La Tavola 1 `e la tavola della funzione di ripartizione della variabile N(0,1): essa fornisce, per numeri x con 0 ≤ x ≤ 4,49 , il valore della funzione

Tavole statistiche

Nelle pagine successive compaiono cinque tavole statistiche: descriviamo brevemente come si usano.

La Tavola 1 `e la tavola della funzione di ripartizione della variabile N(0,1): essa fornisce, per numeri x con 0 ≤ x ≤ 4,49 , il valore della funzione

Φ(x) = 1

√ 2π Z

−∞

e

dt .

Ad esempio, Φ(1,43) = 0,92364 . Per valori di x superiori a 4,49 , si pone Φ(x) = 1 ; invece per valori di x negativi si utilizza l’eguaglianza

Φ(−x) = 1 − Φ(x)

L’eguaglianza sopra scritta `e dovuta al fatto che, poich`e la densit`a N(0, 1)

`e una funzione pari, se la variabile aleatoria X ha densit`a N(0, 1) , si ha P ©

X ≤ −x ª

= P ©

X ≥ x ª .

Per ottenere il quantile q

della variabile N(0, 1) (cio`e il numero q

tale che si abbia P ©

X ≤ q

ª

= Φ(q

) = α) si usa la tavola della funzione di ripartizione al rovescio, cio`e cercando per quale valore di x si ha Φ(x) = α : ad esempio q

= 1,65 . In questo modo per`o si possono ottenere solo i valori di q

per α ≥ 1/2 ; per valori inferiori a 1/2 si usa l’eguaglianza

q

= −q

che `e una immediata conseguenza dell’eguaglianza Φ(−x) = 1 − Φ(x) . La Tavola 2 `e la tavola dei quantili della variabile di Student T(n) : questa tavola permette di trovare direttamente, in funzione dei gradi di libert`a n e del numero α con 0 < α < 1 , il valore del quantile t

. Per la variabile di Student `e stata progettata questa tavole poich`e sono i quantili che vengono utilizzati nella ricerca degli intervalli di fiducia o della regione critica del test di Student, mentre il valore della funzione di ripartizione `e molto meno importante per le applicazioni pratiche. Notiamo tuttavia che questa tavola contiene i quantili per valori di α vicini a 1 (mentre in alcuni test servono per valori piccoli di α , vicini a 0): vale tuttavia quanto `e stato detto per la variabile N(0,1), cio`e poich`e anche la densit`a di Student `e una funzione pari, vale l’eguaglianza

t

= −t

1

La Tavola 3 contiene i quantili della variabile chi-quadro (in fun- zione del numero α con 0 < α < 1 e dei gradi di libert`a n ): il suo uso appare pertanto simile a quello della Tavola dei quantili per la variabile di Student.

C’`e per`o una differenza sostanziale: la densit`a χ

(n) non `e una funzione pari, anzi addirittura `e nulla per valori negativi di x . Di conseguenza non si possono ricavare i quantili con α ≤ 1/2 da quelli con α ≥ 1/2 : per questo motivo tale tavola riporta i quantili χ

per α vicino a 1 e vicino a 0 .

Infine le due Tavole dei quantili della Legge di Fisher riportano, in funzione dei gradi di libert`a (m, n) e limitatamente ad α = 0,95 ed α = 0,99 , i valori dei quantili della legge di Fisher F

. Il suo uso `e simile a quello dei quantili della variabile chi-quadro (anche la densit`a della legge di Fisher

`e eguale a 0 sulla semiretta ¤

−∞, 0 ¤ ).

2

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.50000 0.50399 0.50798 0.51197 0.51595 0.51994 0.52392 0.52790 0.53188 0.53586 0.1 0.53983 0.54380 0.54776 0.55172 0.55567 0.55962 0.56356 0.56749 0.57142 0.57535 0.2 0.57926 0.58317 0.58706 0.59095 0.59483 0.59871 0.60257 0.60642 0.61026 0.61409 0.3 0.61791 0.62172 0.62552 0.62930 0.63307 0.63683 0.64058 0.64431 0.64803 0.65173 0.4 0.65542 0.65910 0.66276 0.66640 0.67003 0.67364 0.67724 0.68082 0.68439 0.68793 0.5 0.69146 0.69497 0.69847 0.70194 0.70540 0.70884 0.71226 0.71566 0.71904 0.72240 0.6 0.72575 0.72907 0.73237 0.73565 0.73891 0.74215 0.74537 0.74857 0.75175 0.75490 0.7 0.75804 0.76115 0.76424 0.76730 0.77035 0.77337 0.77637 0.77935 0.78230 0.78524 0.8 0.78814 0.79103 0.79389 0.79673 0.79955 0.80234 0.80511 0.80785 0.81057 0.81327 0.9 0.81594 0.81859 0.82121 0.82381 0.82639 0.82894 0.83147 0.83398 0.83646 0.83891 1.0 0.84134 0.84375 0.84614 0.84849 0.85083 0.85314 0.85543 0.85769 0.85993 0.86214 1.1 0.86433 0.86650 0.86864 0.87076 0.87286 0.87493 0.87698 0.87900 0.88100 0.88298 1.2 0.88493 0.88686 0.88877 0.89065 0.89251 0.89435 0.89617 0.89796 0.89973 0.90147 1.3 0.90320 0.90490 0.90658 0.90824 0.90988 0.91149 0.91308 0.91466 0.91621 0.91774 1.4 0.91924 0.92073 0.92220 0.92364 0.92507 0.92647 0.92785 0.92922 0.93056 0.93189 1.5 0.93319 0.93448 0.93574 0.93699 0.93822 0.93943 0.94062 0.94179 0.94295 0.94408 1.6 0.94520 0.94630 0.94738 0.94845 0.94950 0.95053 0.95154 0.95254 0.95352 0.95449 1.7 0.95543 0.95637 0.95728 0.95818 0.95907 0.95994 0.96080 0.96164 0.96246 0.96327 1.8 0.96407 0.96485 0.96562 0.96638 0.96712 0.96784 0.96856 0.96926 0.96995 0.97062 1.9 0.97128 0.97193 0.97257 0.97320 0.97381 0.97441 0.97500 0.97558 0.97615 0.97670 2.0 0.97725 0.97778 0.97831 0.97882 0.97932 0.97982 0.98030 0.98077 0.98124 0.98169 2.1 0.98214 0.98257 0.98300 0.98341 0.98382 0.98422 0.98461 0.98500 0.98537 0.98574 2.2 0.98610 0.98645 0.98679 0.98713 0.98745 0.98778 0.98809 0.98840 0.98870 0.98899 2.3 0.98928 0.98956 0.98983 0.99010 0.99036 0.99061 0.99086 0.99111 0.99134 0.99158 2.4 0.99180 0.99202 0.99224 0.99245 0.99266 0.99286 0.99305 0.99324 0.99343 0.99361 2.5 0.99379 0.99396 0.99413 0.99430 0.99446 0.99461 0.99477 0.99492 0.99506 0.99520 2.6 0.99534 0.99547 0.99560 0.99573 0.99585 0.99598 0.99609 0.99621 0.99632 0.99643 2.7 0.99653 0.99664 0.99674 0.99683 0.99693 0.99702 0.99711 0.99720 0.99728 0.99736 2.8 0.99744 0.99752 0.99760 0.99767 0.99774 0.99781 0.99788 0.99795 0.99801 0.99807 2.9 0.99813 0.99819 0.99825 0.99831 0.99836 0.99841 0.99846 0.99851 0.99856 0.99861 3.0 0.99865 0.99869 0.99874 0.99878 0.99882 0.99886 0.99889 0.99893 0.99896 0.99900 3.1 0.99903 0.99906 0.99910 0.99913 0.99916 0.99918 0.99921 0.99924 0.99926 0.99929 3.2 0.99931 0.99934 0.99936 0.99938 0.99940 0.99942 0.99944 0.99946 0.99948 0.99950 3.3 0.99952 0.99953 0.99955 0.99957 0.99958 0.99960 0.99961 0.99962 0.99964 0.99965 3.4 0.99966 0.99968 0.99969 0.99970 0.99971 0.99972 0.99973 0.99974 0.99975 0.99976 3.5 0.99977 0.99978 0.99978 0.99979 0.99980 0.99981 0.99981 0.99982 0.99983 0.99983 3.6 0.99984 0.99985 0.99985 0.99986 0.99986 0.99987 0.99987 0.99988 0.99988 0.99989 3.7 0.99989 0.99990 0.99990 0.99990 0.99991 0.99991 0.99992 0.99992 0.99992 0.99992 3.8 0.99993 0.99993 0.99993 0.99994 0.99994 0.99994 0.99994 0.99995 0.99995 0.99995 3.9 0.99995 0.99995 0.99996 0.99996 0.99996 0.99996 0.99996 0.99996 0.99997 0.99997 4.0 0.99997 0.99997 0.99997 0.99997 0.99997 0.99997 0.99998 0.99998 0.99998 0.99998 4.1 0.99998 0.99998 0.99998 0.99998 0.99998 0.99998 0.99998 0.99998 0.99999 0.99999 4.2 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 4.3 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 4.4 0.99999 0.99999 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000

Tavola della funzione di ripartizione della distribuzione N(0,1)

n 0.75 0.8 0.85 0.9 0.95 0.975 0.99 0.995 0.999 0.9995 1

1.0000 1.3764 1.9626 3.0777 6.3137 12.7062 31.8210 63.6559 318.2888 636.5776

0.8165 1.0607 1.3862 1.8856 2.9200 4.3027 6.9645 9.9250 22.3285 31.5998

0.7649 0.9785 1.2498 1.6377 2.3534 3.1824 4.5407 5.8408 10.2143 12.9244

0.7407 0.9410 1.1896 1.5332 2.1318 2.7765 3.7469 4.6041 7.1729 8.6101

0.7267 0.9195 1.1558 1.4759 2.0150 2.5706 3.3649 4.0321 5.8935 6.8685

0.7176 0.9057 1.1342 1.4398 1.9432 2.4469 3.1427 3.7074 5.2075 5.9587

0.7111 0.8960 1.1192 1.4149 1.8946 2.3646 2.9979 3.4995 4.7853 5.4081

0.7064 0.8889 1.1081 1.3968 1.8595 2.3060 2.8965 3.3554 4.5008 5.0414

0.7027 0.8834 1.0997 1.3830 1.8331 2.2622 2.8214 3.2498 4.2969 4.7809

0.6998 0.8791 1.0931 1.3722 1.8125 2.2281 2.7638 3.1693 4.1437 4.5868

0.6974 0.8755 1.0877 1.3634 1.7959 2.2010 2.7181 3.1058 4.0248 4.4369

0.6955 0.8726 1.0832 1.3562 1.7823 2.1788 2.6810 3.0545 3.9296 4.3178

0.6938 0.8702 1.0795 1.3502 1.7709 2.1604 2.6503 3.0123 3.8520 4.2209

0.6924 0.8681 1.0763 1.3450 1.7613 2.1448 2.6245 2.9768 3.7874 4.1403

0.6912 0.8662 1.0735 1.3406 1.7531 2.1315 2.6025 2.9467 3.7329 4.0728

0.6901 0.8647 1.0711 1.3368 1.7459 2.1199 2.5835 2.9208 3.6861 4.0149

0.6892 0.8633 1.0690 1.3334 1.7396 2.1098 2.5669 2.8982 3.6458 3.9651

0.6884 0.8620 1.0672 1.3304 1.7341 2.1009 2.5524 2.8784 3.6105 3.9217

0.6876 0.8610 1.0655 1.3277 1.7291 2.0930 2.5395 2.8609 3.5793 3.8833

0.6870 0.8600 1.0640 1.3253 1.7247 2.0860 2.5280 2.8453 3.5518 3.8496

0.6864 0.8591 1.0627 1.3232 1.7207 2.0796 2.5176 2.8314 3.5271 3.8193

0.6858 0.8583 1.0614 1.3212 1.7171 2.0739 2.5083 2.8188 3.5050 3.7922

0.6853 0.8575 1.0603 1.3195 1.7139 2.0687 2.4999 2.8073 3.4850 3.7676

0.6848 0.8569 1.0593 1.3178 1.7109 2.0639 2.4922 2.7970 3.4668 3.7454

0.6844 0.8562 1.0584 1.3163 1.7081 2.0595 2.4851 2.7874 3.4502 3.7251

0.6840 0.8557 1.0575 1.3150 1.7056 2.0555 2.4786 2.7787 3.4350 3.7067

0.6837 0.8551 1.0567 1.3137 1.7033 2.0518 2.4727 2.7707 3.4210 3.6895

0.6834 0.8546 1.0560 1.3125 1.7011 2.0484 2.4671 2.7633 3.4082 3.6739

0.6830 0.8542 1.0553 1.3114 1.6991 2.0452 2.4620 2.7564 3.3963 3.6595

0.6828 0.8538 1.0547 1.3104 1.6973 2.0423 2.4573 2.7500 3.3852 3.6460

0.6807 0.8507 1.0500 1.3031 1.6839 2.0211 2.4233 2.7045 3.3069 3.5510

0.6794 0.8489 1.0473 1.2987 1.6759 2.0086 2.4033 2.6778 3.2614 3.4960

0.6786 0.8477 1.0455 1.2958 1.6706 2.0003 2.3901 2.6603 3.2317 3.4602

0.6780 0.8468 1.0442 1.2938 1.6669 1.9944 2.3808 2.6479 3.2108 3.4350

0.6776 0.8461 1.0432 1.2922 1.6641 1.9901 2.3739 2.6387 3.1952 3.4164

0.6772 0.8456 1.0424 1.2910 1.6620 1.9867 2.3685 2.6316 3.1832 3.4019

0.6770 0.8452 1.0418 1.2901 1.6602 1.9840 2.3642 2.6259 3.1738 3.3905

0.6765 0.8446 1.0409 1.2886 1.6576 1.9799 2.3578 2.6174 3.1595 3.3734

0.6762 0.8442 1.0403 1.2876 1.6558 1.9771 2.3533 2.6114 3.1495 3.3613

0.6757 0.8434 1.0391 1.2858 1.6525 1.9719 2.3451 2.6006 3.1315 3.3398

∞ 0.6745 0.8416 1.0364 1.2816 1.6449 1.9600 2.3263 2.5758 3.0902 3.2905

Tavola dei quantili della distribuzione T(n)

Valore della funzione di ripartizione

n0.00050.0010.0050.010.0250.050.10.150.20.250.50.750.80.850.90.950.9750.990.9950.9990.9995 13.929E-071.570E-063.927E-051.571E-049.821E-043.932E-030.01580.03580.06420.10150.45491.32331.64242.07222.70553.84155.02396.63497.879410.827412.1153 29.997E-042.001E-030.01000.02010.05060.10260.21070.32500.44630.57541.38632.77263.21893.79424.60525.99157.37789.210410.596513.815015.2014 30.01530.02430.07170.11480.21580.35180.58440.79781.00521.21252.36604.10834.64165.31706.25147.81479.348411.344912.838116.266017.7311 40.06390.09080.20700.29710.48440.71071.06361.36651.64881.92263.35675.38535.98866.74497.77949.487711.143313.276714.860218.466219.9977 50.15810.21020.41180.55430.83121.14551.61031.99382.34252.67464.35156.62577.28938.11529.236311.070512.832515.086316.749620.514722.1057 60.29940.38100.67570.87211.23731.63542.20412.66133.07013.45465.34817.84088.55819.446110.644612.591614.449416.811918.547522.457524.1016 70.48490.59850.98931.23901.68992.16732.83313.35833.82234.25496.34589.03719.803210.747912.017014.067116.012818.475320.277724.321326.0179 80.71040.85711.34441.64652.17972.73263.48954.07824.59365.07067.344110.218911.030112.027113.361615.507317.534520.090221.954926.123927.8674 90.97181.15191.73492.08792.70043.32514.16824.81655.38015.89888.342811.388712.242113.288014.683716.919019.022821.666023.589327.876729.6669 101.26511.47872.15582.55823.24703.94034.86525.57016.17916.73729.341812.548913.442014.533915.987218.307020.483223.209325.188129.587931.4195 111.58701.83382.60323.05353.81574.57485.57786.33646.98877.584110.341013.700714.631415.767117.275019.675221.920024.725026.756931.263533.1382 121.93452.21413.07383.57064.40385.22606.30387.11387.80738.438411.340314.845415.812016.989318.549321.026123.336726.217028.299732.909234.8211 132.30492.61723.56504.10695.00875.89197.04157.90088.63399.299112.339815.983916.984818.202019.811922.362024.735627.688229.819334.527436.4768 142.69663.04074.07474.66045.62876.57067.78958.69639.467310.165313.339317.116918.150819.406221.064123.684826.118929.141231.319436.123938.1085 153.10733.48254.60095.22946.26217.26098.54689.499310.307011.036514.338918.245119.310720.603022.307124.995827.488430.578032.801537.697839.7173 163.53573.94175.14225.81226.90777.96169.312210.309011.152111.912215.338519.368920.465121.793123.541826.296228.845331.999934.267139.251841.3077 173.98004.41625.69736.40777.56428.671810.085211.124912.002312.791916.338220.488721.614622.977024.769027.587130.191033.408735.718440.791142.8808 184.43914.90486.26487.01498.23079.390410.864911.946212.857013.675317.337921.604922.759524.155525.989428.869331.526434.805237.156442.311944.4337 194.91255.40676.84397.63278.906510.117011.650912.772713.715814.562018.337622.717823.900425.328927.203630.143532.852336.190838.582143.819445.9738 205.39785.92107.43388.26049.590810.850812.442613.603914.578415.451819.337423.827725.037526.497628.412031.410434.169637.566339.996945.314247.4977 215.89546.44678.03368.897210.282911.591313.239614.439315.444616.344420.337224.934826.171127.662029.615132.670635.478938.932241.400946.796349.0096 226.40416.98298.64279.542510.982312.338014.041515.278716.314017.239621.337026.039327.301528.822430.813333.924536.780740.289442.795748.267650.5105 236.92407.52919.260410.195711.688513.090514.848016.121917.186518.137322.336927.141328.428829.979232.006935.172538.075641.638344.181449.727651.9995 247.45288.08479.886210.856312.401113.848415.658716.968618.061819.037323.336728.241229.553331.132533.196236.415039.364142.979845.558451.179053.4776 257.99058.649410.519611.524013.119714.611416.473417.818418.939719.939324.336629.338830.675232.282534.381637.652540.646544.314046.928052.618754.9475 268.53749.222211.160212.198213.843915.379217.291918.671419.820220.843425.336530.434631.794633.429535.563238.885141.923145.641648.289854.051156.4068 279.09299.802911.807712.878514.573416.151418.113919.527220.703021.749426.336331.528432.911734.573636.741240.113343.194546.962849.645055.475157.8556 289.655810.390712.461313.564715.307916.927918.939220.385721.588022.657227.336232.620534.026635.715037.915941.337244.460848.278250.993656.891859.2990 2910.226610.986113.121114.256416.047117.708419.767721.246822.475123.566628.336133.710935.139436.853839.087542.556945.722349.587852.335558.300660.7342 3010.804011.587613.786714.953516.790818.492720.599222.110323.364124.477629.336034.799736.250237.990240.256043.773046.979250.892253.671959.702262.1600 4016.905817.916620.706622.164224.433126.509329.050530.856332.344933.660339.335345.616047.268549.243851.805055.758559.341763.690866.766073.402976.0963 5023.461124.673627.990829.706732.357434.764237.688639.753941.449242.942149.334956.333658.163860.346063.167167.504871.420276.153879.489886.660389.5597 6030.339331.738135.534437.484840.481743.188046.458948.758750.640652.293859.334766.981568.972171.341174.397079.082083.297788.379491.951899.6078102.6971 7037.467139.035843.275345.441748.757551.739355.328957.844359.897861.698369.334577.576679.714782.255385.527090.531395.0231100.4251104.2148112.3167115.5766 8044.791746.519751.171953.540057.153260.391564.277866.993869.207071.144579.334388.130390.405393.105896.5782101.8795106.6285112.3288116.3209124.8389128.2636 9052.276854.155959.196361.754065.646669.126073.291176.195478.558480.624789.334298.6499101.0537103.9040107.5650113.1452118.1359124.1162128.2987137.2082140.7804 10059.894661.918267.327570.065074.221977.929482.358185.440687.945390.133299.3341109.1412111.6667114.6588118.4980124.3421129.5613135.8069140.1697149.4488153.1638 12075.465477.755583.851786.923391.572695.7046100.6236104.0374106.8056109.2197119.3340130.0546132.8063136.0620140.2326146.5673152.2113158.9500163.6485173.6184177.6006 14091.389493.9253100.6547104.0343109.1368113.6594119.0293122.7476125.7580128.3800139.3339150.8941153.8537157.3517161.8270168.6130174.6478181.8405186.8465197.4498201.6804 200140.6591143.8420152.2408156.4321162.7280168.2785174.8353179.3550183.0028186.1717199.3337213.1022216.6088220.7441226.0210233.9942241.0578249.4452255.2638267.5388272.4220

Valore della funzione di ripartizione

Tavola dei quantili della distribuzione χχχχ

(n)

m12345678910111213141516171819202224262830405060708090100120140200∞ 1161.4518.51310.1287.7096.6085.9875.5915.3185.1174.9654.8444.7474.6674.6004.5434.4944.4514.4144.3814.3514.3014.2604.2254.1964.1714.0854.0344.0013.9783.9603.9473.9363.9203.9093.8883.841 2199.5019.0009.5526.9445.7865.1434.7374.4594.2564.1033.9823.8853.8063.7393.6823.6343.5923.5553.5223.4933.4433.4033.3693.3403.3163.2323.1833.1503.1283.1113.0983.0873.0723.0613.0412.996 3215.7119.1649.2776.5915.4094.7574.3474.0663.8633.7083.5873.4903.4113.3443.2873.2393.1973.1603.1273.0983.0493.0092.9752.9472.9222.8392.7902.7582.7362.7192.7062.6962.6802.6692.6502.605 4224.5819.2479.1176.3885.1924.5344.1203.8383.6333.4783.3573.2593.1793.1123.0563.0072.9652.9282.8952.8662.8172.7762.7432.7142.6902.6062.5572.5252.5032.4862.4732.4632.4472.4362.4172.372 5230.1619.2969.0136.2565.0504.3873.9723.6883.4823.3263.2043.1063.0252.9582.9012.8522.8102.7732.7402.7112.6612.6212.5872.5582.5342.4492.4002.3682.3462.3292.3162.3052.2902.2792.2592.214 6233.9919.3298.9416.1634.9504.2843.8663.5813.3743.2173.0952.9962.9152.8482.7902.7412.6992.6612.6282.5992.5492.5082.4742.4452.4212.3362.2862.2542.2312.2142.2012.1912.1752.1642.1442.099 7236.7719.3538.8876.0944.8764.2073.7873.5003.2933.1353.0122.9132.8322.7642.7072.6572.6142.5772.5442.5142.4642.4232.3882.3592.3342.2492.1992.1672.1432.1262.1132.1032.0872.0762.0562.010 8238.8819.3718.8456.0414.8184.1473.7263.4383.2303.0722.9482.8492.7672.6992.6412.5912.5482.5102.4772.4472.3972.3552.3212.2912.2662.1802.1302.0972.0742.0562.0432.0322.0162.0051.9851.938 9240.5419.3858.8125.9994.7724.0993.6773.3883.1793.0202.8962.7962.7142.6462.5882.5382.4942.4562.4232.3932.3422.3002.2652.2362.2112.1242.0732.0402.0171.9991.9861.9751.9591.9471.9271.880 10241.8819.3968.7855.9644.7354.0603.6373.3473.1372.9782.8542.7532.6712.6022.5442.4942.4502.4122.3782.3482.2972.2552.2202.1902.1652.0772.0261.9931.9691.9511.9381.9271.9101.8991.8781.831 11242.9819.4058.7635.9364.7044.0273.6033.3133.1022.9432.8182.7172.6352.5652.5072.4562.4132.3742.3402.3102.2592.2162.1812.1512.1262.0381.9861.9521.9281.9101.8971.8861.8691.8581.8371.789 12243.9019.4128.7455.9124.6784.0003.5753.2843.0732.9132.7882.6872.6042.5342.4752.4252.3812.3422.3082.2782.2262.1832.1482.1182.0922.0031.9521.9171.8931.8751.8611.8501.8341.8221.8011.752 13244.6919.4198.7295.8914.6553.9763.5503.2593.0482.8872.7612.6602.5772.5072.4482.3972.3532.3142.2802.2502.1982.1552.1192.0892.0631.9741.9211.8871.8631.8451.8301.8191.8031.7911.7691.720 14245.3619.4248.7155.8734.6363.9563.5293.2373.0252.8652.7392.6372.5542.4842.4242.3732.3292.2902.2562.2252.1732.1302.0942.0642.0371.9481.8951.8601.8361.8171.8031.7921.7751.7631.7421.692 15245.9519.4298.7035.8584.6193.9383.5113.2183.0062.8452.7192.6172.5332.4632.4032.3522.3082.2692.2342.2032.1512.1082.0722.0412.0151.9241.8711.8361.8121.7931.7791.7681.7501.7381.7171.666 16246.4719.4338.6925.8444.6043.9223.4943.2022.9892.8282.7012.5992.5152.4452.3852.3332.2892.2502.2152.1842.1312.0882.0522.0211.9951.9041.8501.8151.7901.7721.7571.7461.7281.7161.6941.644 17246.9219.4378.6835.8324.5903.9083.4803.1872.9742.8122.6852.5832.4992.4282.3682.3172.2722.2332.1982.1672.1142.0702.0342.0031.9761.8851.8311.7961.7711.7521.7371.7261.7091.6961.6741.623 18247.3219.4408.6755.8214.5793.8963.4673.1732.9602.7982.6712.5682.4842.4132.3532.3022.2572.2172.1822.1512.0982.0542.0181.9871.9601.8681.8141.7781.7531.7341.7201.7081.6901.6781.6561.604 19247.6919.4438.6675.8114.5683.8843.4553.1612.9482.7852.6582.5552.4712.4002.3402.2882.2432.2032.1682.1372.0842.0402.0031.9721.9451.8531.7981.7631.7371.7181.7031.6911.6741.6611.6391.586 20248.0219.4468.6605.8034.5583.8743.4453.1502.9362.7742.6462.5442.4592.3882.3282.2762.2302.1912.1552.1242.0712.0271.9901.9591.9321.8391.7841.7481.7221.7031.6881.6761.6591.6461.6231.571 21248.3119.4488.6545.7954.5493.8653.4353.1402.9262.7642.6362.5332.4482.3772.3162.2642.2192.1792.1442.1122.0592.0151.9781.9461.9191.8261.7711.7351.7091.6891.6751.6631.6451.6321.6091.556 22248.5819.4508.6485.7874.5413.8563.4263.1312.9172.7542.6262.5232.4382.3672.3062.2542.2082.1682.1332.1022.0482.0031.9661.9351.9081.8141.7591.7221.6961.6771.6621.6501.6321.6191.5961.542 23248.8219.4528.6435.7814.5343.8493.4183.1232.9082.7452.6172.5142.4292.3572.2972.2442.1992.1592.1232.0922.0381.9931.9561.9241.8971.8031.7481.7111.6851.6651.6501.6381.6201.6071.5831.529 24249.0519.4548.6385.7744.5273.8413.4103.1152.9002.7372.6092.5052.4202.3492.2882.2352.1902.1502.1142.0822.0281.9841.9461.9151.8871.7931.7371.7001.6741.6541.6391.6271.6081.5951.5721.517 25249.2619.4568.6345.7694.5213.8353.4043.1082.8932.7302.6012.4982.4122.3412.2802.2272.1812.1412.1062.0742.0201.9751.9381.9061.8781.7831.7271.6901.6641.6441.6291.6161.5981.5851.5611.506 26249.4519.4578.6305.7634.5153.8293.3973.1022.8862.7232.5942.4912.4052.3332.2722.2202.1742.1342.0982.0662.0121.9671.9291.8971.8701.7751.7181.6811.6541.6341.6191.6071.5881.5751.5511.496 27249.6319.4598.6265.7594.5103.8233.3913.0952.8802.7162.5882.4842.3982.3262.2652.2122.1672.1262.0902.0592.0041.9591.9211.8891.8621.7661.7101.6721.6461.6261.6101.5981.5791.5661.5421.486 28249.8019.4608.6235.7544.5053.8183.3863.0902.8742.7102.5822.4782.3922.3202.2592.2062.1602.1192.0842.0521.9971.9521.9141.8821.8541.7591.7021.6641.6371.6171.6011.5891.5701.5571.5331.476 29249.9519.4618.6205.7504.5003.8133.3813.0842.8692.7052.5762.4722.3862.3142.2532.2002.1542.1132.0772.0451.9901.9451.9071.8751.8471.7511.6941.6561.6291.6091.5931.5811.5621.5491.5241.467 30250.1019.4638.6175.7464.4963.8083.3763.0792.8642.7002.5702.4662.3802.3082.2472.1942.1482.1072.0712.0391.9841.9391.9011.8691.8411.7441.6871.6491.6221.6021.5861.5731.5541.5411.5161.459 40251.1419.4718.5945.7174.4643.7743.3403.0432.8262.6612.5312.4262.3392.2662.2042.1512.1042.0632.0261.9941.9381.8921.8531.8201.7921.6931.6341.5941.5661.5451.5281.5151.4951.4811.4551.394 50251.7719.4768.5815.6994.4443.7543.3193.0202.8032.6372.5072.4012.3142.2412.1782.1242.0772.0351.9991.9661.9091.8631.8231.7901.7611.6601.5991.5591.5301.5081.4911.4771.4571.4421.4151.350 60252.2019.4798.5725.6884.4313.7403.3043.0052.7872.6212.4902.3842.2972.2232.1602.1062.0582.0171.9801.9461.8891.8421.8031.7691.7401.6371.5761.5341.5051.4821.4651.4501.4291.4141.3861.318 70252.5019.4818.5665.6794.4223.7303.2942.9942.7762.6092.4782.3722.2842.2102.1472.0932.0452.0031.9661.9321.8751.8281.7881.7541.7241.6211.5581.5161.4861.4631.4451.4301.4081.3931.3641.293 80252.7219.4838.5615.6734.4153.7223.2862.9862.7682.6012.4692.3632.2752.2012.1372.0832.0351.9931.9551.9221.8641.8161.7761.7421.7121.6081.5441.5021.4711.4481.4291.4151.3921.3761.3461.273 90252.9019.4858.5575.6684.4093.7163.2802.9802.7612.5942.4622.3562.2672.1932.1302.0752.0271.9851.9471.9131.8561.8081.7671.7331.7031.5971.5341.4911.4591.4361.4171.4021.3791.3631.3321.257 100253.0419.4868.5545.6644.4053.7123.2752.9752.7562.5882.4572.3502.2612.1872.1232.0682.0201.9781.9401.9071.8491.8001.7601.7251.6951.5891.5251.4811.4501.4261.4071.3921.3691.3521.3211.243 120253.2519.4878.5495.6584.3983.7053.2672.9672.7482.5802.4482.3412.2522.1782.1142.0592.0111.9681.9301.8961.8381.7901.7491.7141.6831.5771.5111.4671.4351.4111.3911.3761.3521.3351.3021.221 140253.4119.4898.5465.6544.3943.7003.2622.9612.7422.5742.4422.3352.2462.1712.1072.0522.0041.9611.9231.8891.8301.7821.7411.7061.6751.5671.5021.4571.4241.3991.3801.3641.3401.3221.2891.204 200253.6819.4918.5405.6464.3853.6903.2522.9512.7312.5632.4312.3232.2342.1592.0952.0391.9911.9481.9101.8751.8171.7681.7261.6911.6601.5511.4841.4381.4041.3791.3581.3421.3161.2981.2631.170 ∞254.3119.4968.5265.6284.3653.6693.2302.9282.7072.5382.4042.2962.2062.1312.0662.0101.9601.9171.8781.8431.7831.7331.6911.6541.6221.5091.4381.3891.3531.3251.3021.2831.2541.2321.1891.000

Tavola dei quantili 0.95 della distribuzione F(m,n)