9741 |
7 |
0.3803 |
0.5509 |
0.6694 |
0.7545 |
0.7766 |
0.8329 |
0.8745 |
0.9056 |
0.9350 |
0.9509 |
8 |
0.3468 |
0.5067 |
0.6215 |
0.7067 |
0.7295 |
0.7887 |
0.8343 |
0.8697 |
0.9049 |
0.9249 |
9 |
0.3208 |
0.4716 |
0.5822 |
0.6664 |
0.6892 |
0.7498 |
0.7977 |
0.8359 |
0.8751 |
0.8983 |
10 |
0.2998 |
0.4428 |
0.5494 |
0.6319 |
0.6546 |
0.7155 |
0.7646 |
0.8046 |
0.8467 |
0.8721 |
11 |
0.2825 |
0.4187 |
0.5214 |
0.6021 |
0.6244 |
0.6851 |
0.7348 |
0.7759 |
0.8199 |
0.8470 |
12 |
0.2678 |
0.3981 |
0.4973 |
0.5760 |
0.5980 |
0.6581 |
0.7079 |
0.7496 |
0.7950 |
0.8233 |
13 |
0.2552 |
0.3802 |
0.4762 |
0.5529 |
0.5745 |
0.6339 |
0.6835 |
0.7255 |
0.7717 |
0.8010 |
14 |
0.2443 |
0.3646 |
0.4575 |
0.5324 |
0.5536 |
0.6120 |
0.6614 |
0.7034 |
0.7501 |
0.7800 |
15 |
0.2346 |
0.3507 |
0.4409 |
0.5140 |
0.5347 |
0.5923 |
0.6411 |
0.6831 |
0.7301 |
0.7604 |
16 |
0.2260 |
0.3383 |
0.4259 |
0.4973 |
0.5177 |
0.5742 |
0.6226 |
0.6643 |
0.7114 |
0.7419 |
17 |
0.2183 |
0.3271 |
0.4124 |
0.4821 |
0.5021 |
0.5577 |
0.6055 |
0.6470 |
0.6940 |
0.7247 |
18 |
0.2113 |
0.3170 |
0.4000 |
0.4683 |
0.4878 |
0.5425 |
0.5897 |
0.6308 |
0.6777 |
0.7084 |
19 |
0.2049 |
0.3077 |
0.3887 |
0.4555 |
0.4747 |
0.5285 |
0.5751 |
0.6158 |
0.6624 |
0.6932 |
20 |
0.1991 |
0.2992 |
0.3783 |
0.4438 |
0.4626 |
0.5155 |
0.5614 |
0.6018 |
0.6481 |
0.6788 |
21 |
0.1938 |
0.2914 |
0.3687 |
0.4329 |
0.4513 |
0.5034 |
0.5487 |
0.5886 |
0.6346 |
0.6652 |
22 |
0.1888 |
0.2841 |
0.3598 |
0.4227 |
0.4409 |
0.4921 |
0.5368 |
0.5763 |
0.6219 |
0.6524 |
23 |
0.1843 |
0.2774 |
0.3515 |
0.4132 |
0.4311 |
0.4815 |
0.5256 |
0.5647 |
0.6099 |
0.6402 |
24 |
0.1800 |
0.2711 |
0.3438 |
0.4044 |
0.4219 |
0.4716 |
0.5151 |
0.5537 |
0.5986 |
0.6287 |
25 |
0.1760 |
0.2653 |
0.3365 |
0.3961 |
0.4133 |
0.4622 |
0.5052 |
0.5434 |
0.5879 |
0.6178 |
26 |
0.1723 |
0.2598 |
0.3297 |
0.3882 |
0.4052 |
0.4534 |
0.4958 |
0.5336 |
0.5776 |
0.6074 |
27 |
0.1688 |
0.2546 |
0.3233 |
0.3809 |
0.3976 |
0.4451 |
0.4869 |
0.5243 |
0.5679 |
0.5974 |
28 |
0.1655 |
0.2497 |
0.3172 |
0.3739 |
0.3904 |
0.4372 |
0.4785 |
0.5154 |
0.5587 |
0.5880 |
29 |
0.1624 |
0.2451 |
0.3115 |
0.3673 |
0.3835 |
0.4297 |
0.4705 |
0.5070 |
0.5499 |
0.5790 |
30 |
0.1594 |
0.2407 |
0.3061 |
0.3610 |
0.3770 |
0.4226 |
0.4629 |
0.4990 |
0.5415 |
0.5703 |
40 |
0.1368 |
0.2070 |
0.2638 |
0.3120 |
0.3261 |
0.3665 |
0.4026 |
0.4353 |
0.4741 |
0.5007 |
50 |
0.1217 |
0.1843 |
0.2353 |
0.2787 |
0.2915 |
0.3281 |
0.3610 |
0.3909 |
0.4267 |
0.4514 |
60 |
0.1106 |
0.1678 |
0.2144 |
0.2542 |
0.2659 |
0.2997 |
0.3301 |
0.3578 |
0.3912 |
0.4143 |
80 |
0.0954 |
0.1448 |
0.1852 |
0.2199 |
0.2301 |
0.2597 |
0.2864 |
0.3109 |
0.3405 |
0.3611 |
100 |
0.0851 |
0.1292 |
0.1654 |
0.1966 |
0.2058 |
0.2324 |
0.2565 |
0.2786 |
0.3054 |
0.3242 |
1000 |
0.0266 |
0.0406 |
0.0520 |
0.0620 |
0.0650 |
0.0736 |
0.0814 |
0.0887 |
0.0976 |
0.1039 |
Page T-22