統計学

統計学

「実験のデータが有効かどうか」を調べるには統計学の知識が必要になります。
これによって、データの有効性を知ることができます。

分布表 (t分布表・X2分布表・標準正規分布表・F分布表・Wilcoxon)

　t分布表(両側確率),X2分布表(上側確率)

t分布表
P=0.05 0.01
df=1 12.706 63.655
2 4.303 9.925
3 3.182 5.841
4 2.776 4.604
5 2.571 4.032
6 2.447 3.707
7 2.365 3.500
8 2.306 3.355
9 2.262 3.250
10 2.228 3.169
11 2.201 3.106
12 2.179 3.055
13 2.160 3.012
14 2.145 2.977
15 2.131 2.947
16 2.120 2.921
17 2.110 2.898
18 2.101 2.878
19 2.093 2.861
20 2.086 2.845
21 2.080 2.831
22 2.074 2.819
23 2.069 2.807
24 2.064 2.797
25 2.060 2.787
26 2.056 2.779
27 2.052 2.771
28 2.048 2.763
29 2.045 2.756
30 2.042 2.750
32 2.037 2.738
34 2.032 2.728
36 2.028 2.719
38 2.024 2.712
40 2.021 2.704
42 2.018 2.698
44 2.015 2.692
46 2.013 2.687
48 2.011 2.682
50 2.009 2.678
60 2.000 2.660
70 1.994 2.648
80 1.990 2.639
90 1.987 2.632
100 1.984 2.626
120 1.980 2.617
140 1.977 2.611
160 1.975 2.607
180 1.973 2.603
200 1.972 2.601
X2分布表
P=0.05 0.01
df=1 3.841 51 68.669 1 6.635 51 77.386
2 5.991 52 69.832 2 9.210 52 78.616
3 7.815 53 70.993 3 11.345 53 79.843
4 9.488 54 72.153 4 13.277 54 81.069
5 11.071 55 73.311 5 15.086 55 82.292
6 12.592 56 74.468 6 16.086 56 83.513
7 14.067 57 75.624 7 18.475 57 84.733
8 15.507 58 76.778 8 20.090 58 85.950
9 16.919 59 77.931 9 21.666 59 87.166
10 18.307 60 79.082 10 23.209 60 88.379
11 19.675 61 80.232 11 24.725 61 89.591
12 21.026 62 81.381 12 26.217 62 90.802
13 22.362 63 82.529 13 27.688 63 92.010
14 23.685 64 83.675 14 29.141 64 93.217
15 24.996 65 84.821 15 30.578 65 94.422
16 26.296 66 85.965 16 32.000 66 95.626
17 27.587 67 87.108 17 33.409 67 96.828
18 28.869 68 88.250 18 34.805 68 98.028
19 30.144 69 89.391 19 36.191 69 99.228
20 31.410 70 90.531 20 37.566 70 100.425
21 32.671 71 91.670 21 38.932 71 101.621
22 33.924 72 92.808 22 40.289 72 102.816
23 35.172 73 93.945 23 41.638 73 104.010
24 36.415 74 95.081 24 42.980 74 105.202
25 37.652 75 96.217 25 44.314 75 106.393
26 38.885 76 97.351 26 45.642 76 107.583
27 40.113 77 98.484 27 46.963 77 108.771
28 41.337 78 99.617 28 48.278 78 109.958
29 42.557 79 100.749 29 49.588 79 111.144
30 43.773 80 101.879 30 50.892 80 112.329
31 44.985 81 103.009 31 52.191 81 113.512
32 46.194 82 104.139 32 53.486 82 114.695
33 47.400 83 105.267 33 54.776 83 115.876
34 48.802 84 106.395 34 56.061 84 117.057
35 49.802 85 107.522 35 57.342 85 118.236
36 50.998 86 108.648 36 58.619 86 119.414
37 52.192 87 109.773 37 59.892 87 120.591
38 53.384 88 110.898 38 61.162 88 121.767
39 54.572 89 112.022 39 62.428 89 122.942
40 55.758 90 113.145 40 63.691 90 124.116
41 56.942 91 114.268 41 64.950 91 125.289
42 58.124 92 115.390 42 66.206 92 126.462
43 59.304 93 116.511 43 67.459 93 127.633
44 60.481 94 117.632 44 68.710 94 128.803
45 61.656 95 118.752 45 69.957 95 129.973
46 62.830 96 119.871 46 71.201 96 131.141
47 64.001 97 120.990 47 72.443 97 132.309
48 65.171 98 122.108 48 73.683 98 133.476
49 66.339 99 123.225 49 74.919 99 134.642
50 67.505 100 124.342 50 76.154 100 135.807

　標準正規分布表(両側確率)

　　　

標準正規分布表
.00 .01 .02 .03 .04 .05 .06 .07 .08 .09
0.0 1.0000 .9920 .9840 .9760 .9680 .9602 .9522 .9442 .9362 .9282
0.1 .9204 .9124 .9044 .8966 .8886 .8808 .8728 .8650 .8572 .8494
0.2 .8414 .8336 .8258 .8180 .8104 .8026 .7948 .7872 .7794 .7718
0.3 .7642 .7566 .7490 .7414 .7338 .7264 .7188 .7114 .7040 .6966
0.4 .6892 .6818 .6744 .6672 .6600 .6528 .6456 .6384 .6312 .6242
0.5 .6170 .6100 .6030 .5962 .5892 .5824 .5754 .5686 .5620 .5552
0.6 .5486 .5418 .5352 .5286 .5222 .5156 .5092 .5028 .4964 .4902
0.7 .4840 .4776 .4716 .4654 .4592 .4532 .4472 .4412 .4354 .4296
0.8 .4238 .4180 .4122 .4066 .4010 .3954 .3898 .3842 .3788 .3734
0.9 .3682 .3628 .3576 .3524 .3472 .3422 .3370 .3320 .3270 .3222
1.0 .3174 .3124 .3078 .3030 .2984 .2938 .2892 .2846 .2802 .2758
1.1 .2714 .2670 .2628 .2584 .2542 .2502 .2460 .2420 .2380 .2340
1.2 .2302 .2262 .2224 .2186 .2150 .2112 .2076 .2040 .2006 .1970
1.3 .1936 .1902 .1868 .1836 .1802 .1770 .1738 .1706 .1676 .1646
1.4 .1616 .1586 .1556 .1528 .1498 .1470 .1442 .1416 .1388 .1362
1.5 .1336 .1310 .1286 .1260 .1236 .1212 .1188 .1164 .1142 .1118
1.6 .1096 .1074 .1052 .1030 .1010 .0990 .0970 .0950 .0930 .0910
1.7 .0892 .0872 .0854 .0836 .0818 .0802 .0784 .0768 .0750 .0734
1.8 .0718 .0702 .0688 .0672 .0658 .0644 .0628 .0614 .0602 .0588
1.9 .0574 .0562 .0548 .0536 .0524 .0512 .0500 .0488 .0478 .0466
2.0 .04550 .04444 .04338 .04236 .04134 .04036 .03940 .03846 .03752 .03662
2.1 .03572 .03486 .03400 .03318 .03236 .03156 .03078 .03000 .02926 .02852
2.2 .02780 .02710 .02642 .02574 .02510 .02444 .02382 .02320 .02260 .02202
2.3 .02144 .02088 .02034 .01980 .01928 .01878 .01828 .01778 .01732 .01684
2.4 .01640 .01596 .01552 .01510 .01468 .01428 .01390 .01352 .01314 .01278
2.5 .01242 .01208 .01174 .01140 .01108 .01078 .01046 .01016 .00988 .00960
2.6 .00932 .00906 .00880 .00854 .00830 .00804 .00782 .00758 .00736 .00714
2.7 .00694 .00672 .00652 .00634 .00614 .00596 .00578 .00560 .00544 .00528
2.8 .00510 .00496 .00480 .00466 .00452 .00438 .00424 .00410 .00398 .00386
2.9 .00374 .00362 .00350 .00338 .00328 .00318 .00308 .00298 .00288 .00278
3.0 .00270 .00262 .00252 .00244 .00236 .00228 .00222 .00214 .00206 .00200
3.1 .00194 .00188 .00180 .00174 .00168 .00164 .00158 .00152 .00148 .00142
3.2 .00138 .00132 .00128 .00124 .00120 .00116 .00112 .00108 .0104 .00100
3.3 .00096 .00094 .00090 .00086 .00084 .00080 .00078 .00076 .00072 .00070
3.4 .00068 .00064 .00062 .00060 .00058 .00056 .00054 .00052 .00050 .00048


　F分布表(上側確率)

　P=0.05

F分布表
df1=1 2 3 4 5 6 7 8 9
df2=1 161.5 199.5 215.7 224.6 230.2 234.0 236.8 238.9 240.5
2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38
3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81
4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00
5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77
6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10
7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68
8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39
9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18
10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02
11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90
12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80
13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71
14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65
15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59
16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54
17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49
18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46
19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42
20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39
22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34
24 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30
26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27
28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24
30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21
32 4.15 3.29 2.90 2.67 2.51 2.40 2.31 2.24 2.19
34 4.13 3.28 2.88 2.65 2.49 2.38 2.29 2.23 2.17
36 4.11 3.26 2.87 2.63 2.48 2.36 2.28 2.21 2.15
38 4.10 3.24 2.85 2.62 2.46 2.35 2.26 2.19 2.14
40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12
42 4.07 3.22 2.83 2.59 2.44 2.32 2.24 2.17 2.11
44 4.06 3.21 2.82 2.58 2.43 2.31 2.23 2.16 2.10
46 4.05 3.20 2.81 2.57 2.42 2.30 2.22 2.15 2.09
48 4.04 3.19 2.80 2.57 2.41 2.29 2.21 2.14 2.08
50 4.03 3.18 2.79 2.56 2.40 2.29 2.20 2.13 2.07
60 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04
70 3.98 3.13 2.74 2.50 2.35 2.23 2.14 2.07 2.02
80 3.96 3.11 2.72 2.49 2.33 2.21 2.13 2.06 2.00
90 3.95 3.10 2.71 2.47 2.32 2.20 2.11 2.04 1.99
100 3.94 3.09 2.70 2.46 2.31 2.19 2.10 2.03 1.97
120 3.92 3.07 2.68 2.45 2.29 2.18 2.09 2.02 1.96
140 3.91 3.06 2.67 2.44 2.28 2.16 2.08 2.01 1.95
160 3.90 3.05 2.66 2.43 2.27 2.16 2.07 2.00 1.94
180 3.89 3.05 2.65 2.42 2.26 2.15 2.06 1.99 1.93
200 3.89 3.04 2.65 2.42 2.26 2.14 2.06 1.98 1.93


10 12 15 20 30 40 60 80 120
df2=1 241.9 243.9 246.0 248.0 250.1 251.1 252.2 252.7 253.3
2 19.40 19.41 19.43 19.45 19.46 19.47 19.48 19.48 19.49
3 8.79 8.74 8.70 8.66 8.62 8.59 8.57 8.56 8.55
4 5.96 5.91 5.86 5.80 5.75 5.72 5.69 5.67 5.66
5 4.74 4.68 4.62 4.56 4.50 4.46 4.43 4.41 4.40
6 4.06 4.00 3.94 3.87 3.81 3.77 3.74 3.72 3.70
7 3.64 3.57 3.51 3.44 3.38 3.34 3.30 3.29 3.27
8 3.35 3.28 3.22 3.15 3.08 3.04 3.01 2.99 2.97
9 3.14 3.07 3.01 2.94 2.86 2.83 2.79 2.77 2.75
10 2.98 2.91 2.85 2.77 2.70 2.66 2.62 2.60 2.58
11 2.85 2.79 2.72 2.65 2.57 2.53 2.49 2.47 2.45
12 2.75 2.69 2.62 2.54 2.47 2.43 2.38 2.36 2.34
13 2.67 2.60 2.53 2.46 2.38 2.34 2.30 2.27 2.25
14 2.60 2.53 2.46 2.39 2.31 2.27 2.22 2.20 2.18
15 2.54 2.48 2.40 2.33 2.25 2.20 2.16 2.14 2.11
16 2.49 2.42 2.35 2.28 2.19 2.15 2.11 2.08 2.06
17 2.45 2.38 2.31 2.23 2.15 2.10 2.06 2.03 2.01
18 2.41 2.34 2.27 2.19 2.11 2.06 2.02 1.99 1.97
19 2.38 2.31 2.23 2.16 2.07 2.03 1.98 1.96 1.93
20 2.35 2.28 2.20 2.12 2.04 1.99 1.95 1.92 1.90
22 2.30 2.23 2.15 2.07 1.98 1.94 1.89 1.86 1.84
24 2.25 2.18 2.11 2.03 1.94 1.89 1.84 1.82 1.79
26 2.22 2.15 2.07 1.99 1.90 1.85 1.80 1.78 1.75
28 2.19 2.12 2.04 1.96 1.87 1.82 1.77 1.74 1.71
30 2.16 2.09 2.01 1.93 1.84 1.79 1.74 1.71 1.68
32 2.14 2.07 1.99 1.91 1.82 1.77 1.71 1.69 1.66
34 2.12 2.05 1.97 1.89 1.89 1.75 1.69 1.66 1.63
36 2.11 2.03 1.95 1.87 1.78 1.73 1.67 1.64 1.61
38 2.09 2.02 1.94 1.85 1.76 1.71 1.65 1.62 1.59
40 2.08 2.00 1.92 1.84 1.74 1.69 1.64 1.61 1.58
42 2.06 1.99 1.91 1.83 1.73 1.68 1.62 1.59 1.56
44 2.05 1.98 1.90 1.81 1.72 1.67 1.61 1.58 1.55
46 2.04 1.97 1.89 1.80 1.71 1.65 1.60 1.57 1.53
48 2.03 1.96 1.88 1.79 1.70 1.64 1.59 1.56 1.52
50 2.03 1.95 1.87 1.78 1.69 1.63 1.58 1.54 1.51
60 1.99 1.92 1.84 1.75 1.65 1.59 1.53 1.50 1.47
70 1.97 1.89 1.81 1.72 1.62 1.57 1.50 1.47 1.44
80 1.95 1.88 1.79 1.70 1.60 1.54 1.48 1.45 1.41
90 1.94 1.86 1.78 1.69 1.59 1.53 1.46 1.43 1.39
100 1.93 1.85 1.77 1.68 1.57 1.52 1.45 1.41 1.38
120 1.91 1.83 1.75 1.66 1.55 1.50 1.43 1.39 1.35
140 1.90 1.82 1.74 1.65 1.54 1.48 1.41 1.38 1.33
160 1.89 1.81 1.73 1.64 1.53 1.47 1.40 1.36 1.32
180 1.88 1.81 1.72 1.63 1.52 1.46 1.39 1.35 1.31
200 1.88 1.80 1.72 1.62 1.52 1.46 1.39 1.35 1.30

　Wilcoxon検定表

Wilcoxon検定表
P＜0.05 P＜0.01
n=6 0
7 2
8 3 0
9 5 1
10 8 3
11 10 5
12 13 7
13 17 9
14 21 12
15 25 15
16 29 19
17 34 23
18 40 27
19 46 32
20 52 37
21 58 42
22 65 48
23 73 54
24 81 61
25 89 68
26 98 75
27 107 83
28 116 91
29 126 100
30 137 109
31 147 118
32 159 128
33 170 138
34 182 148
35 195 159
36 208 171
37 221 182
38 235 194
39 249 207
40 264 220
41 279 233
42 294 247
43 310 261
44 327 276
45 343 291
46 361 307
47 378 322
48 396 339
49 415 355
50 434 373