確率分布表

正規分布表Ⅰ

\(\displaystyle P=P_r(Z≧u)= \frac{1}{\sqrt{2π}}\int_{u}^∞e^{\frac{-u^2}{2}du}\)

u*=0123456789
0.0.*0.5000.4960.4920.4880.4840.4800.4760.470.4680.46
0.1.*0.4600.4560.4520.4480.4440.440.4360.4320.4280.424
0.2.*0.4200.4160.4120.4090.4050.4010.3970.3930.3890.385
0.3.*0.3820.3780.3740.3700.3660.3630.3590.3550.3510.348
0.4.*0.3440.3400.3370.3330.3290.3260.320.3190.3150.312
0.5.*0.3080.3050.3010.2980.2940.2910.2870.2840.2800.277
0.6*0.2740.2700.2670.2640.2610.2570.2540.2510.2480.245
0.7*0.2410.2380.2350.2320.2290.2260.2230.2200.2170.214
0.8*0.2110.2080.2060.2030.2000.1970.1940.1920.1890.186
0.9*0.1840.1810.1780.1760.1730.1710.1680.1660.1630.161
1.0*0.1580.1560.1530.1510.1490.1460.1440.1420.1400.137
1.1*0.1350.1330.1310.1290.1270.1250.1230.1210.1190.117
1.2*0.1150.1130.1110.1090.1070.1050.1030.1020.1000.098
1.3*0.0960.0950.0930.0910.0900.0880.0860.0850.0830.082
1.4*0.0800.0790.0770.0760.0740.0730.0720.0700.0690.068
1.5*0.0660.0650.0640.0630.0610.0600.0590.0580.0570.055
1.6*0.0540.0530.0520.0510.0500.0490.0480.0470.0460.045
1.7*0.0440.0430.0420.0410.0400.0400.0390.0380.0370.036
1.8*0.0350.0350.0340.0330.0320.0320.0310.0300.0300.029
1.9*0.0280.0280.0270.0260.0260.0250.0250.0240.0230.023
2.0*0.0220.0220.0210.0210.0200.0200.0190.0190.0180.018
2.1*0.0170.0170.0170.0160.0160.0150.0150.0150.0140.014
2.2*0.0130.0130.0130.0120.0120.0120.0110.0110.0110.011
2.3*0.010.010.010.0090.0090.0090.0090.0080.0080.008
2.4*0.0080.0070.0070.0070.0070.0070.0060.0060.0060.006
2.5*0.0060.0060.0050.0050.0050.0050.0050.0050.0040.004
2.6*0.0040.0040.0040.0040.0040.0040.0030.0030.0030.003
2.7*0.0030.0030.0030.0030.0030.0020.0020.0020.0020.002
2.8*0.0020.0020.0020.0020.0020.0020.0020.0020.0010.001
2.9*0.0010.0010.0010.0010.0010.0010.0010.0010.0010.001
3.0*0.0010.0010.0010.0010.0010.0010.0010.0010.0010.001
4.0*0.000030.000030.000030.000030.000030.000020.000020.000020.000020.00002

正規分布表Ⅱ

P0.0010.0050.010.0250.050.10.20.30.4
u3.092.5762.3761.961.6451.2820.8450.5240.253

\(χ^2\)表

\(自由度Φ,片側上限確率Pからχ^2(Φ,P)\)を求める表

Φ/P0.9950.990.9750.950.50.10.050.0250.010.005
10.000040.00020.0010.00390.4552.7103.845.026.637.88
20.010030.020100.05060.10261.3864.615.997.389.2110.6
30.071720.11480.21580.3522.376.257.819.3511.312.8
40.20700.29710.4840.7113.367.789.4911.113.314.9
50.41170.5540.8311.154.359.2411.0712.815.116.8
60.6760.8721.241.645.3510.6412.614.516.818.6
70.9891.241.692.176.3512.0214.116.018.520.3
81.341.652.182.737.3413.415.517.520.122.0
91.732.092.703.338.3414.716.919.021.723.6
102.162.563.253.949.3416.018.320.523.225.2
112.603.053.824.5710.317.319.721.924.726.8
123.073.574.405.2311.318.621.023.326.228.3
133.574.115.015.8912.319.822.424.727.729.8
144.074.665.636.5713.321.123.726.129.131.3
154.605.236.267.2614.322.325.027.530.632.8
165.145.816.917.9615.323.526.328.932.034.3
175.706.417.568.6716.324.827.630.233.435.7
186.267.018.239.3917.326.028.931.534.837.2
196.847.638.9110.118.327.230.132.936.238.6
207.438.269.5910.919.328.431.434.237.640.0
218.038.9010.311.620.329.632.735.538.941.4
228.649.5411.012.321.330.833.936.840.342.8
239.2610.211.713.122.332.035.238.141.644.2
249.8910.912.413.923.333.236.439.443.045.6
2510.511.513.114.624.334.437.740.744.346.9
2611.212.213.815.425.335.638.941.945.648.3
2711.812.914.616.226.336.740.143.247.049.6
2812.513.615.316.927.337.941.344.548.351.0
2913.114.316.117.728.339.142.645.749.652.3
3013.815.016.818.529.340.343.847.050.953.7
4020.722.224.426.539.351.855.859.363.766.8
5028.029.732.434.849.363.267.571.476.279.5
6035.537.540.543.259.374.479.183.388.492.0
8051.253.557.260.479.396.6101.9106.6112.3116.3
10067.370.174.277.999.3118.5124.3129.6135.8140.2

t 表

\(t(Φ,P)\)

\(自由度Φと両側確率Pからtを求める表\)

Φ/P0.50.40.30.20.10.050.020.010.001
11.0001.3761.9633.0786.31412.70631.82163.657636.619
20.8161.00611.3861.8862.9204.3036.9659.92531.599
30.7650.9781.251.6382.3533.1824.5415.84112.924
40.7410.9411.1901.5332.1322.7763.7474.6048.610
50.7270.9201.1561.4762.0152.5713.3654.0326.869
60.7180.9061.1341.4401.9432.4473.1433.7075.959
70.7110.8961.1191.4151.8952.3652.9983.4995.408
80.7060.8891.1081.3971.8602.3062.8963.3555.041
90.7030.8831.1001.3831.8332.2622.8213.2504.781
100.7000.8791.0931.3721.8122.2282.7643.1694.587
110.6970.8761.0881.3631.7962.2012.7183.1064.437
120.6950.8731.0831.3561.7822.1792.6813.0554.318
130.6940.8701.0791.3501.7712.1602.6503.0124.221
140.6920.8681.0761.3451.7612.1452.6242.9774.140
150.6910.8661.0741.3411.7532.1312.6022.9474.073
160.690.8651.0711.3371.7462.1202.5832.9214.015
170.6890.8631.0691.3331.7402.1102.5672.8983.965
180.6880.8621.0671.3301.7342.1012.5522.8783.922
190.6880.8611.0661.3281.7292.0932.5392.8613.883
200.6870.8601.0641.3251.7252.0862.5282.8453.850
210.6860.8591.0631.3231.7212.0802.5182.8312.819
220.6860.8581.0611.3211.7172.0742.5082.8193.792
230.6850.8581.0601.3191.7142.0692.5002.8073.768
240.6850.8571.0591.3181.7112.0642.4922.7973.745
250.6840.8561.0581.3161.7082.0602.4852.7873.725
260.6840.8561.0571.3151.7062.0562.4792.7793.707
270.6840.8551.0561.3141.7032.0522.4732.7713.690
280.6830.8551.0561.3131.7012.0482.4672.7633.674
290.6830.8541.0551.3111.6992.0452.4622.7563.659
300.6830.8541.0551.3101.6972.0422.4572.7503.646
400.6810.8511.0501.3031.6842.0212.4232.7043.551
600.6790.8481.0451.2961.6712.0002.3902.6603.460
1200.6770.8451.0411.2891.6581.9802.3582.6173.373
0.6740.8421.0361.2821.6451.9602.3262.5763.291

F表(5%,1%)

\(F(Φ_1,Φ_2:P)\)
P=0.05・・細字
P=0.01・・太字

上側確率5%と1%を求める表

Φ2/Φ11234567891012152024304060120
1161
4052
200
5000
216
5403
225
5625
230
5764
234
5859
237
5928
239
5981
241
6022
242
6056
244
6106
246
6157
248
6209
249
6235
250
6261
251
6287
252
6313
253
6339
254
6366
218.5
98.5
19.0
99.0
19.2
99.2
19.2
99.2
19.3
99.3
19.3
99.3
19.4
99.4
19.4
99.4
19.4
99.4
19.4
99.4
19.4
99.4
19.4
99.4
19.4
99.4
19.5
99.5
19.5
99.5
19.5
99.5
19.5
99.5
19.5
99.5
19.5
99.5
310.1
34.1
9.55
30.8
9.28
29.5
9.12
28.7
9.01
28.2
8.94
29.5
8.89
28.7
8.85
28.2
8.81
27.9
8.79
27.7
8.74
27.5
8.7
27.3
8.66
26.7
8.64
26.6
8.62
26.5
8.59
26.4
8.57
26.3
8.55
26.2
8.53
26.1
47.71
21.2
6.94
18.0
6.59
16.7
6.39
16.0
6.26
15.5
6.16
15.2
6.09
15.0
6.04
14.8
6.00
14.7
5.96
14.5
5.91
14.4
5.86
14.2
5.8
14.0
5.77
13.9
5.75
13.8
5.72
13.7
5.69
13.7
5.66
13.6
5.63
13.5
56.61
16.3
5.79
5.41
5.41
12.1
5.19
11.4
5.05
11.0
4.95
10.7
4.88
10.5
4.82
10.3
4.77
10.2
4.74
10.1
4.68
9.89
4.62
9.72
4.56
9.55
4.53
9.47
4.5
9.38
4.46
9.29
4.43
9.2
4.4
9.11
4.36
9.02
65.99
13.7
5.14
10.9
4.76
9.78
4.53
9.15
4.39
8.75
4.28
8.47
4.21
8.26
4.15
8.10
4.10
7.98
4.06
7.87
4.00
7.72
3.94
7.56
3.87
7.40
3.84
7.31
3.81
7.23
3.77
7.14
3.74
7.06
3.70
6.97
3.67
6.88
75.59
13.7
4.74
9.55
4.35
8.45
4.12
7.85
3.97
7.46
3.87
7.19
3.79
6.99
3.73
6.84
3.68
6.72
3.64
6.62
3.57
6.47
3.51
6.31
3.44
6.16
3.41
6.07
3.38
5.99
3.34
5.91
3.30
5.82
3.27
5.74
3.23
5.65
85.32
11.3
4.46
8.65
4.07
7.59
3.84
7.01
3.69
6.63
3.58
6.37
3.50
6.18
3.44
6.03
3.39
5.
91
3.35
5.81
3.28
5.67
3.22
5.52
3.15
5.36
3.12
5.28
3.08
5.20
3.04
5.12
3.01
5.03
2.97
4.95
2.93
4.86
95.12
10.6
4.26
8.02
3.86
6.99
3.63
6.42
3.48
6.06
3.37
5.80
3.29
5.61
3.23
5.43
3.18
5.35
3.14
5.26
3.07
5.11
3.01
4.96
2.94
4.81
2.90
4.73
2.86
4.65
2.83
4.57
2.79
4.48
2.75
4.40
2.71
4.31
104.96
10.0
4.10
7.56
3.71
6.55
3.48
5.99
3.33
5.64
3.22
5.39
3.14
5.20
3.07
5.06
3.02
4.94
2.98
4.85
2.91
4.71
2.85
4.56
2.77
4.41
2.74
4.33
2.70
4.25
2.66
4.17
2.62
4.08
2.58
4.00
2.54
3.91
114.84
9.65
3.98
7.21
3.59
6.22
3.36
5.67
3.20
5.32
3.09
5.07
3.01
4.89
2.95
4.74
2.90
4.63
2.85
4.54
2.79
4.40
2.72
4.25
2.65
4.10
2.61
4.02
2.57
3.94
2.53
3.86
2.49
3.78
2.45
3.69
2.40
3.60
124.75
9.33
3.89
6.93
3.49
5.95
3.26
5.41
3.11
5.06
3.00
4.82
2.91
4.64
2.85
4.50
2.80
4.39
2.75
4.30
2.69
4.16
2.62
4.01
2.54
3.86
2.51
3.78
2.47
3.70
2.43
3.62
2.38
3.54
2.34
3.45
2.30
3.36
134.67
9.07
3.81
6.70
3.41
5.74
3.18
5.21
3.03
4.86
2.92
4.62
2.83
4.44
2.77
4.3
2.71
4.19
2.67
4.10
2.60
3.96
2.53
3.85
2.46
3.66
2.42
3.59
2.38
3.51
2.34
3.43
2.30
3.34
2.25
3.25
2.21
3.17
144.60
8.86
3.74
6.51
3.34
5.56
3.11
5.04
2.96
4.69
2.85
4.46
2.76
4.28
2.70
4.14
2.65
3.94
2.60
3.94
2.53
3.80
2.46
3.66
2.39
3.51
2.35
3.43
2.31
3.35
2.27
3.27
2.22
3.18
2.18
3.09
2.13
3.00
154.54
8.68
3.68
6.36
3.29
5.42
3.06
4.86
2.90
4.56
2.79
4.32
2.71
4.14
2.64
4.00
2.59
3.89
2.54
3.80
2.48
3.67
2.40
3.52
2.33
3.37
2.29
3.29
2.25
3.21
2.20
3.13
2.16
3.05
2.11
2.96
2.07
2.87
164.49
8.53
3.63
6.23
3.24
5.29
3.01
4.77
2.85
4.44
2.74
4.20
2.66
4.03
2.59
3.89
2.54
3.78
2.49
3.69
2.42
3.69
2.35
3.41
2.28
3.26
2.24
3.18
2.19
3.10
2.15
3.02
2.11
2.93
2.06
2.84
2.01
2.75
174.45
8.40
3.59
6.11
3.20
5.18
2.96
4.67
2.81
4.34
2.70
4.10
2.61
3.93
2.55
3.79
2.49
3.68
2.45
3.45
2.38
3.46
2.31
3.31
2.23
3.15
2.19
3.08
2.15
3.00
2.10
2.92
2.06
2.83
2.01
2.75
1.96
2.65
184.41
8.29
3.55
6.01
3.16
5.09
2.93
4.58
2.77
4.25
2.66
4.01
2.58
3.84
2.51
3.71
2.46
3.60
2.41
3.51
2.34
3.60
2.27
3.23
2.19
3.08
2.15
3.00
2.11
2.92
2.06
2.84
2.02
2.75
1.97
2.66
1.92
2.57
194.38
8.18
3.52
5.93
3.13
5.01
2.90
4.50
2.74
4.17
2.63
3.94
2.54
3.77
2.48
3.63
2.42
3.52
2.38
3.43
2.31
3.30
2.23
3.15
2.16
3.00
2.11
2.93
2.07
2.84
2.03
2.76
1.98
2.67
1.93
2.58
1.88
2.49
204.35
8.10
3.49
5.85
3.10
4.94
2.87
4.43
2.71
4.10
2.60
3.87
2.51
3.70
2.45
3.56
2.39
3.46
2.35
3.37
2.28
3.23
2.20
3.09
2.12
2.94
2.08
2.86
2.04
2.78
1.99
2.69
1.95
2.61
1.90
2.52
1.84
2.42
214.32
8.02
3.47
5.78
3.07
4.87
2.84
4.37
2.68
4.04
2.57
3.81
2.49
3.64
2.42
3.52
2.37
3.40
2.32
3.31
2.25
3.17
2.18
3.03
2.10
2.88
2.05
2.80
2.01
2.72
1.96
2.64
1.92
2.55
1.87
2.46
1.81
2.36
224.30
7.95
3.44
5.72
3.05
4.82
2.82
4.31
2.66
3.99
2.55
3.76
2.46
3.59
2.40
3.45
2.34
3.35
2.30
3.26
2.23
3.12
2.15
2.98
2.07
2.83
2.03
2.75
1.98
2.67
1.94
2.58
1.89
2.50
1.84
2.40
1.78
2.31
234.28
7.88
3.42
5.66
3.03
4.76
2.80
4.260
2.64
3.94
2.53
3.71
2.44
3.54
2.37
3.41
2.32
3.30
2.27
3.21
2.20
3.20
2.13
2.93
2.05
2.78
2.01
2.70
1.96
2.62
1.91
2.54
1.86
2.45
1.81
2.35
1.76
2.26
244.26
7.82
3.40
5.61
3.01
4.72
2.78
4.22
2.62
3.90
2.51
3.67
2.42
3.51
2.36
3.36
2.30
3.26
2.25
3.17
2.18
3.03
2.11
2.89
2.03
2.74
1.98
2.66
1.94
2.58
1.89
2.49
1.84
2.40
1.79
2.31
1.73
2.21
254.24
7.77
3.39
5.57
2.99
4.68
2.76
4.18
2.60
3.85
2.49
3.63
2.40
3.46
2.34
3.32
2.28
3.22
2.24
3.13
2.16
2.99
2.09
2.85
2.01
2.70
1.96
2.62
1.92
2.54
1.87
2.45
1.82
2.36
1.77
2.27
1.71
2.17
264.23
7.72
3.37
5.56
2.98
4.64
2.74
4.14
2.59
3.82
2.47
3.59
2.39
3.42
2.32
3.29
2.27
3.18
2.22
3.09
2.15
2.96
2.07
2.81
1.99
2.66
1.95
2.58
1.90
2.50
1.85
2.42
1.80
2.33
1.75
2.23
1.69
2.13
274.21
7.68
3.35
5.49
2.96
4.60
2.73
4.11
2.57
3.78
2.46
3.56
2.37
3.39
2.31
3.26
2.25
3.15
2.20
3.06
2.13
2.90
2.06
2.78
1.97
2.63
1.93
2.55
1.88
2.47
1.84
2.38
1.79
2.29
1.73
2.20
1.67
2.10
284.20
7.64
3.34
5.45
2.95
4.57
2.71
4.07
2.56
3.75
2.45
3.53
2.36
3.36
2.29
3.23
2.24
3.12
2.19
3.03
2.12
2.90
2.04
2.75
1.96
2.60
1.91
2.52
1.87
2.44
1.82
2.35
1.77
2.26
1.71
2.17
1.65
2.06
294.18
7.60
3.33
5.42
2.93
4.54
2.70
4.04
2.55
3.73
2.43
3.50
2.35
3.33
2.28
3.20
2.22
3.09
2.18
3.00
2.10
2.87
2.03
2.73
1.94
2.57
1.90
2.49
1.85
2.41
1.81
2.33
1.75
2.23
1.70
2.14
1.64
2.03
304.17
7.56
3.32
5.39
2.92
4.51
2.69
4.02
2.53
3.70
2.42
3.47
2.33
3.30
2.27
3.17
2.21
3.07
2.16
2.98
2.09
2.84
2.01
2.70
1.93
2.55
1.89
2.47
1.84
2.37
1.79
2.30
1.74
2.21
1.68
2.11
1.62
2.01
404.08
7.31
3.23
5.18
2.84
4.31
2.61
3.83
2.45
3.51
2.34
3.29
2.25
3.12
2.18
2.99
2.12
2.89
2.08
2.80
2.00
2.66
1.92
2.52
1.84
2.37
1.79
2.29
1.74
2.20
1.69
2.11
1.64
2.02
1.58
1.92
1.51
1.80
604.00
7.08
3.15
4.98
2.76
4.13
2.53
3.65
2.37
3.34
2.25
3.12
2.17
2.95
2.10
2.82
2.04
2.72
1.99
2.63
1.92
2.50
1.84
2.35
1.75
2.20
1.70
2.12
1.65
2.03
1.59
1.94
1.53
1.84
1.47
1.73
1.39
1.60
1203.92
6.85
3.07
4.79
2.68
3.95
2.45
3.48
2.29
3.17
2.18
2.96
2.09
2.79
2.02
2.66
1.96
2.56
1.91
2.47
1.83
2.34
1.75
2.19
1.66
2.03
1.61
1.95
1.55
1.86
1.50
1.76
1.43
1.66
1.35
1.53
1.25
1.38
3.84
6.63
3.00
4.61
3.00
3.78
2.37
3.32
2.21
3.02
2.10
2.80
2.01
2.64
1.94
2.51
1.88
2.41
1.83
2.32
1.75
2.18
1.67
2.04
1.57
1.88
1.52
1.79
1.46
1.70
1.39
1.59
1.32
1.47
1.22
1.32
1.0
1.0

F表(10%)

Φ2/Φ1123456789101112131415161718192021222324252627
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
40
60
120

R表

\(Φ/P\)0.10.050.020.01
100.4970.57600.65810.7029
110.47620.55290.63390.6835
120.47450.53240.61200.6614
130.44090.51400.59230.6411
140.42590.49730.57420.6226
150.41240.48210.55770.6055
160.40000.46830.54250.5897
170.38870.45550.52850.5751
180.37830.44380.51550.5614
190.36870.43290.50340.5487
200.35980.42270.49210.5368
250.32330.38090.44510.4869
300.29600.34940.40930.4487
350.27460.32460.38100.4182
400.25730.30440.35780.3932
500.23060.27320.32180.3542
600.21080.25000.29480.3248
700.19540.23190.27370.3017
800.18290.21720.25650.2830
900.17260.20500.24220.2673
1000.16380.19460.23010.2540
近似式\(\displaystyle \frac{1.645}{\sqrt{Φ+1}}\)\(\displaystyle \frac{1.960}{\sqrt{Φ+1}}\)\(\displaystyle \frac{2.326}{\sqrt{Φ+1}}\)\(\displaystyle \frac{2.576}{\sqrt{Φ+1}}\)
タイトルとURLをコピーしました