Н.А. Спирин, В.В. Лавров - Методы планирования и обработки результатов инженерного эксперимента, страница 39

Для m>1000,90,50,016 0,4550,211 1,3860,584 2,3661,064 3,3571,610 4,3512,204 5,3482,833 6,3463,490 7,3444,168 8,3434,865 9,3425,578 10,346,304 11,347,041 12,347,790 13,348,547 14,349,312 15,3410,09 16,3410,86 17,3411,65 18,3412,44 19,3413,24 20,3414,04 21,3414,85 22,3415,66 23,3416,47 24,3417,29 25,3418,11 26,3418,94 27,3419,77 28,3420,60 29,3429,05 39,3437,69 49,3346,46 59,3355,33 69,3364,28 79,3373,29 89,3382,36 99,331χ α2 ,m ≈ ( Z (1−α ) +22490,12,7064,6056,2517,7799,23610,6412,0213,3614,6815,9917,2818,5519,8121,0622,3123,5424,7725,9927,2028,4129,6230,8132,0133,2034,3835,5636,7437,9239,0940,2651,8163,1774,4085,5396,58107,6118,52 m − 1) 20,053,8415,9917,8159,48811,0712,5914,0715,5116,9218,3119,6821,0322,3623,6825,0026,3027,5928,8730,1431,4132,6733,9235,1736,4237,6538,8940,1141,3442,5643,7755,7667,5079,0890,53101,9113,1124,30,0255,0247,3789,34811,1412,8314,4516,0117,5319,0220,4821,9223,3424,7426,1227,4928,8530,1931,5332,8534,1735,4836,7838,0839,3640,6541,9243,1944,4645,7246,9859,3471,4283,3095,02106,6118,1129,60,016,6359,21011,3413,2815,0916,8118,4820,0921,6723,2124,7326,2227,6929,1430,5832,0033,4134,8136,1937,5738,9340,2941,6442,9844,3145,6446,9648,2849,5950,8963,6976,1588,38100,4112,3124,1135,80,0057,87910,6012,8414,8616,7518,5520,2821,9523,5925,1926,7628,3029,8231,3232,8034,2735,7237,1638,5840,0041,4042,8044,1845,5646,9348,2949,6550,9952,3453,6766,7779,4991,95104,2116,3128,3140,2Квантили Fα ,m1 ,m2Таблица П.4распределения Фишера (F-распределения)для уровня значимости α=0,05 в зависимости от числа степенейсвободы m и m 2m21234567891011121314151617181920212223242526272829304060120m1123456789101215304060120161,4 199,5 215,7 224,6 230,2 234,0 236,8 238,9 240,5 241,9 243,9 245,9 250,1 251,1 252,2 253,318,510,17,716,615,995,595,325,124,964,844,754,674,604,544,494,454,414,384,354,324,304,284,264,244,234,214,204,184,174,084,003,9219,09,556,945,795,144,744,464,264,103,983,893,813,743,683,633,593,553,523,493,473,443,423,403,393,373,353,343,333,323,233,153,0719,19,286,595,414,764,354,073,863,713,593,493,413,343,293,243,203,163,133,103,073,053,033,012,992,982,962,952,932,922,842,762,6819,29,126,395,194,534,123,843,633,483,363,263,183,113,063,012,962,932,902,872,842,822,802,782,762,742,732,712,702,692,612,532,4519,39,016,265,054,393,973,693,483,333,203,113,032,962,902,852,812,772,742,712,682,662,642,622,602,592,572,562,552,532,452,372,2919,38,946,164,954,283,873,583,373,223,093,002,922,852,792,742,702,662,632,602,572,552,532,512,492,472,462,452,432,422,342,252,1819,38,896,094,884,213,793,503,293,143,012,912,832,762,712,662,612,582,542,512,492,462,442,422,402,392,372,362,352,332,252,172,0919,38,856,044,824,153,733,443,233,072,952,852,772,702,642,592,552,512,482,452,422,402,372,362,342,322,312,292,282,272,182,102,0219,38,816,004,774,103,683,393,183,022,902,802,712,652,592,542,492,462,422,392,372,342,322,302,282,272,252,242,222,212,122,041,9625019,48,795,964,744,063,643,353,142,982,852,752,672,602,542,492,452,412,382,352,322,302,272,252,242,222,202,192,182,162,081,991,9119,48,745,914,684,003,573,283,072,912,792,692,602,532,482,422,382,342,312,282,252,232,202,182,162,152,132,122,102,092,001,921,8319,48,705,864,623,943,513,223,012,852,722,622,532,462,402,352,312,272,232,202,182,152,132,112,092,072,062,042,032,011,921,841,7519,48,625,754,503,813,383,082,862,702,572,472,382,312,252,192,152,112,072,042,011,981,961,941,921,901,881,871,851,841,741,651,5519,48,595,724,463,773,343,042,832,662,532,432,342,272,202,152,102,062,031,991,961,941,911,891,871,851,841,821,811,791,691,591,5019,48,575,694,433,743,303,012,792,622,492,382,302,222,162,112,062,021,981,951,921,891,861,841,821,801,791,771,751,741,641,531,4319,48,555,664,403,703,272,972,752,582,452,342,252,182,112,062,011,971,931,901,871,841,811,791,771,751,731,711,701,681,581,471,35Квантили Fα ,m1 ,m2Таблица П.5распределения Фишера (F-распределения)для уровня значимости α=0,025 в зависимости от числа степенейсвободы m и m 2m21234567891011121314151617181920212223242526272829304060120m1123456789101215304060120647,8 799,5 864,2 899,6 921,8 937,1 948,2 956,6 963,3 968,6 976,7 984,9 1001 1006 1010 101438,517,412,210,08,818,077,577,216,946,726,556,416,306,206,126,045,985,925,875,835,795,755,725,695,665,635,615,595,575,425,295,1539,016,010,68,437,266,546,065,715,465,265,104,974,864,774,694,624,564,514,464,424,384,354,324,294,274,244,224,204,184,053,933,8039,115,49,987,766,605,895,425,084,834,634,474,354,244,154,084,013,953,903,863,823,783,753,723,693,673,653,633,613,593,463,343,2339,215,19,607,396,235,525,054,724,474,284,124,003,893,803,733,663,613,563,513,483,443,413,383,353,333,313,293,273,253,133,012,8939,314,89,367,155,995,294,824,484,244,043,893,773,663,583,503,443,383,333,293,253,223,183,153,133,103,083,063,043,032,902,792,6739,314,79,206,985,825,124,654,324,073,883,733,603,503,413,343,283,223,173,133,093,053,022,992,972,942,922,902,882,872,742,632,5239,314,69,076,855,704,994,534,203,953,763,613,483,383,293,223,163,103,053,012,972,932,902,872,852,822,802,782,762,752,622,512,3939,314,58,986,765,604,904,434,103,853,663,513,393,293,203,123,063,012,962,912,872,842,812,782,752,732,712,692,672,652,532,412,3025139,314,48,906,685,524,824,364,033,783,593,443,313,213,123,052,982,932,882,842,802,762,732,702,682,652,632,612,592,572,452,332,2239,414,48,846,625,464,764,303,963,723,533,373,253,153,062,992,922,872,822,772,732,702,672,642,612,592,572,552,532,512,392,272,1639,414,38,756,525,374,674,203,873,623,433,283,153,052,962,892,822,772,722,682,642,602,572,542,512,492,472,452,432,412,292,172,0539,414,28,666,435,274,574,103,773,523,333,183,052,952,862,792,722,672,622,572,532,502,472,442,412,392,362,342,322,312,182,061,9439,414,08,466,235,074,363,893,563,313,122,962,842,732,642,572,502,442,392,352,312,272,242,212,182,162,132,112,092,071,941,821,6939,414,08,416,185,014,313,843,513,263,062,912,782,672,592,512,442,382,332,292,252,212,182,152,122,092,072,052,032,011,881,741,6139,413,98,366,124,964,253,783,453,203,002,852,722,612,522,452,382,322,272,222,182,142,112,082,052,032,001,981,961,941,801,671,5339,413,98,316,074,904,203,733,393,142,942,792,662,552,462,382,322,262,202,162,112,082,042,011,981,951,931,911,891,871,721,581,43Двусторонние пределы tα ,mТаблица П.6распределения Стьюдента (t-распределения)в зависимости от уровня значимости α и числа степеней свободы mm1234567891011121314151617181920212223242526272829304060120500α0,16,3142,9202,3532,1322,0151,9431,8951,8601,8331,8121,7961,7821,7711,7611,7531,7461,7401,7341,7291,7251,7211,7171,7141,7111,7081,7061,7031,7011,6991,6971,6841,6711,6581,6480,0512,7064,3033,1822,7762,5712,4472,3652,3062,2622,2282,2012,1792,1602,1452,1312,1202,1102,1012,0932,0862,0802,0742,0692,0642,0602,0562,0522,0482,0452,0422,0212,0001,9801,9650,02525,4526,2054,1773,4953,1632,9692,8412,7522,6852,6342,5932,5602,5332,5102,4902,4732,4582,4452,4332,4232,4142,4052,3982,3912,3852,3792,3732,3682,3642,3602,3292,2992,2702,248Примечаниие.

Для m >500 tα ,m ≈ Z p =1−α / 22520,0163,6569,9255,8414,6044,0323,7073,4993,3553,2503,1693,1063,0553,0122,9772,9472,9212,8982,8782,8612,8452,8312,8192,8072,7972,7872,7792,7712,7632,7562,7502,7042,6602,6172,5860,005127,32114,0897,4535,5984,7734,3174,0293,8333,6903,5813,4973,4283,3723,3263,2863,2523,2223,1973,1743,1533,1353,1193,1043,0913,0783,0673,0573,0473,0383,0302,9712,9152,8602,820Таблица П.7Критические значения критерия Н.В. Смирнова uαn в зависимости отобъема выборки n и уровня значимости αn345678910111213141516171819202122232425α=0,101,151,421,601,731,831,911,982,032,092,132,172,212,252,282,312,342,362,382,412,432,452,472,49253uαnα=0,051,151,461,671,821,942,032,112,182,232,292,332,372,412,442,482,502,532,532,582,602,622,642,66α=0,011,151,491,751,942,102,222,322,412,482,552,612,662,702,752,782,822,852,882,912,942,962,993,01Таблица П.8Коэффициенты Диксона в зависимости от объема выборки nи уровня значимости αn345678910456789101112131415161718192021222324252627282930α = 0,100,8860,6790,5570,4820,4340,4790,4410,4090,9350,7820,6700,5960,5450,5050,4740,5170,4900,4670,4920,4720,4540,4380,4240,4120,4010,3910,3820,3740,3670,3600,3540,3480,3420,3370,332α = 0,050,9410,7650,6420,5600,5070,5540,5120,4770,9670,8450,7360,6610,6070,5650,5310,5760,5460,5210,5460,5250,5070,4900,4750,4620,4500,4400,4300,4210,4130,4060,3990,3930,3870,3810,376α = 0,010,9880,8890,7800,6980,6370,6830,6350,5970,9920,9290,8360,7780,7100,6670,6320,6790,6420,6150,6410,6160,5950,5770,5610,5470,5350,5240,5140,5050,4970,4890,4860,4750,4690,4630,457254α = 0,0050,9940,9260,8210,7400,6800,7250,6770,6390,9960,9500,8650,8140,7460,7000,6640,7130,6750,6490,6740,6470,6240,6050,5890,5750,5620,5510,5410,5320,5240,5160,5080,5010,4950,4890,483Статистикаr10r11r20r21r22Таблица П.9Квантили Gα ,m1 ,m2 распределения Кохрена для уровня значимостиα = 0,05 в зависимости от числа степеней свободы m и m 2m1258m21234567891016361442345678910121520243040601200,99850,96690,90650,84120,78080,97500,87090,76790,68380,61610,93920,79770,68410,59810,53210,90570,74570,62870,54410,48030,87720,70710,58950,50650,44470,85340,67710,55980,47830,41840,83330,65300,53650,45640,39800,81590,63330,51750,43870,38170,80100,61670,50170,42410,36820,78800,60250,48840,41180,35680,73410,54660,43660,36450,31350,66020,47480,37200,30660,26120,58130,40310,30930,25130,29190,72710,67980,63850,60200,54100,47090,38940,34340,29290,23700,17370,09980,56120,51570,47750,44500,39240,33460,27050,23540,19800,15760,11310,06320,48000,43770,40270,37330,32640,27580,22050,19070,15930,12590,08950,04950,43070,39100,35840,33110,28800,24190,19210,16560,13770,10820,07650,04190,39740,35950,32860,30290,26260,21950,17350,14930,12370,09680,06820,03710,37260,33620,30670,28230,24390,20340,16020,13740,11370,08870,06230,03370,35350,31850,29010,26660,22990,19110,15010,12860,10610,08270,05830,03120,33840,30430,27680,25410,21870,18150,14220,12160,10020,07800,05520,02920,32590,29260,26590,24390,20980,17360,13570,11600,09580,07450,05200,02790,31540,28290,25680,23550,20200,16710,13030,11130,09210,07130,04970,02660,27560,24620,22260,20320,17370,14290,11080,09420,07710,05950,07110,02180,22780,20220,18200,16550,14030,11440,08790,07430,06040,04620,03160,01680,18330,16160,14460,13080,11000,08890,06750,05670,04570,03470,02450,0120Таблица П.10Критические значения критерия Колмогорова-СмирноваnD0,10D0,05nD0,10D0,0530,6360,708230,2470,27540,5650,624240,2420,26950,5090,563250,2380,26460,4680,519260,2330,25970,4360,483270,2290,25480,4100,454280,2250,25090,3870,430290,2210,246100,3690,409300,2180,242110,3520,391310,2140,238120,3380,375320,2110,234130,3250,361330,2080,231140,3140,349340,2050,227150,3040,338350,2020,224160,2950,327360,1990,221170,2860,318370,1960,218180,2780,309380,1940,215190,2710,301390,1910,213200,2650,294400,1890,210210,2590,287500,1700,177220,2530,2811000,1210,134256Спирин Николай АлександровичЛавров Владислав ВасильевичМЕТОДЫ ПЛАНИРОВАНИЯИ ОБРАБОТКИ РЕЗУЛЬТАТОВИНЖЕНЕРНОГО ЭКСПЕРИМЕНТАКонспект лекций(отдельные главы из учебника для вузов)Редактор Л.Ю.КозяйчеваИД №06263 от 12.11.2001 г.Подписано в печать 21.04.2003Бумага офсетнаяПечать офсетнаяУч.-изд.л.

12,88Тираж 300ЗаказФормат 60х88 1/16Усл.печ.л. 15,1Цена "С"Редакционно-издательский отдел ГОУ ВПО УГТУ-УПИ620002, Екатеринбург, ул. Мира, 19.