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)
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標準正規分布表(両側確率)
標準正規分布表 |
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.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 |
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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 |
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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 |
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