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F分布表(上側5パーセント点)

1. F分布(0.05)  |  2. F分布(0.025)  |  3. F分布(0.01)  |  4. F分布(0.005)

F分布の上側 0.05 点

α=0.05 のとき,表頭の自由度 m と表側の自由度 n に対して,F分布の上側 α 点 Fα(m,n) を示す。 \[ \alpha \longmapsto F_\alpha(m,n),\qquad \text{Pr}\{X>F_\alpha(m,n)\}=\alpha \] F1-α(m,n) と Fα(n,m) について, \[ F_{1-\alpha}(m,n)=\frac{1}{F_\alpha(n,m)},\qquad F_{0.95}(m,n)=\frac{1}{F_{0.05}(n,m)} \] が成り立つから,この表を用いて上側 0.95 点を求めることができる。

m=1 ~ 10

n∖m12345678910
1161.4199.5215.7224.6230.2234.0236.8238.9240.5241.9
218.5119.0019.1619.2519.3019.3319.3519.3719.3819.40
310.139.5529.2779.1179.0138.9418.8878.8458.8128.786
47.7096.9446.5916.3886.2566.1636.0946.0415.9995.964
56.6085.7865.4095.1925.0504.9504.8764.8184.7724.735
65.9875.1434.7574.5344.3874.2844.2074.1474.0994.060
75.5914.7374.3474.1203.9723.8663.7873.7263.6773.637
85.3184.4594.0663.8383.6873.5813.5003.4383.3883.347
95.1174.2563.8633.6333.4823.3743.2933.2303.1793.137
104.9654.1033.7083.4783.3263.2173.1353.0723.0202.978
12345678910
114.8443.9823.5873.3573.2043.0953.0122.9482.8962.854
124.7473.8853.4903.2593.1062.9962.9132.8492.7962.753
134.6673.8063.4113.1793.0252.9152.8322.7672.7142.671
144.6003.7393.3443.1122.9582.8482.7642.6992.6462.602
154.5433.6823.2873.0562.9012.7902.7072.6412.5882.544
164.4943.6343.2393.0072.8522.7412.6572.5912.5382.494
174.4513.5923.1972.9652.8102.6992.6142.5482.4942.450
184.4143.5553.1602.9282.7732.6612.5772.5102.4562.412
194.3813.5223.1272.8952.7402.6282.5442.4772.4232.378
204.3513.4933.0982.8662.7112.5992.5142.4472.3932.348
12345678910
214.3253.4673.0722.8402.6852.5732.4882.4202.3662.321
224.3013.4433.0492.8172.6612.5492.4642.3972.3422.297
234.2793.4223.0282.7962.6402.5282.4422.3752.3202.275
244.2603.4033.0092.7762.6212.5082.4232.3552.3002.255
254.2423.3852.9912.7592.6032.4902.4052.3372.2822.236
264.2253.3692.9752.7432.5872.4742.3882.3212.2652.220
274.2103.3542.9602.7282.5722.4592.3732.3052.2502.204
284.1963.3402.9472.7142.5582.4452.3592.2912.2362.190
294.1833.3282.9342.7012.5452.4322.3462.2782.2232.177
304.1713.3162.9222.6902.5342.4212.3342.2662.2112.165
12345678910
314.1603.3052.9112.6792.5232.4092.3232.2552.1992.153
324.1493.2952.9012.6682.5122.3992.3132.2442.1892.142
334.1393.2852.8922.6592.5032.3892.3032.2352.1792.133
344.1303.2762.8832.6502.4942.3802.2942.2252.1702.123
354.1213.2672.8742.6412.4852.3722.2852.2172.1612.114
364.1133.2592.8662.6342.4772.3642.2772.2092.1532.106
374.1053.2522.8592.6262.4702.3562.2702.2012.1452.098
384.0983.2452.8522.6192.4632.3492.2622.1942.1382.091
394.0913.2382.8452.6122.4562.3422.2552.1872.1312.084
404.0853.2322.8392.6062.4492.3362.2492.1802.1242.077
12345678910
414.0793.2262.8332.6002.4432.3302.2432.1742.1182.071
424.0733.2202.8272.5942.4382.3242.2372.1682.1122.065
434.0673.2142.8222.5892.4322.3182.2322.1632.1062.059
444.0623.2092.8162.5842.4272.3132.2262.1572.1012.054
454.0573.2042.8122.5792.4222.3082.2212.1522.0962.049
464.0523.2002.8072.5742.4172.3042.2162.1472.0912.044
474.0473.1952.8022.5702.4132.2992.2122.1432.0862.039
484.0433.1912.7982.5652.4092.2952.2072.1382.0822.035
494.0383.1872.7942.5612.4042.2902.2032.1342.0772.030
504.0343.1832.7902.5572.4002.2862.1992.1302.0732.026
12345678910
604.0013.1502.7582.5252.3682.2542.1672.0972.0401.993
703.9783.1282.7362.5032.3462.2312.1432.0742.0171.969
803.9603.1112.7192.4862.3292.2142.1262.0561.9991.951
903.9473.0982.7062.4732.3162.2012.1132.0431.9861.938
1003.9363.0872.6962.4632.3052.1912.1032.0321.9751.927
1103.9273.0792.6872.4542.2972.1822.0942.0241.9661.918
1203.9203.0722.6802.4472.2902.1752.0872.0161.9591.910
1303.9143.0662.6742.4412.2842.1692.0812.0101.9531.904
1403.9093.0612.6692.4362.2792.1642.0762.0051.9471.899
1503.9043.0562.6652.4322.2742.1602.0712.0011.9431.894
12345678910
1603.9003.0532.6612.4282.2712.1562.0671.9971.9391.890
1703.8973.0492.6582.4252.2672.1522.0641.9931.9351.887
1803.8943.0462.6552.4222.2642.1492.0611.9901.9321.884
1903.8913.0432.6522.4192.2622.1472.0581.9871.9291.881
2003.8883.0412.6502.4172.2592.1442.0561.9851.9271.878
2103.8863.0392.6482.4152.2572.1422.0531.9831.9251.876
2203.8843.0372.6462.4132.2552.1402.0511.9811.9231.874
2303.8823.0352.6442.4112.2532.1382.0501.9791.9211.872
2403.8803.0332.6422.4092.2522.1362.0481.9771.9191.870
2503.8793.0322.6412.4082.2502.1352.0461.9761.9171.869

m=11 ~ 20

n∖m11121314151617181920
1243.0243.9244.7245.4245.9246.5246.9247.3247.7248.0
219.4019.4119.4219.4219.4319.4319.4419.4419.4419.45
38.7638.7458.7298.7158.7038.6928.6838.6758.6678.660
45.9365.9125.8915.8735.8585.8445.8325.8215.8115.803
54.7044.6784.6554.6364.6194.6044.5904.5794.5684.558
64.0274.0003.9763.9563.9383.9223.9083.8963.8843.874
73.6033.5753.5503.5293.5113.4943.4803.4673.4553.445
83.3133.2843.2593.2373.2183.2023.1873.1733.1613.150
93.1023.0733.0483.0253.0062.9892.9742.9602.9482.936
102.9432.9132.8872.8652.8452.8282.8122.7982.7852.774
11121314151617181920
112.8182.7882.7612.7392.7192.7012.6852.6712.6582.646
122.7172.6872.6602.6372.6172.5992.5832.5682.5552.544
132.6352.6042.5772.5542.5332.5152.4992.4842.4712.459
142.5652.5342.5072.4842.4632.4452.4282.4132.4002.388
152.5072.4752.4482.4242.4032.3852.3682.3532.3402.328
162.4562.4252.3972.3732.3522.3332.3172.3022.2882.276
172.4132.3812.3532.3292.3082.2892.2722.2572.2432.230
182.3742.3422.3142.2902.2692.2502.2332.2172.2032.191
192.3402.3082.2802.2562.2342.2152.1982.1822.1682.155
202.3102.2782.2502.2252.2032.1842.1672.1512.1372.124
11121314151617181920
212.2832.2502.2222.1972.1762.1562.1392.1232.1092.096
222.2592.2262.1982.1732.1512.1312.1142.0982.0842.071
232.2362.2042.1752.1502.1282.1092.0912.0752.0612.048
242.2162.1832.1552.1302.1082.0882.0702.0542.0402.027
252.1982.1652.1362.1112.0892.0692.0512.0352.0212.007
262.1812.1482.1192.0942.0722.0522.0342.0182.0031.990
272.1662.1322.1032.0782.0562.0362.0182.0021.9871.974
282.1512.1182.0892.0642.0412.0212.0031.9871.9721.959
292.1382.1042.0752.0502.0272.0071.9891.9731.9581.945
302.1262.0922.0632.0372.0151.9951.9761.9601.9451.932
11121314151617181920
312.1142.0802.0512.0262.0031.9831.9651.9481.9331.920
322.1032.0702.0402.0151.9921.9721.9531.9371.9221.908
332.0932.0602.0302.0041.9821.9611.9431.9261.9111.898
342.0842.0502.0211.9951.9721.9521.9331.9171.9021.888
352.0752.0412.0121.9861.9631.9421.9241.9071.8921.878
362.0672.0332.0031.9771.9541.9341.9151.8991.8831.870
372.0592.0251.9951.9691.9461.9261.9071.8901.8751.861
382.0512.0171.9881.9621.9391.9181.8991.8831.8671.853
392.0442.0101.9811.9541.9311.9111.8921.8751.8601.846
402.0382.0031.9741.9481.9241.9041.8851.8681.8531.839
11121314151617181920
412.0311.9971.9671.9411.9181.8971.8791.8621.8461.832
422.0251.9911.9611.9351.9121.8911.8721.8551.8401.826
432.0201.9851.9551.9291.9061.8851.8661.8491.8341.820
442.0141.9801.9501.9241.9001.8791.8611.8441.8281.814
452.0091.9741.9451.9181.8951.8741.8551.8381.8231.808
462.0041.9691.9401.9131.8901.8691.8501.8331.8171.803
471.9991.9651.9351.9081.8851.8641.8451.8281.8121.798
481.9951.9601.9301.9041.8801.8591.8401.8231.8071.793
491.9901.9561.9261.8991.8761.8551.8361.8191.8031.789
501.9861.9521.9211.8951.8711.8501.8311.8141.7981.784
11121314151617181920
601.9521.9171.8871.8601.8361.8151.7961.7781.7631.748
701.9281.8931.8631.8361.8121.7901.7711.7531.7371.722
801.9101.8751.8451.8171.7931.7721.7521.7341.7181.703
901.8971.8611.8301.8031.7791.7571.7371.7201.7031.688
1001.8861.8501.8191.7921.7681.7461.7261.7081.6911.676
1101.8771.8411.8101.7831.7581.7361.7161.6981.6821.667
1201.8691.8341.8031.7751.7501.7281.7091.6901.6741.659
1301.8631.8271.7961.7691.7441.7221.7021.6841.6671.652
1401.8581.8221.7911.7631.7381.7161.6961.6781.6611.646
1501.8531.8171.7861.7581.7341.7111.6911.6731.6561.641
11121314151617181920
1601.8491.8131.7821.7541.7291.7071.6871.6691.6521.637
1701.8451.8101.7781.7501.7261.7031.6831.6651.6481.633
1801.8421.8061.7751.7471.7221.7001.6801.6611.6451.629
1901.8391.8031.7721.7441.7191.6971.6771.6581.6421.626
2001.8371.8011.7691.7421.7171.6941.6741.6561.6391.623
2101.8341.7991.7671.7391.7141.6921.6721.6531.6361.621
2201.8321.7961.7651.7371.7121.6901.6691.6511.6341.618
2301.8301.7941.7631.7351.7101.6881.6671.6491.6321.616
2401.8291.7931.7611.7331.7081.6861.6651.6471.6301.614
2501.8271.7911.7591.7321.7071.6841.6641.6451.6281.613

m=30 ~ 120

n∖m30405060708090100110120
1250.1251.1251.8252.2252.5252.7252.9253.0253.2253.3
219.4619.4719.4819.4819.4819.4819.4819.4919.4919.49
38.6178.5948.5818.5728.5668.5618.5578.5548.5518.549
45.7465.7175.6995.6885.6795.6735.6685.6645.6615.658
54.4964.4644.4444.4314.4224.4154.4094.4054.4014.398
63.8083.7743.7543.7403.7303.7223.7163.7123.7083.705
73.3763.3403.3193.3043.2943.2863.2803.2753.2713.267
83.0793.0433.0203.0052.9942.9862.9802.9752.9702.967
92.8642.8262.8032.7872.7762.7682.7612.7562.7512.748
102.7002.6612.6372.6212.6102.6012.5942.5882.5842.580
30405060708090100110120
112.5702.5312.5072.4902.4782.4692.4622.4572.4522.448
122.4662.4262.4012.3842.3722.3632.3562.3502.3452.341
132.3802.3392.3142.2972.2842.2752.2672.2612.2572.252
142.3082.2662.2412.2232.2102.2012.1932.1872.1822.178
152.2472.2042.1782.1602.1472.1372.1302.1232.1182.114
162.1942.1512.1242.1062.0932.0832.0752.0682.0632.059
172.1482.1042.0772.0582.0452.0352.0272.0202.0152.011
182.1072.0632.0352.0172.0031.9931.9851.9781.9731.968
192.0712.0261.9991.9801.9661.9551.9471.9401.9351.930
202.0391.9941.9661.9461.9321.9221.9131.9071.9011.896
30405060708090100110120
212.0101.9651.9361.9161.9021.8911.8831.8761.8701.866
221.9841.9381.9091.8891.8751.8641.8561.8491.8431.838
231.9611.9141.8851.8651.8501.8391.8301.8231.8181.813
241.9391.8921.8631.8421.8281.8161.8081.8001.7951.790
251.9191.8721.8421.8221.8071.7961.7871.7791.7731.768
261.9011.8531.8231.8031.7881.7761.7671.7601.7541.749
271.8841.8361.8061.7851.7701.7581.7491.7421.7361.731
281.8691.8201.7901.7691.7541.7421.7331.7251.7191.714
291.8541.8061.7751.7541.7381.7261.7171.7101.7031.698
301.8411.7921.7611.7401.7241.7121.7031.6951.6891.683
30405060708090100110120
311.8281.7791.7481.7261.7111.6991.6891.6811.6751.670
321.8171.7671.7361.7141.6981.6861.6761.6691.6621.657
331.8061.7561.7241.7021.6861.6741.6651.6571.6501.645
341.7951.7451.7131.6911.6751.6631.6531.6451.6391.633
351.7861.7351.7031.6811.6651.6521.6431.6351.6281.623
361.7761.7261.6941.6711.6551.6431.6331.6251.6181.612
371.7681.7171.6851.6621.6461.6331.6231.6151.6081.603
381.7601.7081.6761.6531.6371.6241.6141.6061.5991.594
391.7521.7001.6681.6451.6281.6161.6061.5971.5911.585
401.7441.6931.6601.6371.6211.6081.5971.5891.5821.577
30405060708090100110120
411.7371.6861.6531.6301.6131.6001.5901.5811.5751.569
421.7311.6791.6461.6231.6061.5931.5821.5741.5671.561
431.7241.6721.6391.6161.5991.5861.5751.5671.5601.554
441.7181.6661.6331.6091.5921.5791.5691.5601.5531.547
451.7131.6601.6261.6031.5861.5731.5621.5541.5471.541
461.7071.6541.6211.5971.5801.5671.5561.5471.5401.534
471.7021.6491.6151.5911.5741.5611.5501.5411.5341.528
481.6971.6441.6101.5861.5681.5551.5441.5361.5281.522
491.6921.6391.6041.5811.5631.5501.5391.5301.5231.517
501.6871.6341.5991.5761.5581.5441.5341.5251.5181.511
30405060708090100110120
601.6491.5941.5591.5341.5161.5021.4911.4811.4741.467
701.6221.5661.5301.5051.4861.4711.4591.4501.4421.435
801.6021.5451.5081.4821.4631.4481.4361.4261.4181.411
901.5861.5281.4911.4651.4451.4291.4171.4071.3991.391
1001.5731.5151.4771.4501.4301.4151.4021.3921.3831.376
1101.5631.5041.4661.4391.4181.4021.3901.3791.3701.363
1201.5541.4951.4571.4291.4081.3921.3791.3691.3601.352
1301.5471.4881.4491.4211.4001.3831.3701.3591.3501.343
1401.5411.4811.4421.4141.3931.3761.3631.3521.3421.335
1501.5351.4751.4361.4071.3861.3691.3561.3451.3351.327
30405060708090100110120
1601.5311.4701.4301.4021.3811.3641.3501.3391.3291.321
1701.5261.4661.4261.3971.3761.3591.3451.3341.3241.316
1801.5231.4621.4221.3931.3711.3541.3401.3291.3191.311
1901.5191.4581.4181.3891.3671.3501.3361.3241.3151.306
2001.5161.4551.4151.3861.3641.3461.3321.3211.3111.302
2101.5141.4521.4121.3821.3601.3431.3291.3171.3071.299
2201.5111.4501.4091.3801.3571.3401.3261.3141.3041.295
2301.5091.4471.4061.3771.3551.3371.3231.3111.3011.292
2401.5071.4451.4041.3751.3521.3351.3201.3081.2981.290
2501.5051.4431.4021.3721.3501.3321.3181.3061.2961.287

分布表のタイプを選択

1 2 3 4 Home

F分布表(上側2.5パーセント点)

1. F分布(0.05)  |  2. F分布(0.025)  |  3. F分布(0.01)  |  4. F分布(0.005)

F分布の上側 0.025 点

α=0.025 のとき,表頭の自由度 m と表側の自由度 n に対して,F分布の上側 α 点 Fα(m,n) を示す。 \[ \alpha \longmapsto F_\alpha(m,n),\qquad \text{Pr}\{X>F_\alpha(m,n)\}=\alpha \] F1-α(m,n) と Fα(n,m) について, \[ F_{1-\alpha}(m,n)=\frac{1}{F_\alpha(n,m)},\qquad F_{0.975}(m,n)=\frac{1}{F_{0.025}(n,m)} \] が成り立つから,この表を用いて上側 0.975 点を求めることができる。

m=1 ~ 10

n∖m12345678910
1647.8799.5864.2899.6921.8937.1948.2956.7963.3968.6
238.5139.0039.1739.2539.3039.3339.3639.3739.3939.40
317.4416.0415.4415.1014.8814.7314.6214.5414.4714.42
412.2210.659.9799.6059.3649.1979.0748.9808.9058.844
510.018.4347.7647.3887.1466.9786.8536.7576.6816.619
68.8137.2606.5996.2275.9885.8205.6955.6005.5235.461
78.0736.5425.8905.5235.2855.1194.9954.8994.8234.761
87.5716.0595.4165.0534.8174.6524.5294.4334.3574.295
97.2095.7155.0784.7184.4844.3204.1974.1024.0263.964
106.9375.4564.8264.4684.2364.0723.9503.8553.7793.717
12345678910
116.7245.2564.6304.2754.0443.8813.7593.6643.5883.526
126.5545.0964.4744.1213.8913.7283.6073.5123.4363.374
136.4144.9654.3473.9963.7673.6043.4833.3883.3123.250
146.2984.8574.2423.8923.6633.5013.3803.2853.2093.147
156.2004.7654.1533.8043.5763.4153.2933.1993.1233.060
166.1154.6874.0773.7293.5023.3413.2193.1253.0492.986
176.0424.6194.0113.6653.4383.2773.1563.0612.9852.922
185.9784.5603.9543.6083.3823.2213.1003.0052.9292.866
195.9224.5083.9033.5593.3333.1723.0512.9562.8802.817
205.8714.4613.8593.5153.2893.1283.0072.9132.8372.774
12345678910
215.8274.4203.8193.4753.2503.0902.9692.8742.7982.735
225.7864.3833.7833.4403.2153.0552.9342.8392.7632.700
235.7504.3493.7503.4083.1833.0232.9022.8082.7312.668
245.7174.3193.7213.3793.1552.9952.8742.7792.7032.640
255.6864.2913.6943.3533.1292.9692.8482.7532.6772.613
265.6594.2653.6703.3293.1052.9452.8242.7292.6532.590
275.6334.2423.6473.3073.0832.9232.8022.7072.6312.568
285.6104.2213.6263.2863.0632.9032.7822.6872.6112.547
295.5884.2013.6073.2673.0442.8842.7632.6692.5922.529
305.5684.1823.5893.2503.0262.8672.7462.6512.5752.511
12345678910
315.5494.1653.5733.2343.0102.8512.7302.6352.5582.495
325.5314.1493.5573.2182.9952.8362.7152.6202.5432.480
335.5154.1343.5433.2042.9812.8222.7012.6062.5292.466
345.4994.1203.5293.1912.9682.8082.6882.5932.5162.453
355.4854.1063.5173.1792.9562.7962.6762.5812.5042.440
365.4714.0943.5053.1672.9442.7852.6642.5692.4922.429
375.4584.0823.4933.1562.9332.7742.6532.5582.4812.418
385.4464.0713.4833.1452.9232.7632.6432.5482.4712.407
395.4354.0613.4733.1352.9132.7542.6332.5382.4612.397
405.4244.0513.4633.1262.9042.7442.6242.5292.4522.388
12345678910
415.4144.0423.4543.1172.8952.7362.6152.5202.4432.379
425.4044.0333.4463.1092.8872.7272.6072.5122.4352.371
435.3954.0243.4383.1012.8792.7192.5992.5042.4272.363
445.3864.0163.4303.0932.8712.7122.5912.4962.4192.355
455.3774.0093.4223.0862.8642.7052.5842.4892.4122.348
465.3694.0013.4153.0792.8572.6982.5772.4822.4052.341
475.3613.9943.4093.0732.8512.6912.5712.4762.3992.335
485.3543.9873.4023.0662.8442.6852.5652.4702.3932.329
495.3473.9813.3963.0602.8382.6792.5592.4642.3872.323
505.3403.9753.3903.0542.8332.6742.5532.4582.3812.317
12345678910
605.2863.9253.3433.0082.7862.6272.5072.4122.3342.270
705.2473.8903.3092.9752.7542.5952.4742.3792.3022.237
805.2183.8643.2842.9502.7302.5712.4502.3552.2772.213
905.1963.8443.2652.9322.7112.5522.4322.3362.2592.194
1005.1793.8283.2502.9172.6962.5372.4172.3212.2442.179
1105.1643.8153.2372.9042.6842.5252.4052.3092.2322.167
1205.1523.8053.2272.8942.6742.5152.3952.2992.2222.157
1305.1423.7963.2182.8862.6662.5072.3862.2912.2132.148
1405.1343.7883.2112.8792.6582.5002.3792.2842.2062.141
1505.1263.7813.2042.8722.6522.4942.3732.2782.2002.135
12345678910
1605.1203.7753.1992.8672.6472.4882.3682.2722.1942.129
1705.1143.7703.1942.8622.6422.4832.3632.2672.1892.125
1805.1093.7663.1892.8582.6382.4792.3592.2632.1852.120
1905.1043.7613.1862.8542.6342.4752.3552.2592.1812.116
2005.1003.7583.1822.8502.6302.4722.3512.2562.1782.113
2105.0973.7543.1792.8472.6272.4692.3482.2532.1752.110
2205.0933.7513.1762.8442.6252.4662.3452.2502.1722.107
2305.0903.7493.1732.8422.6222.4642.3432.2472.1692.104
2405.0883.7463.1712.8392.6202.4612.3412.2452.1672.102
2505.0853.7443.1692.8372.6182.4592.3382.2432.1652.100

m=11 ~ 20

n∖m11121314151617181920
1973.0976.7979.8982.5984.9986.9988.7990.3991.8993.1
239.4139.4139.4239.4339.4339.4439.4439.4439.4539.45
314.3714.3414.3014.2814.2514.2314.2114.2014.1814.17
48.7948.7518.7158.6848.6578.6338.6118.5928.5758.560
56.5686.5256.4886.4566.4286.4036.3816.3626.3446.329
65.4105.3665.3295.2975.2695.2445.2225.2025.1845.168
74.7094.6664.6284.5964.5684.5434.5214.5014.4834.467
84.2434.2004.1624.1304.1014.0764.0544.0344.0163.999
93.9123.8683.8313.7983.7693.7443.7223.7013.6833.667
103.6653.6213.5833.5503.5223.4963.4743.4533.4353.419
11121314151617181920
113.4743.4303.3923.3593.3303.3043.2823.2613.2433.226
123.3213.2773.2393.2063.1773.1523.1293.1083.0903.073
133.1973.1533.1153.0823.0533.0273.0042.9832.9652.948
143.0953.0503.0122.9792.9492.9232.9002.8792.8612.844
153.0082.9632.9252.8912.8622.8362.8132.7922.7732.756
162.9342.8892.8512.8172.7882.7612.7382.7172.6982.681
172.8702.8252.7862.7532.7232.6972.6732.6522.6332.616
182.8142.7692.7302.6962.6672.6402.6172.5962.5762.559
192.7652.7202.6812.6472.6172.5912.5672.5462.5262.509
202.7212.6762.6372.6032.5732.5472.5232.5012.4822.464
11121314151617181920
212.6822.6372.5982.5642.5342.5072.4832.4622.4422.425
222.6472.6022.5632.5282.4982.4722.4482.4262.4072.389
232.6152.5702.5312.4972.4662.4402.4162.3942.3742.357
242.5862.5412.5022.4682.4372.4112.3862.3652.3452.327
252.5602.5152.4762.4412.4112.3842.3602.3382.3182.300
262.5362.4912.4512.4172.3872.3602.3352.3142.2942.276
272.5142.4692.4292.3952.3642.3372.3132.2912.2712.253
282.4942.4482.4092.3742.3442.3172.2922.2702.2512.232
292.4752.4302.3902.3552.3252.2982.2732.2512.2312.213
302.4582.4122.3722.3382.3072.2802.2552.2332.2132.195
11121314151617181920
312.4422.3962.3562.3212.2912.2632.2392.2172.1972.178
322.4262.3812.3412.3062.2752.2482.2232.2012.1812.163
332.4122.3662.3272.2922.2612.2342.2092.1872.1672.148
342.3992.3532.3132.2782.2482.2202.1952.1732.1532.135
352.3872.3412.3012.2662.2352.2072.1832.1602.1402.122
362.3752.3292.2892.2542.2232.1962.1712.1482.1282.110
372.3642.3182.2782.2432.2122.1842.1602.1372.1172.098
382.3532.3072.2672.2322.2012.1742.1492.1262.1062.088
392.3442.2982.2572.2222.1912.1642.1392.1162.0962.077
402.3342.2882.2482.2132.1822.1542.1292.1072.0862.068
11121314151617181920
412.3252.2792.2392.2042.1732.1452.1202.0982.0772.059
422.3172.2712.2312.1962.1642.1372.1122.0892.0692.050
432.3092.2632.2232.1872.1562.1282.1032.0812.0602.042
442.3022.2552.2152.1802.1492.1212.0962.0732.0522.034
452.2942.2482.2082.1722.1412.1132.0882.0662.0452.026
462.2872.2412.2012.1652.1342.1062.0812.0582.0382.019
472.2812.2342.1942.1592.1272.1002.0742.0522.0312.012
482.2742.2282.1882.1522.1212.0932.0682.0452.0242.006
492.2682.2222.1822.1462.1152.0872.0622.0392.0181.999
502.2632.2162.1762.1402.1092.0812.0562.0332.0121.993
11121314151617181920
602.2162.1692.1292.0932.0612.0332.0081.9851.9641.944
702.1832.1362.0952.0592.0281.9991.9741.9501.9291.910
802.1582.1112.0712.0352.0031.9741.9481.9251.9041.884
902.1402.0922.0512.0151.9831.9551.9291.9051.8841.864
1002.1242.0772.0362.0001.9681.9391.9131.8901.8681.849
1102.1122.0652.0241.9881.9551.9271.9011.8771.8551.836
1202.1022.0552.0141.9771.9451.9161.8901.8661.8451.825
1302.0942.0462.0051.9691.9361.9071.8811.8571.8361.816
1402.0862.0391.9981.9611.9291.9001.8731.8501.8281.808
1502.0802.0321.9911.9551.9221.8931.8671.8431.8211.801
11121314151617181920
1602.0742.0271.9861.9491.9171.8871.8611.8371.8161.796
1702.0692.0221.9811.9441.9121.8821.8561.8321.8101.790
1802.0652.0181.9761.9401.9071.8781.8521.8281.8061.786
1902.0612.0141.9721.9361.9031.8741.8481.8241.8021.782
2002.0582.0101.9691.9321.9001.8701.8441.8201.7981.778
2102.0552.0071.9661.9291.8961.8671.8411.8171.7951.775
2202.0522.0041.9631.9261.8931.8641.8381.8141.7921.772
2302.0492.0021.9601.9231.8911.8611.8351.8111.7891.769
2402.0471.9991.9581.9211.8881.8591.8331.8081.7871.766
2502.0451.9971.9551.9191.8861.8571.8301.8061.7841.764

m=30 ~ 120

n∖m30405060708090100110120
11001100610081010101110121013101310141014
239.4639.4739.4839.4839.4839.4939.4939.4939.4939.49
314.0814.0414.0113.9913.9813.9713.9613.9613.9513.95
48.4618.4118.3818.3608.3468.3358.3268.3198.3148.309
56.2276.1756.1446.1236.1076.0966.0876.0806.0746.069
65.0655.0124.9804.9594.9434.9324.9234.9154.9094.904
74.3624.3094.2764.2544.2394.2274.2184.2104.2044.199
83.8943.8403.8073.7843.7683.7563.7473.7393.7333.728
93.5603.5053.4723.4493.4333.4213.4113.4033.3973.392
103.3113.2553.2213.1983.1823.1693.1603.1523.1453.140
30405060708090100110120
113.1183.0613.0273.0042.9872.9742.9642.9562.9502.944
122.9632.9062.8712.8482.8312.8182.8082.8002.7932.787
132.8372.7802.7442.7202.7032.6902.6802.6712.6652.659
142.7322.6742.6382.6142.5972.5832.5732.5652.5582.552
152.6442.5852.5492.5242.5062.4932.4822.4742.4672.461
162.5682.5092.4722.4472.4292.4152.4052.3962.3892.383
172.5022.4422.4052.3802.3622.3482.3372.3292.3212.315
182.4452.3842.3472.3212.3032.2892.2782.2692.2622.256
192.3942.3332.2952.2702.2512.2372.2262.2172.2092.203
202.3492.2872.2492.2232.2052.1902.1792.1702.1622.156
30405060708090100110120
212.3082.2462.2082.1822.1632.1482.1372.1282.1202.114
222.2722.2102.1712.1452.1252.1112.0992.0902.0822.076
232.2392.1762.1372.1112.0912.0772.0652.0562.0482.041
242.2092.1462.1072.0802.0602.0452.0342.0242.0162.010
252.1822.1182.0792.0522.0322.0172.0051.9961.9881.981
262.1572.0932.0532.0262.0061.9911.9791.9691.9611.954
272.1332.0692.0292.0021.9821.9661.9541.9451.9371.930
282.1122.0482.0071.9801.9591.9441.9321.9221.9141.907
292.0922.0281.9871.9591.9391.9231.9111.9011.8931.886
302.0742.0091.9681.9401.9201.9041.8921.8821.8731.866
30405060708090100110120
312.0571.9911.9501.9221.9021.8861.8731.8631.8551.848
322.0411.9751.9341.9051.8851.8691.8561.8461.8381.831
332.0261.9601.9181.8901.8691.8531.8401.8301.8221.815
342.0121.9461.9041.8751.8541.8381.8251.8151.8071.799
351.9991.9321.8901.8611.8401.8241.8111.8011.7921.785
361.9861.9191.8771.8481.8271.8111.7981.7871.7791.772
371.9741.9071.8651.8361.8151.7981.7851.7751.7661.759
381.9631.8961.8541.8241.8031.7861.7731.7631.7541.747
391.9531.8851.8431.8131.7921.7751.7621.7511.7431.735
401.9431.8751.8321.8031.7811.7641.7511.7411.7321.724
30405060708090100110120
411.9331.8661.8231.7931.7711.7541.7411.7301.7211.714
421.9241.8561.8131.7831.7611.7451.7311.7201.7111.704
431.9161.8481.8041.7741.7521.7351.7221.7111.7021.694
441.9081.8391.7961.7661.7431.7261.7131.7021.6931.685
451.9001.8311.7881.7571.7351.7181.7051.6941.6841.677
461.8931.8241.7801.7501.7271.7101.6961.6851.6761.668
471.8851.8161.7721.7421.7201.7021.6891.6781.6681.661
481.8791.8091.7651.7351.7121.6951.6811.6701.6611.653
491.8721.8031.7591.7281.7051.6881.6741.6631.6531.646
501.8661.7961.7521.7211.6981.6811.6671.6561.6471.639
30405060708090100110120
601.8151.7441.6991.6671.6431.6251.6111.5991.5891.581
701.7791.7071.6601.6281.6041.5851.5701.5581.5481.539
801.7521.6791.6321.5991.5741.5551.5401.5271.5171.508
901.7311.6571.6101.5761.5511.5311.5161.5031.4921.483
1001.7151.6401.5921.5581.5321.5121.4961.4831.4721.463
1101.7011.6261.5771.5431.5171.4971.4801.4671.4561.447
1201.6901.6141.5651.5301.5041.4831.4671.4541.4421.433
1301.6801.6041.5551.5191.4931.4721.4561.4421.4311.421
1401.6721.5961.5461.5101.4831.4631.4461.4321.4201.411
1501.6651.5881.5381.5021.4751.4541.4371.4231.4121.402
30405060708090100110120
1601.6591.5821.5311.4951.4681.4471.4301.4161.4041.394
1701.6531.5761.5251.4891.4621.4401.4231.4091.3971.387
1801.6491.5711.5201.4841.4561.4351.4171.4031.3911.381
1901.6441.5661.5151.4791.4511.4291.4121.3981.3851.375
2001.6401.5621.5111.4741.4471.4251.4071.3931.3801.370
2101.6371.5581.5071.4701.4421.4211.4031.3881.3761.365
2201.6341.5551.5031.4671.4391.4171.3991.3841.3721.361
2301.6311.5521.5001.4631.4351.4131.3951.3811.3681.357
2401.6281.5491.4971.4601.4321.4101.3921.3771.3651.354
2501.6251.5461.4951.4571.4291.4071.3891.3741.3611.351

分布表のタイプを選択

1 2 3 4 Home

F分布表(上側1パーセント点)

1. F分布(0.05)  |  2. F分布(0.025)  |  3. F分布(0.01)  |  4. F分布(0.005)

F分布の上側 0.01 点

α=0.01 のとき,表頭の自由度 m と表側の自由度 n に対して,F分布の上側 α 点 Fα(m,n) を示す。 \[ \alpha \longmapsto F_\alpha(m,n),\qquad \text{Pr}\{X>F_\alpha(m,n)\}=\alpha \] F1-α(m,n) と Fα(n,m) について, \[ F_{1-\alpha}(m,n)=\frac{1}{F_\alpha(n,m)},\qquad F_{0.99}(m,n)=\frac{1}{F_{0.01}(n,m)} \] が成り立つから,この表を用いて上側 0.99 点を求めることができる。

m=1 ~ 10

n∖m12345678910
14052499954035625576458595928598160226056
298.5099.0099.1799.2599.3099.3399.3699.3799.3999.40
334.1230.8229.4628.7128.2427.9127.6727.4927.3527.23
421.2018.0016.6915.9815.5215.2114.9814.8014.6614.55
516.2613.2712.0611.3910.9710.6710.4610.2910.1610.05
613.7510.929.7809.1488.7468.4668.2608.1027.9767.874
712.259.5478.4517.8477.4607.1916.9936.8406.7196.620
811.268.6497.5917.0066.6326.3716.1786.0295.9115.814
910.568.0226.9926.4226.0575.8025.6135.4675.3515.257
1010.047.5596.5525.9945.6365.3865.2005.0574.9424.849
12345678910
119.6467.2066.2175.6685.3165.0694.8864.7444.6324.539
129.3306.9275.9535.4125.0644.8214.6404.4994.3884.296
139.0746.7015.7395.2054.8624.6204.4414.3024.1914.100
148.8626.5155.5645.0354.6954.4564.2784.1404.0303.939
158.6836.3595.4174.8934.5564.3184.1424.0043.8953.805
168.5316.2265.2924.7734.4374.2024.0263.8903.7803.691
178.4006.1125.1854.6694.3364.1023.9273.7913.6823.593
188.2856.0135.0924.5794.2484.0153.8413.7053.5973.508
198.1855.9265.0104.5004.1713.9393.7653.6313.5233.434
208.0965.8494.9384.4314.1033.8713.6993.5643.4573.368
12345678910
218.0175.7804.8744.3694.0423.8123.6403.5063.3983.310
227.9455.7194.8174.3133.9883.7583.5873.4533.3463.258
237.8815.6644.7654.2643.9393.7103.5393.4063.2993.211
247.8235.6144.7184.2183.8953.6673.4963.3633.2563.168
257.7705.5684.6754.1773.8553.6273.4573.3243.2173.129
267.7215.5264.6374.1403.8183.5913.4213.2883.1823.094
277.6775.4884.6014.1063.7853.5583.3883.2563.1493.062
287.6365.4534.5684.0743.7543.5283.3583.2263.1203.032
297.5985.4204.5384.0453.7253.4993.3303.1983.0923.005
307.5625.3904.5104.0183.6993.4733.3043.1733.0672.979
12345678910
317.5305.3624.4843.9933.6753.4493.2813.1493.0432.955
327.4995.3364.4593.9693.6523.4273.2583.1273.0212.934
337.4715.3124.4373.9483.6303.4063.2383.1063.0002.913
347.4445.2894.4163.9273.6113.3863.2183.0872.9812.894
357.4195.2684.3963.9083.5923.3683.2003.0692.9632.876
367.3965.2484.3773.8903.5743.3513.1833.0522.9462.859
377.3735.2294.3603.8733.5583.3343.1673.0362.9302.843
387.3535.2114.3433.8583.5423.3193.1523.0212.9152.828
397.3335.1944.3273.8433.5283.3053.1373.0062.9012.814
407.3145.1794.3133.8283.5143.2913.1242.9932.8882.801
12345678910
417.2965.1634.2993.8153.5013.2783.1112.9802.8752.788
427.2805.1494.2853.8023.4883.2663.0992.9682.8632.776
437.2645.1364.2733.7903.4763.2543.0872.9572.8512.764
447.2485.1234.2613.7783.4653.2433.0762.9462.8402.754
457.2345.1104.2493.7673.4543.2323.0662.9352.8302.743
467.2205.0994.2383.7573.4443.2223.0562.9252.8202.733
477.2075.0874.2283.7473.4343.2133.0462.9162.8112.724
487.1945.0774.2183.7373.4253.2043.0372.9072.8022.715
497.1825.0664.2083.7283.4163.1953.0282.8982.7932.706
507.1715.0574.1993.7203.4083.1863.0202.8902.7852.698
12345678910
607.0774.9774.1263.6493.3393.1192.9532.8232.7182.632
707.0114.9224.0743.6003.2913.0712.9062.7772.6722.585
806.9634.8814.0363.5633.2553.0362.8712.7422.6372.551
906.9254.8494.0073.5353.2283.0092.8452.7152.6112.524
1006.8954.8243.9843.5133.2062.9882.8232.6942.5902.503
1106.8714.8033.9653.4953.1882.9702.8062.6772.5732.486
1206.8514.7873.9493.4803.1742.9562.7922.6632.5592.472
1306.8344.7723.9363.4673.1612.9442.7802.6512.5472.460
1406.8194.7603.9253.4563.1512.9332.7692.6412.5362.450
1506.8074.7493.9153.4473.1422.9242.7612.6322.5282.441
12345678910
1606.7964.7403.9063.4393.1342.9172.7532.6242.5202.434
1706.7864.7323.8993.4313.1272.9102.7462.6172.5132.427
1806.7784.7253.8923.4253.1202.9042.7402.6112.5072.421
1906.7704.7193.8863.4193.1152.8982.7352.6062.5022.415
2006.7634.7133.8813.4143.1102.8932.7302.6012.4972.411
2106.7574.7083.8763.4103.1052.8892.7252.5972.4932.406
2206.7514.7033.8723.4063.1012.8852.7212.5932.4892.402
2306.7464.6993.8683.4023.0982.8812.7182.5892.4852.399
2406.7424.6953.8643.3983.0942.8782.7142.5862.4822.395
2506.7374.6913.8613.3953.0912.8752.7112.5832.4792.392

m=11 ~ 20

n∖m11121314151617181920
16083610661266143615761706181619262016209
299.4199.4299.4299.4399.4399.4499.4499.4499.4599.45
327.1327.0526.9826.9226.8726.8326.7926.7526.7226.69
414.4514.3714.3114.2514.2014.1514.1114.0814.0514.02
59.9639.8889.8259.7709.7229.6809.6439.6109.5809.553
67.7907.7187.6577.6057.5597.5197.4837.4517.4227.396
76.5386.4696.4106.3596.3146.2756.2406.2096.1816.155
85.7345.6675.6095.5595.5155.4775.4425.4125.3845.359
95.1785.1115.0555.0054.9624.9244.8904.8604.8334.808
104.7724.7064.6504.6014.5584.5204.4874.4574.4304.405
11121314151617181920
114.4624.3974.3424.2934.2514.2134.1804.1504.1234.099
124.2204.1554.1004.0524.0103.9723.9393.9093.8833.858
134.0253.9603.9053.8573.8153.7783.7453.7163.6893.665
143.8643.8003.7453.6983.6563.6193.5863.5563.5293.505
153.7303.6663.6123.5643.5223.4853.4523.4233.3963.372
163.6163.5533.4983.4513.4093.3723.3393.3103.2833.259
173.5193.4553.4013.3533.3123.2753.2423.2123.1863.162
183.4343.3713.3163.2693.2273.1903.1583.1283.1013.077
193.3603.2973.2423.1953.1533.1163.0843.0543.0273.003
203.2943.2313.1773.1303.0883.0513.0182.9892.9622.938
11121314151617181920
213.2363.1733.1193.0723.0302.9932.9602.9312.9042.880
223.1843.1213.0673.0192.9782.9412.9082.8792.8522.827
233.1373.0743.0202.9732.9312.8942.8612.8322.8052.781
243.0943.0322.9772.9302.8892.8522.8192.7892.7622.738
253.0562.9932.9392.8922.8502.8132.7802.7512.7242.699
263.0212.9582.9042.8572.8152.7782.7452.7152.6882.664
272.9882.9262.8712.8242.7832.7462.7132.6832.6562.632
282.9592.8962.8422.7952.7532.7162.6832.6532.6262.602
292.9312.8682.8142.7672.7262.6892.6562.6262.5992.574
302.9062.8432.7892.7422.7002.6632.6302.6002.5732.549
11121314151617181920
312.8822.8202.7652.7182.6772.6402.6062.5772.5502.525
322.8602.7982.7442.6962.6552.6182.5842.5552.5272.503
332.8402.7772.7232.6762.6342.5972.5642.5342.5072.482
342.8212.7582.7042.6572.6152.5782.5452.5152.4882.463
352.8032.7402.6862.6392.5972.5602.5272.4972.4702.445
362.7862.7232.6692.6222.5802.5432.5102.4802.4532.428
372.7702.7072.6532.6062.5642.5272.4942.4642.4372.412
382.7552.6922.6382.5912.5492.5122.4792.4492.4212.397
392.7412.6782.6242.5772.5352.4982.4652.4342.4072.382
402.7272.6652.6112.5632.5222.4842.4512.4212.3942.369
11121314151617181920
412.7152.6522.5982.5512.5092.4722.4382.4082.3812.356
422.7032.6402.5862.5392.4972.4602.4262.3962.3692.344
432.6912.6292.5752.5272.4852.4482.4152.3852.3572.332
442.6802.6182.5642.5162.4752.4372.4042.3742.3462.321
452.6702.6082.5532.5062.4642.4272.3932.3632.3362.311
462.6602.5982.5442.4962.4542.4172.3842.3532.3262.301
472.6512.5882.5342.4872.4452.4082.3742.3442.3162.291
482.6422.5792.5252.4782.4362.3992.3652.3352.3072.282
492.6332.5712.5172.4692.4272.3902.3562.3262.2992.274
502.6252.5622.5082.4612.4192.3822.3482.3182.2902.265
11121314151617181920
602.5592.4962.4422.3942.3522.3152.2812.2512.2232.198
702.5122.4502.3952.3482.3062.2682.2342.2042.1762.150
802.4782.4152.3612.3132.2712.2332.1992.1692.1412.115
902.4512.3892.3342.2862.2442.2062.1722.1422.1142.088
1002.4302.3682.3132.2652.2232.1852.1512.1202.0922.067
1102.4132.3502.2962.2482.2062.1682.1342.1032.0752.049
1202.3992.3362.2822.2342.1922.1542.1192.0892.0602.035
1302.3872.3242.2702.2222.1792.1412.1072.0762.0482.022
1402.3772.3142.2602.2122.1692.1312.0972.0662.0382.012
1502.3682.3052.2512.2032.1602.1222.0882.0572.0292.003
11121314151617181920
1602.3602.2982.2432.1952.1532.1142.0802.0492.0211.995
1702.3542.2912.2362.1882.1462.1082.0732.0422.0141.988
1802.3482.2852.2302.1822.1402.1022.0672.0362.0081.982
1902.3422.2802.2252.1772.1342.0962.0622.0312.0021.976
2002.3382.2752.2202.1722.1292.0912.0572.0261.9971.971
2102.3332.2702.2162.1682.1252.0872.0522.0211.9931.967
2202.3292.2662.2122.1642.1212.0832.0482.0171.9891.963
2302.3262.2632.2082.1602.1172.0792.0452.0141.9851.959
2402.3222.2602.2052.1572.1142.0762.0412.0101.9821.956
2502.3192.2572.2022.1542.1112.0732.0382.0071.9791.953

m=30 ~ 120

n∖m30405060708090100110120
16261628763036313632163266331633463376339
299.4799.4799.4899.4899.4899.4999.4999.4999.4999.49
326.5026.4126.3526.3226.2926.2726.2526.2426.2326.22
413.8413.7513.6913.6513.6313.6113.5913.5813.5713.56
59.3799.2919.2389.2029.1769.1579.1429.1309.1209.112
67.2297.1437.0917.0577.0327.0136.9986.9876.9776.969
75.9925.9085.8585.8245.7995.7815.7665.7555.7455.737
85.1985.1165.0655.0325.0074.9894.9754.9634.9544.946
94.6494.5674.5174.4834.4594.4414.4264.4154.4064.398
104.2474.1654.1154.0824.0584.0394.0254.0144.0043.996
30405060708090100110120
113.9413.8603.8103.7763.7523.7343.7193.7083.6983.690
123.7013.6193.5693.5353.5113.4933.4783.4673.4573.449
133.5073.4253.3753.3413.3173.2983.2843.2723.2633.255
143.3483.2663.2153.1813.1573.1383.1243.1123.1023.094
153.2143.1323.0813.0473.0223.0042.9892.9772.9682.959
163.1013.0182.9672.9332.9082.8892.8752.8632.8532.845
173.0032.9202.8692.8352.8102.7912.7762.7642.7542.746
182.9192.8352.7842.7492.7242.7052.6902.6782.6682.660
192.8442.7612.7092.6742.6492.6302.6142.6022.5922.584
202.7782.6952.6432.6082.5822.5632.5482.5352.5252.517
30405060708090100110120
212.7202.6362.5842.5482.5232.5032.4882.4752.4652.457
222.6672.5832.5312.4952.4692.4502.4342.4222.4122.403
232.6202.5352.4832.4472.4212.4012.3862.3732.3632.354
242.5772.4922.4402.4032.3772.3572.3422.3292.3192.310
252.5382.4532.4002.3642.3372.3172.3022.2892.2782.270
262.5032.4172.3642.3272.3012.2812.2652.2522.2412.233
272.4702.3842.3302.2942.2672.2472.2312.2182.2072.198
282.4402.3542.3002.2632.2362.2162.2002.1872.1762.167
292.4122.3252.2712.2342.2072.1872.1712.1582.1472.138
302.3862.2992.2452.2082.1812.1602.1442.1312.1202.111
30405060708090100110120
312.3622.2752.2202.1832.1562.1352.1192.1062.0952.086
322.3402.2522.1982.1602.1332.1122.0952.0822.0712.062
332.3192.2312.1762.1392.1112.0902.0742.0602.0492.040
342.2992.2112.1562.1182.0912.0702.0532.0402.0282.019
352.2812.1932.1372.0992.0722.0502.0342.0202.0092.000
362.2632.1752.1202.0822.0542.0322.0162.0021.9911.981
372.2472.1592.1032.0652.0372.0151.9981.9851.9731.964
382.2322.1432.0872.0492.0211.9991.9821.9681.9571.947
392.2172.1282.0722.0342.0051.9841.9671.9531.9421.932
402.2032.1142.0582.0191.9911.9691.9521.9381.9271.917
30405060708090100110120
412.1902.1012.0452.0061.9771.9561.9381.9241.9131.903
422.1782.0882.0321.9931.9641.9431.9251.9111.9001.890
432.1662.0762.0201.9811.9521.9301.9131.8991.8871.877
442.1552.0652.0081.9691.9401.9181.9011.8871.8751.865
452.1442.0541.9971.9581.9291.9071.8891.8751.8631.853
462.1342.0441.9871.9471.9181.8961.8781.8641.8521.842
472.1242.0341.9771.9371.9081.8861.8681.8541.8421.832
482.1152.0241.9671.9271.8981.8761.8581.8441.8321.822
492.1062.0151.9581.9181.8891.8661.8481.8341.8221.812
502.0982.0071.9491.9091.8801.8571.8391.8251.8131.803
30405060708090100110120
602.0281.9361.8771.8361.8061.7831.7641.7491.7371.726
701.9801.8861.8261.7851.7541.7301.7111.6951.6831.672
801.9441.8491.7881.7461.7141.6901.6711.6551.6421.630
901.9161.8201.7591.7161.6841.6591.6391.6231.6101.598
1001.8931.7971.7351.6921.6591.6341.6141.5981.5841.572
1101.8751.7781.7161.6721.6391.6141.5931.5771.5631.551
1201.8601.7631.7001.6561.6231.5971.5761.5591.5451.533
1301.8471.7501.6861.6421.6081.5821.5621.5441.5301.518
1401.8361.7381.6751.6301.5961.5701.5491.5321.5171.505
1501.8271.7291.6651.6201.5861.5591.5381.5201.5061.493
30405060708090100110120
1601.8191.7201.6561.6101.5761.5501.5281.5111.4961.483
1701.8111.7131.6481.6021.5681.5411.5201.5021.4871.474
1801.8051.7061.6411.5951.5611.5341.5121.4941.4791.466
1901.7991.7001.6351.5891.5541.5271.5051.4871.4721.459
2001.7941.6941.6291.5831.5481.5211.4991.4811.4661.453
2101.7891.6901.6241.5781.5431.5161.4941.4751.4601.447
2201.7851.6851.6201.5731.5381.5111.4891.4701.4551.442
2301.7811.6811.6161.5691.5341.5061.4841.4651.4501.437
2401.7781.6771.6121.5651.5301.5021.4801.4611.4461.432
2501.7741.6741.6081.5611.5261.4981.4761.4571.4411.428

分布表のタイプを選択

1 2 3 4 Home

F分布表(上側0.5パーセント点)

1. F分布(0.05)  |  2. F分布(0.025)  |  3. F分布(0.01)  |  4. F分布(0.005)

F分布の上側 0.005 点

α=0.005 のとき,表頭の自由度 m と表側の自由度 n に対して,F分布の上側 α 点 Fα(m,n) を示す。 \[ \alpha \longmapsto F_\alpha(m,n),\qquad \text{Pr}\{X>F_\alpha(m,n)\}=\alpha \] F1-α(m,n) と Fα(n,m) について, \[ F_{1-\alpha}(m,n)=\frac{1}{F_\alpha(n,m)},\qquad F_{0.995}(m,n)=\frac{1}{F_{0.005}(n,m)} \] が成り立つから,この表を用いて上側 0.995 点を求めることができる。

m=1 ~ 10

n∖m12345678910
116211199992161522500230562343723715239252409124224
2198.5199.0199.2199.2199.3199.3199.4199.4199.4199.4
355.5549.8047.4746.1945.3944.8444.4344.1343.8843.69
431.3326.2824.2623.1522.4621.9721.6221.3521.1420.97
522.7818.3116.5315.5614.9414.5114.2013.9613.7713.62
618.6314.5412.9212.0311.4611.0710.7910.5710.3910.25
716.2412.4010.8810.059.5229.1558.8858.6788.5148.380
814.6911.049.5968.8058.3027.9527.6947.4967.3397.211
913.6110.118.7177.9567.4717.1346.8856.6936.5416.417
1012.839.4278.0817.3436.8726.5456.3026.1165.9685.847
12345678910
1112.238.9127.6006.8816.4226.1025.8655.6825.5375.418
1211.758.5107.2266.5216.0715.7575.5255.3455.2025.085
1311.378.1866.9266.2335.7915.4825.2535.0764.9354.820
1411.067.9226.6805.9985.5625.2575.0314.8574.7174.603
1510.807.7016.4765.8035.3725.0714.8474.6744.5364.424
1610.587.5146.3035.6385.2124.9134.6924.5214.3844.272
1710.387.3546.1565.4975.0754.7794.5594.3894.2544.142
1810.227.2156.0285.3754.9564.6634.4454.2764.1414.030
1910.077.0935.9165.2684.8534.5614.3454.1774.0433.933
209.9446.9865.8185.1744.7624.4724.2574.0903.9563.847
12345678910
219.8306.8915.7305.0914.6814.3934.1794.0133.8803.771
229.7276.8065.6525.0174.6094.3224.1093.9443.8123.703
239.6356.7305.5824.9504.5444.2594.0473.8823.7503.642
249.5516.6615.5194.8904.4864.2023.9913.8263.6953.587
259.4756.5985.4624.8354.4334.1503.9393.7763.6453.537
269.4066.5415.4094.7854.3844.1033.8933.7303.5993.492
279.3426.4895.3614.7404.3404.0593.8503.6873.5573.450
289.2846.4405.3174.6984.3004.0203.8113.6493.5193.412
299.2306.3965.2764.6594.2623.9833.7753.6133.4833.377
309.1806.3555.2394.6234.2283.9493.7423.5803.4503.344
12345678910
319.1336.3175.2044.5904.1963.9183.7113.5493.4203.314
329.0906.2815.1714.5594.1663.8893.6823.5213.3923.286
339.0506.2485.1414.5314.1383.8613.6553.4953.3663.260
349.0126.2175.1134.5044.1123.8363.6303.4703.3413.235
358.9766.1885.0864.4794.0883.8123.6073.4473.3183.212
368.9436.1615.0624.4554.0653.7903.5853.4253.2963.191
378.9126.1355.0384.4334.0433.7693.5643.4043.2763.171
388.8826.1115.0164.4124.0233.7493.5453.3853.2573.152
398.8546.0884.9954.3924.0043.7313.5263.3673.2393.134
408.8286.0664.9764.3743.9863.7133.5093.3503.2223.117
12345678910
418.8036.0464.9574.3563.9693.6963.4923.3343.2063.101
428.7796.0274.9404.3393.9533.6803.4773.3183.1913.086
438.7576.0084.9234.3243.9373.6653.4623.3043.1763.071
448.7355.9914.9074.3083.9233.6513.4483.2903.1623.057
458.7155.9744.8924.2943.9093.6383.4353.2763.1493.044
468.6955.9584.8774.2803.8963.6253.4223.2643.1373.032
478.6775.9434.8644.2673.8833.6123.4103.2523.1253.020
488.6595.9294.8504.2553.8713.6013.3983.2403.1133.009
498.6425.9154.8384.2433.8603.5893.3873.2293.1022.998
508.6265.9024.8264.2323.8493.5793.3763.2193.0922.988
12345678910
608.4955.7954.7294.1403.7603.4923.2913.1343.0082.904
708.4035.7204.6614.0763.6983.4313.2323.0762.9502.846
808.3355.6654.6114.0293.6523.3873.1883.0322.9072.803
908.2825.6234.5733.9923.6173.3523.1542.9992.8732.770
1008.2415.5894.5423.9633.5893.3253.1272.9722.8472.744
1108.2075.5624.5183.9403.5673.3033.1052.9512.8262.723
1208.1795.5394.4973.9213.5483.2853.0872.9332.8082.705
1308.1555.5204.4803.9043.5333.2703.0722.9182.7932.690
1408.1355.5044.4653.8903.5193.2563.0592.9052.7812.678
1508.1185.4904.4533.8783.5083.2453.0482.8942.7702.667
12345678910
1608.1025.4784.4413.8683.4973.2353.0392.8852.7602.657
1708.0895.4674.4323.8593.4893.2273.0302.8762.7522.649
1808.0775.4574.4233.8513.4813.2193.0222.8692.7442.642
1908.0675.4494.4153.8433.4743.2123.0162.8622.7382.635
2008.0575.4414.4083.8373.4673.2063.0102.8562.7322.629
2108.0495.4344.4023.8313.4623.2003.0042.8512.7272.624
2208.0415.4284.3963.8263.4563.1952.9992.8462.7222.619
2308.0345.4224.3913.8213.4523.1912.9952.8412.7172.615
2408.0275.4174.3873.8163.4473.1872.9912.8372.7132.610
2508.0215.4124.3823.8123.4433.1832.9872.8332.7092.607

m=11 ~ 20

n∖m11121314151617181920
124334244262450524572246302468124727247672480324836
2199.4199.4199.4199.4199.4199.4199.4199.4199.4199.4
343.5243.3943.2743.1743.0843.0142.9442.8842.8342.78
420.8220.7020.6020.5120.4420.3720.3120.2620.2120.17
513.4913.3813.2913.2113.1513.0913.0312.9812.9412.90
610.1310.039.9509.8779.8149.7589.7099.6649.6259.589
78.2708.1768.0978.0287.9687.9157.8687.8267.7887.754
87.1047.0156.9386.8726.8146.7636.7186.6786.6416.608
96.3146.2276.1536.0896.0325.9835.9395.8995.8645.832
105.7465.6615.5895.5265.4715.4225.3795.3405.3055.274
11121314151617181920
115.3205.2365.1655.1035.0495.0014.9594.9214.8864.855
124.9884.9064.8364.7754.7214.6744.6324.5954.5614.530
134.7244.6434.5734.5134.4604.4134.3724.3344.3014.270
144.5084.4284.3594.2994.2474.2004.1594.1224.0894.059
154.3294.2504.1814.1224.0704.0243.9833.9463.9133.883
164.1794.0994.0313.9723.9203.8753.8343.7973.7643.734
174.0503.9713.9033.8443.7933.7473.7073.6703.6373.607
183.9383.8603.7933.7343.6833.6373.5973.5603.5273.498
193.8413.7633.6963.6383.5873.5413.5013.4653.4323.402
203.7563.6783.6113.5533.5023.4573.4163.3803.3473.318
11121314151617181920
213.6803.6023.5363.4783.4273.3823.3423.3053.2733.243
223.6123.5353.4693.4113.3603.3153.2753.2393.2063.176
233.5513.4753.4083.3513.3003.2553.2153.1793.1463.116
243.4973.4203.3543.2963.2463.2013.1613.1253.0923.062
253.4473.3703.3043.2473.1963.1513.1113.0753.0433.013
263.4023.3253.2593.2023.1513.1073.0673.0312.9982.968
273.3603.2843.2183.1613.1103.0663.0262.9902.9572.928
283.3223.2463.1803.1233.0733.0282.9882.9522.9192.890
293.2873.2113.1453.0883.0382.9932.9532.9172.8852.855
303.2553.1793.1133.0563.0062.9612.9212.8852.8532.823
11121314151617181920
313.2253.1493.0833.0262.9762.9312.8912.8552.8232.793
323.1973.1213.0562.9982.9482.9042.8642.8282.7952.766
333.1713.0953.0302.9732.9222.8782.8382.8022.7692.740
343.1463.0713.0052.9482.8982.8542.8142.7782.7452.716
353.1243.0482.9832.9262.8762.8312.7912.7552.7232.693
363.1023.0272.9612.9052.8542.8102.7702.7342.7012.672
373.0823.0072.9412.8852.8342.7902.7502.7142.6812.652
383.0632.9882.9232.8662.8162.7712.7312.6952.6632.633
393.0452.9702.9052.8482.7982.7532.7132.6772.6452.615
403.0282.9532.8882.8312.7812.7372.6972.6612.6282.598
11121314151617181920
413.0122.9372.8722.8152.7652.7212.6812.6452.6122.583
422.9972.9222.8572.8002.7502.7062.6662.6302.5972.567
432.9832.9082.8432.7862.7362.6912.6512.6152.5832.553
442.9692.8942.8292.7722.7222.6782.6382.6022.5692.540
452.9562.8812.8162.7592.7092.6652.6252.5892.5562.527
462.9442.8692.8042.7472.6972.6532.6132.5772.5442.514
472.9322.8572.7922.7352.6852.6412.6012.5652.5322.502
482.9212.8462.7812.7242.6742.6302.5902.5542.5212.491
492.9102.8352.7702.7132.6632.6192.5792.5432.5102.480
502.9002.8252.7602.7032.6532.6092.5692.5332.5002.470
11121314151617181920
602.8172.7422.6772.6202.5702.5262.4862.4502.4172.387
702.7592.6842.6192.5632.5132.4682.4282.3922.3592.329
802.7162.6412.5772.5202.4702.4252.3852.3492.3162.286
902.6832.6082.5442.4872.4372.3932.3532.3162.2832.253
1002.6572.5832.5182.4612.4112.3672.3262.2902.2572.227
1102.6362.5612.4972.4402.3902.3452.3052.2692.2362.206
1202.6182.5442.4792.4232.3732.3282.2882.2512.2182.188
1302.6042.5292.4652.4082.3582.3132.2732.2372.2042.173
1402.5912.5172.4522.3962.3452.3012.2602.2242.1912.161
1502.5802.5062.4412.3852.3352.2902.2502.2132.1802.150
11121314151617181920
1602.5712.4962.4322.3752.3252.2802.2402.2042.1702.140
1702.5622.4882.4242.3672.3172.2722.2322.1952.1622.132
1802.5552.4812.4162.3602.3092.2652.2242.1882.1552.124
1902.5482.4742.4102.3532.3032.2582.2182.1812.1482.118
2002.5432.4682.4042.3472.2972.2522.2122.1752.1422.112
2102.5372.4632.3982.3422.2922.2472.2062.1702.1372.106
2202.5322.4582.3942.3372.2872.2422.2022.1652.1322.101
2302.5282.4542.3892.3332.2822.2382.1972.1612.1272.097
2402.5242.4502.3852.3292.2782.2332.1932.1572.1232.093
2502.5202.4462.3812.3252.2752.2302.1892.1532.1192.089

m=30 ~ 120

n∖m30405060708090100110120
125044251482521125253252832530625323253372534925359
2199.5199.5199.5199.5199.5199.5199.5199.5199.5199.5
342.4742.3142.2142.1542.1042.0742.0442.0242.0041.99
419.8919.7519.6719.6119.5719.5419.5219.5019.4819.47
512.6612.5312.4512.4012.3712.3412.3212.3012.2912.27
69.3589.2419.1709.1229.0889.0629.0429.0269.0129.001
77.5347.4227.3547.3097.2767.2517.2327.2177.2047.193
86.3966.2886.2226.1776.1456.1216.1036.0886.0756.065
95.6255.5195.4545.4105.3795.3565.3375.3225.3105.300
105.0714.9664.9024.8594.8284.8054.7874.7724.7604.750
30405060708090100110120
114.6544.5514.4884.4454.4144.3914.3734.3594.3474.337
124.3314.2284.1654.1234.0924.0694.0514.0374.0254.015
134.0733.9703.9083.8663.8353.8123.7943.7803.7683.758
143.8623.7603.6983.6553.6253.6023.5843.5693.5573.547
153.6873.5853.5233.4803.4503.4273.4093.3943.3823.372
163.5393.4373.3753.3323.3023.2793.2613.2463.2343.224
173.4123.3113.2483.2063.1753.1523.1343.1193.1073.097
183.3033.2013.1393.0963.0653.0423.0243.0092.9972.987
193.2083.1063.0433.0002.9702.9462.9282.9132.9012.891
203.1233.0222.9592.9162.8852.8612.8432.8282.8162.806
30405060708090100110120
213.0492.9472.8842.8412.8102.7862.7682.7532.7402.730
222.9822.8802.8172.7742.7422.7192.7002.6852.6732.663
232.9222.8202.7562.7132.6822.6582.6392.6242.6122.602
242.8682.7652.7022.6582.6272.6032.5842.5692.5572.546
252.8192.7162.6522.6092.5772.5532.5342.5192.5072.496
262.7742.6712.6072.5632.5322.5082.4892.4732.4612.450
272.7332.6302.5652.5222.4902.4662.4472.4312.4192.408
282.6952.5922.5272.4832.4512.4272.4082.3922.3802.369
292.6602.5572.4922.4482.4162.3912.3722.3572.3442.333
302.6282.5242.4592.4152.3832.3582.3392.3232.3112.300
30405060708090100110120
312.5982.4942.4292.3852.3522.3282.3082.2932.2802.269
322.5702.4662.4012.3562.3242.2992.2802.2642.2512.240
332.5442.4402.3742.3302.2972.2722.2532.2372.2242.213
342.5202.4152.3502.3052.2722.2472.2282.2122.1992.188
352.4972.3922.3272.2822.2492.2242.2042.1882.1752.164
362.4752.3712.3052.2602.2272.2022.1822.1662.1522.141
372.4552.3502.2842.2392.2062.1812.1612.1452.1312.120
382.4362.3312.2652.2202.1862.1612.1412.1252.1122.100
392.4182.3132.2472.2012.1682.1432.1222.1062.0932.081
402.4012.2962.2302.1842.1502.1252.1052.0882.0752.064
30405060708090100110120
412.3852.2802.2132.1672.1342.1082.0882.0722.0582.047
422.3702.2642.1982.1522.1182.0922.0722.0562.0422.030
432.3562.2502.1832.1372.1032.0772.0572.0402.0272.015
442.3422.2362.1692.1232.0892.0632.0422.0262.0122.000
452.3292.2222.1552.1092.0752.0492.0292.0121.9981.987
462.3162.2102.1432.0962.0622.0362.0151.9991.9851.973
472.3042.1982.1302.0842.0502.0242.0031.9861.9721.960
482.2932.1862.1192.0722.0382.0121.9911.9741.9601.948
492.2822.1752.1072.0612.0262.0001.9791.9621.9481.937
502.2722.1642.0972.0502.0151.9891.9681.9511.9371.925
30405060708090100110120
602.1872.0792.0101.9621.9271.9001.8781.8611.8461.834
702.1282.0191.9491.9001.8641.8371.8151.7971.7821.769
802.0841.9741.9031.8541.8171.7891.7671.7481.7331.720
902.0511.9391.8681.8181.7811.7521.7301.7111.6951.682
1002.0241.9121.8401.7901.7521.7231.7001.6811.6651.652
1102.0021.8901.8171.7661.7281.6991.6761.6561.6401.627
1201.9841.8711.7981.7471.7091.6791.6551.6361.6191.606
1301.9691.8551.7821.7301.6921.6621.6381.6181.6021.588
1401.9561.8421.7681.7161.6781.6471.6231.6031.5861.572
1501.9441.8301.7561.7041.6651.6351.6101.5901.5731.559
30405060708090100110120
1601.9351.8201.7461.6931.6541.6241.5991.5791.5621.547
1701.9261.8111.7371.6841.6451.6141.5891.5691.5511.537
1801.9181.8031.7291.6761.6361.6051.5801.5601.5421.528
1901.9111.7961.7211.6681.6281.5971.5721.5511.5341.519
2001.9051.7901.7151.6611.6211.5901.5651.5441.5271.512
2101.9001.7841.7091.6551.6151.5841.5581.5381.5201.505
2201.8941.7791.7031.6501.6101.5781.5531.5321.5141.499
2301.8901.7741.6981.6451.6041.5731.5471.5261.5081.493
2401.8861.7701.6941.6401.6001.5681.5421.5211.5031.488
2501.8821.7651.6901.6361.5951.5631.5381.5161.4981.483

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