4сем / Лекции _4_сем pdf / ТВ_и_МС
.pdfПриложения |
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ПРИЛОЖЕНИЕ 3
Критические точки распределения χ2 (Пирсона)
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0,001 |
0,005 |
0,01 |
0,025 |
0,05 |
0,1 |
0,2 |
0,3 |
0,7 |
0,8 |
0,9 |
0,95 |
0,975 |
0,99 |
0,995 |
0,999 |
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1 |
10,83 |
7,879 |
6,635 |
5,024 |
3,841 |
2,706 |
1,642 |
1,074 |
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0,1480,0640,0160,0040,001 |
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1,571E-043,927E-051,570E-06 |
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2 |
13,82 |
10,60 |
9,210 |
7,378 |
5,991 |
4,605 |
3,219 |
2,408 |
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0,7130,4460,2110,1030,051 |
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0,020 |
0,010 |
0,002 |
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3 |
16,27 |
12,84 |
11,34 |
9,348 |
7,815 |
6,251 |
4,642 |
3,665 |
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1,4241,0050,5840,3520,216 |
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0,115 |
0,072 |
0,024 |
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4 |
18,47 |
14,86 |
13,28 |
11,14 |
9,488 |
7,779 |
5,989 |
4,878 |
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2,1951,6491,0640,7110,484 |
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0,297 |
0,207 |
0,091 |
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5 |
20,51 |
16,75 |
15,09 |
12,83 |
11,07 |
9,24 |
7,29 |
6,06 |
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3,0002,3431,6101,1450,831 |
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0,554 |
0,412 |
0,210 |
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6 |
22,46 |
18,55 |
16,81 |
14,45 |
12,59 |
10,64 |
8,56 |
7,23 |
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3,8283,0702,2041,6351,237 |
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0,872 |
0,676 |
0,381 |
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7 |
24,32 |
20,28 |
18,48 |
16,01 |
14,07 |
12,02 |
9,80 |
8,38 |
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4,6713,8222,8332,1671,690 |
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1,239 |
0,989 |
0,599 |
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8 |
26,12 |
21,95 |
20,09 |
17,53 |
15,51 |
13,36 |
11,03 |
9,52 |
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5,5274,5943,4902,7332,180 |
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1,647 |
1,344 |
0,857 |
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9 |
27,88 |
23,59 |
21,67 |
19,02 |
16,92 |
14,68 |
12,24 |
10,66 |
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6,3935,3804,1683,3252,700 |
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2,088 |
1,735 |
1,152 |
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10 |
29,59 |
25,19 |
23,21 |
20,48 |
18,31 |
15,99 |
13,44 |
11,78 |
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7,2676,1794,8653,9403,247 |
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2,558 |
2,156 |
1,479 |
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11 |
31,26 |
26,76 |
24,73 |
21,92 |
19,68 |
17,28 |
14,63 |
12,90 |
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8,1486,9895,5784,5753,816 |
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3,053 |
2,603 |
1,834 |
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12 |
32,91 |
28,30 |
26,22 |
23,34 |
21,03 |
18,55 |
15,81 |
14,01 |
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9,0347,8076,3045,2264,404 |
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3,571 |
3,074 |
2,214 |
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13 |
34,53 |
29,82 |
27,69 |
24,74 |
22,36 |
19,81 |
16,98 |
15,12 |
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9,9268,6347,0415,8925,009 |
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4,107 |
3,565 |
2,617 |
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14 |
36,12 |
31,32 |
29,14 |
26,12 |
23,68 |
21,06 |
18,15 |
16,22 |
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10,829,4677,7906,5715,629 |
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4,660 |
4,075 |
3,041 |
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15 |
37,70 |
32,80 |
30,58 |
27,49 |
25,00 |
22,31 |
19,31 |
17,32 |
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11,7210,318,5477,2616,262 |
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5,229 |
4,601 |
3,483 |
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16 |
39,25 |
34,27 |
32,00 |
28,85 |
26,30 |
23,54 |
20,47 |
18,42 |
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12,6211,159,3127,9626,908 |
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5,812 |
5,142 |
3,942 |
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17 |
40,79 |
35,72 |
33,41 |
30,19 |
27,59 |
24,77 |
21,61 |
19,51 |
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13,5312,0010,098,6727,564 |
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6,408 |
5,697 |
4,416 |
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18 |
42,31 |
37,16 |
34,81 |
31,53 |
28,87 |
25,99 |
22,76 |
20,60 |
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14,4412,8610,869,3908,231 |
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7,015 |
6,265 |
4,905 |
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19 |
43,82 |
38,58 |
36,19 |
32,85 |
30,14 |
27,20 |
23,90 |
21,69 |
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15,3513,7211,6510,128,907 |
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7,633 |
6,844 |
5,407 |
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20 |
45,31 |
40,00 |
37,57 |
34,17 |
31,41 |
28,41 |
25,04 |
22,77 |
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16,2714,5812,4410,859,591 |
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8,260 |
7,434 |
5,921 |
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21 |
46,80 |
41,40 |
38,93 |
35,48 |
32,67 |
29,62 |
26,17 |
23,86 |
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17,1815,4413,2411,5910,28 |
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8,897 |
8,034 |
6,447 |
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22 |
48,27 |
42,80 |
40,29 |
36,78 |
33,92 |
30,81 |
27,30 |
24,94 |
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18,1016,3114,0412,3410,98 |
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9,542 |
8,643 |
6,983 |
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23 |
49,73 |
44,18 |
41,64 |
38,08 |
35,17 |
32,01 |
28,43 |
26,02 |
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19,0217,1914,8513,0911,69 |
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10,20 |
9,260 |
7,529 |
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24 |
51,18 |
45,56 |
42,98 |
39,36 |
36,42 |
33,20 |
29,55 |
27,10 |
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19,9418,0615,6613,8512,40 |
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10,86 |
9,886 |
8,085 |
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25 |
52,62 |
46,93 |
44,31 |
40,65 |
37,65 |
34,38 |
30,68 |
28,17 |
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20,8718,9416,4714,6113,12 |
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11,52 |
10,52 |
8,649 |
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26 |
54,05 |
48,29 |
45,64 |
41,92 |
38,89 |
35,56 |
31,79 |
29,25 |
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21,7919,8217,2915,3813,84 |
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12,20 |
11,16 |
9,222 |
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27 |
55,48 |
49,65 |
46,96 |
43,19 |
40,11 |
36,74 |
32,91 |
30,32 |
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22,7220,7018,1116,1514,57 |
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12,88 |
11,81 |
9,803 |
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28 |
56,89 |
50,99 |
48,28 |
44,46 |
41,34 |
37,92 |
34,03 |
31,39 |
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23,6521,5918,9416,9315,31 |
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13,56 |
12,46 |
10,39 |
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29 |
58,30 |
52,34 |
49,59 |
45,72 |
42,56 |
39,09 |
35,14 |
32,46 |
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24,5822,4819,7717,7116,05 |
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14,26 |
13,12 |
10,99 |
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30 |
59,70 |
53,67 |
50,89 |
46,98 |
43,77 |
40,26 |
36,25 |
33,53 |
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25,5123,3620,6018,4916,79 |
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14,95 |
13,79 |
11,59 |
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35 |
66,62 |
60,27 |
57,34 |
53,20 |
49,80 |
46,06 |
41,78 |
38,86 |
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30,1827,8424,8022,4720,57 |
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18,51 |
17,19 |
14,69 |
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174
40 |
73,40 |
66,77 |
63,69 |
59,34 |
55,76 |
51,81 |
47,27 |
44,16 |
34,8732,3429,0526,5124,43 |
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22,16 |
20,71 |
17,92 |
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45 |
80,08 |
73,17 |
69,96 |
65,41 |
61,66 |
57,51 |
52,73 |
49,45 |
39,5836,8833,3530,6128,37 |
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25,90 |
24,31 |
21,25 |
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50 |
86,66 |
79,49 |
76,15 |
71,42 |
67,50 |
63,17 |
58,16 |
54,72 |
44,3141,4537,6934,7632,36 |
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29,71 |
27,99 |
24,67 |
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55 |
93,17 |
85,75 |
82,29 |
77,38 |
73,31 |
68,80 |
63,58 |
59,98 |
49,0646,0442,0638,9636,40 |
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33,57 |
31,73 |
28,17 |
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60 |
99,61 |
91,95 |
88,38 |
83,30 |
79,08 |
74,40 |
68,97 |
65,23 |
53,8150,6446,4643,1940,48 |
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37,48 |
35,53 |
31,74 |
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65 |
105,99 |
98,10 |
94,42 |
89,18 |
84,82 |
79,97 |
74,35 |
70,46 |
58,5755,2650,8847,4544,60 |
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41,44 |
39,38 |
35,36 |
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70 |
112,32104,21100,43 |
95,02 |
90,53 |
85,53 |
79,71 |
75,69 |
63,3559,9055,3351,7448,76 |
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45,44 |
43,28 |
39,04 |
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75 |
118,60110,29106,39100,84 |
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96,22 |
91,06 |
85,07 |
80,91 |
68,1364,5559,7956,0552,94 |
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49,48 |
47,21 |
42,76 |
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80 |
124,84116,32112,33106,63101,88 |
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96,58 |
90,41 |
86,12 |
72,9269,2164,2860,3957,15 |
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53,54 |
51,17 |
46,52 |
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85 |
131,04122,32118,24112,39107,52102,08 |
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95,73 |
91,32 |
77,7173,8868,7864,7561,39 |
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57,63 |
55,17 |
50,32 |
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90 |
137,21128,30124,12118,14113,15107,57101,05 |
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96,52 |
82,5178,5673,2969,1365,65 |
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61,75 |
59,20 |
54,16 |
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95 |
143,34134,25129,97123,86118,75113,04106,36101,7287,3283,2577,8273,5269,92 |
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65,90 |
63,25 |
58,02 |
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100 |
149,45140,17135,81129,56124,34118,50111,67106,9192,1387,9582,3677,9374,22 |
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70,06 |
67,33 |
61,92 |
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Таблица значений q = q (n,γ )
n |
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γ |
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n |
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γ |
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0,95 |
0,99 |
0,999 |
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0,95 |
0,99 |
0,999 |
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5 |
1,37 |
2,67 |
5,64 |
20 |
0,37 |
0,58 |
0,88 |
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6 |
1,09 |
2,01 |
3,88 |
25 |
0,32 |
0,49 |
0,73 |
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7 |
0,92 |
1,62 |
2,98 |
30 |
0,28 |
0,43 |
0,63 |
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8 |
0,80 |
1,38 |
2,42 |
35 |
0,26 |
0,38 |
0,56 |
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9 |
0,71 |
1,20 |
2,06 |
40 |
0,24 |
0,35 |
0,50 |
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10 |
0,65 |
1,08 |
1,80 |
45 |
0,22 |
0,32 |
0,46 |
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11 |
0,59 |
0,98 |
1,60 |
50 |
0,21 |
0,30 |
0,43 |
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12 |
0,55 |
0,90 |
1,45 |
60 |
0,188 |
0,269 |
0,38 |
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13 |
0,52 |
0,83 |
1,33 |
70 |
0,174 |
0,245 |
0,34 |
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14 |
0,48 |
0,78 |
1,23 |
80 |
0,161 |
0,226 |
0,31 |
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15 |
0,46 |
0,73 |
1,15 |
90 |
0,151 |
0,211 |
0,29 |
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16 |
0,44 |
0,70 |
1,07 |
100 |
0,143 |
0,198 |
0,27 |
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17 |
0,42 |
0,66 |
1,01 |
150 |
0,115 |
0,160 |
0,211 |
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18 |
0,40 |
0,63 |
0,96 |
200 |
0,099 |
0,136 |
0,185 |
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19 |
0,39 |
0,60 |
0,92 |
250 |
0,089 |
0,120 |
0,162 |
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Приложения |
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177 |
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28 |
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1,313 |
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1,701 |
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2,048 |
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2,467 |
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2,763 |
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3,047 |
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3,408 |
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3,674 |
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1,175 |
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29 |
1,174 |
1,311 |
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1,699 |
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2,045 |
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2,462 |
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2,756 |
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3,038 |
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3,396 |
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3,660 |
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30 |
1,173 |
1,310 |
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1,697 |
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2,042 |
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2,457 |
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2,750 |
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3,030 |
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3,385 |
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3,646 |
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40 |
1,167 |
1,303 |
|
1,684 |
|
2,021 |
|
2,423 |
|
2,704 |
|
2,971 |
|
3,307 |
|
3,551 |
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50 |
1,164 |
1,299 |
|
1,676 |
|
2,009 |
|
2,403 |
|
2,678 |
|
2,937 |
|
3,261 |
|
3,496 |
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60 |
1,162 |
1,296 |
|
1,671 |
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2,000 |
|
2,390 |
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2,660 |
|
2,915 |
|
3,232 |
|
3,460 |
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70 |
1,160 |
1,294 |
|
1,667 |
|
1,994 |
|
2,381 |
|
2,648 |
|
2,899 |
|
3,211 |
|
3,435 |
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80 |
1,159 |
1,292 |
|
1,664 |
|
1,990 |
|
2,374 |
|
2,639 |
|
2,887 |
|
3,195 |
|
3,416 |
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90 |
1,158 |
1,291 |
|
1,662 |
|
1,987 |
|
2,368 |
|
2,632 |
|
2,878 |
|
3,183 |
|
3,402 |
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100 |
1,157 |
1,290 |
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1,660 |
|
1,984 |
|
2,364 |
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2,626 |
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2,871 |
|
3,174 |
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3,390 |
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200 |
1,154 |
1,286 |
|
1,653 |
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1,972 |
|
2,345 |
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2,601 |
|
2,838 |
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3,131 |
|
3,340 |
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180
ПРИЛОЖЕНИЕ 5 (продолжение)
Таблица 5
Квантили F-распределения Фишера-Снедекора k1 - число степеней свободы большей дисперсии (числитель) k2 - число степеней свободы меньшей дисперсии (знаменатель)
Уровень значимости a = 0,01
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k1 |
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k2 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
1 |
4052,24999,35403,55624,3 |
5764 |
5859 5928,3 5981 6022,46055,96083,46106,76125,8 |
6143 |
6157 |
||||||||||
2 |
98,502 |
99 |
99,164 |
99,251 |
99,302 |
99,33199,35799,375 99,39 99,39799,40899,419 |
99,422 |
99,42699,433 |
|||||||
3 |
34,11630,816 |
29,457 28,71 |
28,237 |
27,91127,67127,48927,34527,22827,13227,052 |
26,983 |
26,92426,872 |
|||||||||
4 |
21,198 |
18 |
16,694 |
15,977 |
15,522 |
15,20714,97614,79914,65914,54614,45214,374 |
14,306 |
14,24914,198 |
|||||||
5 |
16,25813,274 |
12,06 |
11,392 |
10,967 |
10,67210,45610,28910,15810,0519,96269,8883 |
9,8248 |
9,77 |
9,7223 |
|||||||
6 |
13,74510,9259,77969,14848,7459 |
8,466 |
8,26 |
8,1017 7,976 7,87427,78967,71837,6575 |
7,605 |
7,559 |
|||||||||
7 |
12,2469,54658,45137,84677,46047,19146,99296,84016,71886,62016,53816,4691 |
6,41 |
6,359 6,3144 |
||||||||||||
8 |
11,2598,6491 |
7,591 |
7,00616,63186,37076,17766,02885,91065,81435,73435,66675,60895,55885,5152 |
||||||||||||
9 |
10,5628,0215 |
6,992 |
6,42216,05695,80185,61285,46715,35115,25655,17795,11155,05455,00524,9621 |
||||||||||||
10 |
10,0447,55956,55235,99445,63645,38585,20015,05674,94244,84914,77164,70584,64964,60084,5582 |
||||||||||||||
11 |
9,64617,20576,21675,6683 |
5,316 |
5,0692 4,886 4,74454,63154,53934,46244,39744,34164,29334,2509 |
||||||||||||
12 |
9,33036,92665,95255,41195,06444,82054,63954,49944,38754,29614,21984,15534,09984,05174,0096 |
||||||||||||||
13 |
9,07386,70095,73945,20534,86164,6203 4,441 4,30214,19114,10034,02453,96033,90523,85733,8154 |
||||||||||||||
14 |
8,86176,51495,56395,0354 |
4,695 |
4,45584,2779 |
4,14 |
4,02973,9394 3,864 3,80023,74523,69763,6557 |
||||||||||
15 |
8,68326,3588 |
5,417 |
4,89324,55564,31834,14164,00443,89483,80493,72993,66623,61153,56393,5222 |
||||||||||||
16 |
8,53096,22635,29224,77264,43744,20164,02593,88963,78043,69093,61623,55273,49813,4506 3,409 |
||||||||||||||
17 |
8,39986,1121 |
5,185 |
4,6689 |
4,336 |
4,10153,92673,79093,68233,59313,51853,4552 |
3,4007 |
3,35333,3117 |
||||||||
18 |
8,28556,01295,0919 4,579 |
4,24794,01463,84063,70543,59713,50813,43383,37063,31623,26893,2273 |
|||||||||||||
19 |
8,185 5,92595,01034,50024,17083,93863,76533,63053,52253,43383,35963,29653,24223,19493,1533 |
||||||||||||||
20 |
8,096 |
5,849 4,93824,43074,10273,87143,69873,56443,45673,36823,29413,23113,17693,1296 3,088 |
Приложения |
181 |
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ПРИЛОЖЕНИЕ 5 (продолжение)
Уровень значимости a = 0,02
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k1 |
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k2 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
1 |
1012,51249,51350,51405,81440,61464,41481,8 1495 1505,41513,71520,61526,31531,21535,4 |
1539 |
|||||||||||||
2 |
48,505 |
49 |
49,16549,24949,29849,33249,35649,37349,38749,39849,40749,41549,42249,427 |
49,431 |
|||||||||||
3 |
20,61818,858 18,11 17,69417,42917,245 17,11 17,00716,926 16,86 16,80516,759 16,72 16,686 |
16,657 |
|||||||||||||
4 |
14,04 12,14211,34310,89910,61610,41910,27410,16210,07410,0039,94369,89389,85149,8148 |
9,7829 |
|||||||||||||
5 |
11,3239,45448,6702 8,233 |
7,953 7,75767,6137 7,503 7,41517,34387,28477,23487,19237,1555 |
7,1234 |
||||||||||||
6 |
9,87648,0521 7,287 6,85946,58476,39286,25086,14156,05465,98395,92525,87575,83345,7968 |
5,7648 |
|||||||||||||
7 |
8,98777,20266,45396,03475,76475,57565,43555,32735,24135,17125,11285,06365,0214 |
4,985 |
4,9531 |
||||||||||||
8 |
8,38956,63665,90145,48895,22275,03594,8972 |
4,79 |
4,70464,63484,57684,52774,48574,4493 |
4,4174 |
|||||||||||
9 |
7,9605 6,234 5,50975,10274,83954,65454,51694,41054,3255 4,256 4,19824,14934,10734,0709 |
4,039 |
|||||||||||||
10 |
7,63845,93365,21824,8157 4,555 4,37144,23474,12884,0442 3,975 3,91733,86843,8264 |
3,79 |
3,7581 |
||||||||||||
11 |
7,38795,70124,99324,59434,33574,15334,01743,91193,82753,75843,70083,65193,60993,5735 |
3,5415 |
|||||||||||||
12 |
7,18775,51634,81454,41874,16173,9804 3,845 3,73983,65573,5867 3,529 3,48023,43813,4017 |
3,3696 |
|||||||||||||
13 |
7,02415,36574,6692 4,276 4,02053,83993,70513,60013,51613,44723,38963,34073,2986 |
3,262 |
3,2299 |
||||||||||||
14 |
6,88795,24074,54884,15783,90363,72373,58923,48453,40063,33173,27413,2252 3,183 3,1464 |
3,1142 |
|||||||||||||
15 |
6,77295,13554,44744,05843,8052 3,626 3,49183,38733,30353,2346 3,177 |
3,128 3,0858 |
3,049 |
3,0168 |
|||||||||||
16 |
6,67445,04554,36093,97373,72143,54263,40873,30443,22063,15183,0941 3,045 3,0028 |
2,966 |
2,9336 |
||||||||||||
17 |
6,58924,96784,28633,90063,64913,47073,33713,23293,14923,08033,02262,97352,93122,8943 |
2,8619 |
|||||||||||||
18 |
6,51474,90014,22133,83683,58613,40813,27473,17063,0869 3,018 2,96032,91122,86882,8318 |
2,7993 |
|||||||||||||
19 |
6,449 4,84044,16413,78093,53073,35313,21993,11593,03222,96332,90552,85632,81392,7769 |
2,7443 |
|||||||||||||
20 |
6,39074,78764,11343,73133,48173,30443,17133,06742,98372,9148 2,857 2,80772,76522,7281 |
2,6955 |
182
ПРИЛОЖЕНИЕ 5 (продолжение)
Уровень значимости a = 0,05
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k1 |
|
|
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|
k2 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
1 |
161,45 199,5 215,71224,58230,16233,99236,77238,88240,54241,88242,98 243,9 244,69245,36245,95 |
||||||||||||||
2 |
18,513 |
19 |
19,16419,24719,29619,32919,35319,37119,38519,39619,40519,41219,41919,42419,429 |
||||||||||||
3 |
10,1289,55219,27669,11729,01348,94078,88678,84528,81238,78558,76338,74478,72868,71498,7028 |
||||||||||||||
4 |
7,70866,94436,59146,38826,25616,16316,0942 6,041 5,99885,96445,93585,91175,89115,87335,8578 |
||||||||||||||
5 |
6,60795,78615,40945,19225,05034,95034,87594,81834,77254,7351 4,704 4,67774,65524,63584,6188 |
||||||||||||||
6 |
5,98745,14324,75714,53374,38744,28394,20674,1468 4,099 |
4,06 |
4,02743,99993,97643,95593,9381 |
||||||||||||
7 |
5,59154,73744,34684,12033,9715 3,866 3,78713,72573,67673,6365 3,603 3,57473,55033,52923,5107 |
||||||||||||||
8 |
5,3176 4,459 4,06623,83793,68753,58063,50053,43813,38813,34723,31293,2839 3,259 3,23743,2184 |
||||||||||||||
9 |
5,11744,25653,86253,63313,48173,37383,29273,22963,17893,13733,10253,07293,04753,02553,0061 |
||||||||||||||
10 |
4,96464,10283,7083 3,478 3,32583,21723,13553,07173,02042,9782 2,943 |
2,913 2,88722,8647 2,845 |
|||||||||||||
11 |
4,84433,98233,58743,35673,20393,09463,0123 2,948 2,89622,85362,81792,78762,76142,73862,7186 |
||||||||||||||
12 |
4,74723,88533,49033,25923,10592,99612,91342,84862,79642,75342,71732,68662,66022,63712,6169 |
||||||||||||||
13 |
4,66723,80563,41053,17913,02542,91532,83212,76692,7144 2,671 2,63462,60372,57692,55362,5331 |
||||||||||||||
14 |
4,60013,73893,34393,11222,95822,84772,76422,69872,64582,60222,56552,53422,50732,4837 2,463 |
||||||||||||||
15 |
4,54313,68233,28743,05562,90132,79052,70662,64082,58762,54372,50682,47532,44812,42442,4034 |
||||||||||||||
16 |
4,494 3,63373,23893,00692,85242,74132,65722,59112,53772,49352,45642,42472,39732,37332,3522 |
||||||||||||||
17 |
4,45133,59153,19682,9647 |
2,81 |
2,69872,6143 2,548 2,49432,44992,41262,38072,3531 2,329 2,3077 |
||||||||||||
18 |
4,41393,55463,15992,92772,77292,66132,57672,51022,45632,41172,37422,34212,3143 |
2,29 |
2,2686 |
||||||||||||
19 |
4,38083,52193,12742,89512,74012,62832,54352,47682,42272,37792,3402 2,308 |
2,28 |
2,25562,2341 |
||||||||||||
20 |
4,35133,49283,09842,86612,7109 2,599 |
2,514 2,44712,39282,3479 |
2,31 |
2,27762,2495 2,225 2,2033 |