1/26
TABELAS DE ESTATÍSTICA
Valores da Função Distribuição Normal Reduzida
Φ( z ) =
z
-4,4
-4,3
-4,2
-4,1
-4,0
-3,9
-3,8
-3,7
-3,6
-3,5
-3,4
-3,3
-3,2
-3,1
-3,0
-2,9
-2,8
-2,7
-2,6
-2,5
-2,4
-2,3
-2,2
-2,1
-2,0
-1,9
-1,8
-1,7
-1,6
-1,5
-1,4
-1,3
-1,2
-1,1
-1,0
-0,9
-0,8
-0,7
-0,6
-0,5
-0,4
-0,3
-0,2
-0,1
-0,0
0
0,00000
0,00000
0,00001
0,00002
0,00003
0,00005
0,00007
0,00011
0,00016
0,00023
0,00034
0,00048
0,00069
0,00097
0,00135
0,00187
0,00256
0,00347
0,00466
0,00621
0,00820
0,01072
0,01390
0,01786
0,02275
0,02872
0,03593
0,04457
0,05480
0,06681
0,08076
0,09680
0,11507
0,13567
0,15866
0,18406
0,21186
0,24196
0,27425
0,30854
0,34458
0,38209
0,42074
0,46017
0,50000
UA 2003/2004
1
0,00000
0,00000
0,00001
0,00002
0,00003
0,00005
0,00007
0,00010
0,00015
0,00022
0,00032
0,00047
0,00066
0,00094
0,00131
0,00181
0,00248
0,00336
0,00453
0,00604
0,00798
0,01044
0,01355
0,01743
0,02222
0,02807
0,03515
0,04363
0,05370
0,06552
0,07927
0,09510
0,11314
0,13350
0,15625
0,18141
0,20897
0,23885
0,27093
0,30503
0,34090
0,37828
0,41683
0,45620
0,49601
2
0,00000
0,00000
0,00001
0,00002
0,00003
0,00004
0,00007
0,00010
0,00015
0,00022
0,00031
0,00045
0,00064
0,00090
0,00126
0,00175
0,00240
0,00326
0,00440
0,00587
0,00776
0,01017
0,01321
0,01700
0,02169
0,02743
0,03438
0,04272
0,05262
0,06426
0,07780
0,09342
0,11123
0,13136
0,15386
0,17879
0,20611
0,23576
0,26763
0,30153
0,33724
0,37448
0,41294
0,45224
0,49202
∫
z
−∞
3
0,00000
0,00000
0,00001
0,00002
0,00003
0,00004
0,00006
0,00010
0,00014
0,00021
0,00030
0,00043
0,00062
0,00087
0,00122
0,00169
0,00233
0,00317
0,00427
0,00570
0,00755
0,00990
0,01287
0,01659
0,02118
0,02680
0,03362
0,04182
0,05155
0,06301
0,07636
0,09176
0,10935
0,12924
0,15151
0,17619
0,20327
0,23270
0,26435
0,29806
0,33360
0,37070
0,40905
0,44828
0,48803
2
1
e − u 2 d u = P( Z ≤ z )
2π
4
0,00000
0,00000
0,00001
0,00002
0,00003
0,00004
0,00006
0,00009
0,00014
0,00020
0,00029
0,00042
0,00060
0,00084
0,00118
0,00164
0,00226
0,00307
0,00415
0,00554
0,00734
0,00964
0,01255
0,01618
0,02068
0,02619
0,03288
0,04093
0,05050
0,06178
0,07493
0,09012
0,10749
0,12714
0,14917
0,17361
0,20045
0,22965
0,26109
0,29460
0,32997
0,36693
0,40517
0,44433
0,48405
5
0,00000
0,00000
0,00001
0,00002
0,00003
0,00004
0,00006
0,00009
0,00013
0,00019
0,00028
0,00040
0,00058
0,00082
0,00114
0,00159
0,00219
0,00298
0,00402
0,00539
0,00714
0,00939
0,01222
0,01578
0,02018
0,02559
0,03216
0,04006
0,04947
0,06057
0,07353
0,08851
0,10565
0,12507
0,14686
0,17106
0,19766
0,22663
0,25785
0,29116
0,32636
0,36317
0,40129
0,44038
0,48006
6
0,00000
0,00000
0,00001
0,00002
0,00002
0,00004
0,00006
0,00008
0,00013
0,00019
0,00027
0,00039
0,00056
0,00079
0,00111
0,00154
0,00212
0,00289
0,00391
0,00523
0,00695
0,00914
0,01191
0,01539
0,01970
0,02500
0,03144
0,03920
0,04846
0,05938
0,07215
0,08692
0,10383
0,12302
0,14457
0,16853
0,19489
0,22363
0,25463
0,28774
0,32276
0,35942
0,39743
0,43644
0,47608
7
0,00000
0,00000
0,00000
0,00002
0,00002
0,00004
0,00005
0,00008
0,00012
0,00018
0,00026
0,00038
0,00054
0,00076
0,00107
0,00149
0,00205
0,00280
0,00379
0,00508
0,00676
0,00889
0,01160
0,01500
0,01923
0,02442
0,03074
0,03836
0,04746
0,05821
0,07078
0,08534
0,10204
0,12100
0,14231
0,16602
0,19215
0,22065
0,25143
0,28434
0,31918
0,35569
0,39358
0,43251
0,47210
8
0,00000
0,00000
0,00000
0,00001
0,00002
0,00003
0,00005
0,00008
0,00012
0,00017
0,00025
0,00036
0,00052
0,00074
0,00104
0,00144
0,00199
0,00272
0,00368
0,00494
0,00657
0,00866
0,01130
0,01463
0,01876
0,02385
0,03005
0,03754
0,04648
0,05705
0,06944
0,08379
0,10027
0,11900
0,14007
0,16354
0,18943
0,21770
0,24825
0,28096
0,31561
0,35197
0,38974
0,42858
0,46812
9
0,00000
0,00000
0,00000
0,00001
0,00002
0,00003
0,00005
0,00008
0,00011
0,00017
0,00024
0,00035
0,00050
0,00071
0,00100
0,00139
0,00193
0,00264
0,00357
0,00480
0,00639
0,00842
0,01101
0,01426
0,01831
0,02330
0,02938
0,03673
0,04551
0,05592
0,06811
0,08226
0,09853
0,11702
0,13786
0,16109
0,18673
0,21476
0,24510
0,27760
0,31207
0,34827
0,38591
0,42465
0,46414
CMM
2/26
TABELAS DE ESTATÍSTICA
Valores da Função Distribuição Normal Reduzida - Continuação
Φ( z ) =
z
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
1,1
1,2
1,3
1,4
1,5
1,6
1,7
1,8
1,9
2,0
2,1
2,2
2,3
2,4
2,5
2,6
2,7
2,8
2,9
3,0
3,1
3,2
3,3
3,4
3,5
3,6
3,7
3,8
3,9
4,0
4,1
4,2
4,3
4,4
0
0,50000
0,53983
0,57926
0,61791
0,65542
0,69146
0,72575
0,75804
0,78814
0,81594
0,84134
0,86433
0,88493
0,90320
0,91924
0,93319
0,94520
0,95543
0,96407
0,97128
0,97725
0,98214
0,98610
0,98928
0,99180
0,99379
0,99534
0,99653
0,99744
0,99813
0,99865
0,99903
0,99931
0,99952
0,99966
0,99977
0,99984
0,99989
0,99993
0,99995
0,99997
0,99998
0,99999
0,99999
0,99999
UA 2003/2004
1
0,50399
0,54380
0,58317
0,62172
0,65910
0,69497
0,72907
0,76115
0,79103
0,81859
0,84375
0,86650
0,88686
0,90490
0,92073
0,93448
0,94630
0,95637
0,96485
0,97193
0,97778
0,98257
0,98645
0,98956
0,99202
0,99396
0,99547
0,99664
0,99752
0,99819
0,99869
0,99906
0,99934
0,99953
0,99968
0,99978
0,99985
0,99990
0,99993
0,99995
0,99997
0,99998
0,99999
0,99999
0,99999
2
0,50798
0,54776
0,58706
0,62552
0,66276
0,69847
0,73237
0,76424
0,79389
0,82121
0,84614
0,86864
0,88877
0,90658
0,92220
0,93574
0,94738
0,95728
0,96562
0,97257
0,97831
0,98300
0,98679
0,98983
0,99224
0,99413
0,99560
0,99674
0,99760
0,99825
0,99874
0,99910
0,99936
0,99955
0,99969
0,99978
0,99985
0,99990
0,99993
0,99996
0,99997
0,99998
0,99999
0,99999
1,00000
∫
z
−∞
3
0,51197
0,55172
0,59095
0,62930
0,66640
0,70194
0,73565
0,76730
0,79673
0,82381
0,84849
0,87076
0,89065
0,90824
0,92364
0,93699
0,94845
0,95818
0,96638
0,97320
0,97882
0,98341
0,98713
0,99010
0,99245
0,99430
0,99573
0,99683
0,99767
0,99831
0,99878
0,99913
0,99938
0,99957
0,99970
0,99979
0,99986
0,99990
0,99994
0,99996
0,99997
0,99998
0,99999
0,99999
1,00000
2
1
e − u 2 d u = P( Z ≤ z )
2π
4
0,51595
0,55567
0,59483
0,63307
0,67003
0,70540
0,73891
0,77035
0,79955
0,82639
0,85083
0,87286
0,89251
0,90988
0,92507
0,93822
0,94950
0,95907
0,96712
0,97381
0,97932
0,98382
0,98745
0,99036
0,99266
0,99446
0,99585
0,99693
0,99774
0,99836
0,99882
0,99916
0,99940
0,99958
0,99971
0,99980
0,99986
0,99991
0,99994
0,99996
0,99997
0,99998
0,99999
0,99999
1,00000
5
0,51994
0,55962
0,59871
0,63683
0,67364
0,70884
0,74215
0,77337
0,80234
0,82894
0,85314
0,87493
0,89435
0,91149
0,92647
0,93943
0,95053
0,95994
0,96784
0,97441
0,97982
0,98422
0,98778
0,99061
0,99286
0,99461
0,99598
0,99702
0,99781
0,99841
0,99886
0,99918
0,99942
0,99960
0,99972
0,99981
0,99987
0,99991
0,99994
0,99996
0,99997
0,99998
0,99999
0,99999
1,00000
6
0,52392
0,56356
0,60257
0,64058
0,67724
0,71226
0,74537
0,77637
0,80511
0,83147
0,85543
0,87698
0,89617
0,91308
0,92785
0,94062
0,95154
0,96080
0,96856
0,97500
0,98030
0,98461
0,98809
0,99086
0,99305
0,99477
0,99609
0,99711
0,99788
0,99846
0,99889
0,99921
0,99944
0,99961
0,99973
0,99981
0,99987
0,99992
0,99994
0,99996
0,99998
0,99998
0,99999
0,99999
1,00000
7
0,52790
0,56749
0,60642
0,64431
0,68082
0,71566
0,74857
0,77935
0,80785
0,83398
0,85769
0,87900
0,89796
0,91466
0,92922
0,94179
0,95254
0,96164
0,96926
0,97558
0,98077
0,98500
0,98840
0,99111
0,99324
0,99492
0,99621
0,99720
0,99795
0,99851
0,99893
0,99924
0,99946
0,99962
0,99974
0,99982
0,99988
0,99992
0,99995
0,99996
0,99998
0,99998
0,99999
0,99999
1,00000
8
0,53188
0,57142
0,61026
0,64803
0,68439
0,71904
0,75175
0,78230
0,81057
0,83646
0,85993
0,88100
0,89973
0,91621
0,93056
0,94295
0,95352
0,96246
0,96995
0,97615
0,98124
0,98537
0,98870
0,99134
0,99343
0,99506
0,99632
0,99728
0,99801
0,99856
0,99896
0,99926
0,99948
0,99964
0,99975
0,99983
0,99988
0,99992
0,99995
0,99997
0,99998
0,99999
0,99999
0,99999
1,00000
9
0,53586
0,57535
0,61409
0,65173
0,68793
0,72240
0,75490
0,78524
0,81327
0,83891
0,86214
0,88298
0,90147
0,91774
0,93189
0,94408
0,95449
0,96327
0,97062
0,97670
0,98169
0,98574
0,98899
0,99158
0,99361
0,99520
0,99643
0,99736
0,99807
0,99861
0,99900
0,99929
0,99950
0,99965
0,99976
0,99983
0,99989
0,99992
0,99995
0,99997
0,99998
0,99999
0,99999
0,99999
1,00000
CMM
3/26
TABELAS DE ESTATÍSTICA
Valores da Função Distribuição T de Student
G.l.
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
31
32
33
34
35
36
37
38
39
40
50
60
70
80
90
100
110
120
∞
UA 2003/2004
t0,95
6,31375
2,91999
2,35336
2,13185
2,01505
1,94318
1,89458
1,85955
1,83311
1,81246
1,79588
1,78229
1,77093
1,76131
1,75305
1,74588
1,73961
1,73406
1,72913
1,72472
1,72074
1,71714
1,71387
1,71088
1,70814
1,70562
1,70329
1,70113
1,69913
1,69726
1,69552
1,69389
1,69236
1,69092
1,68957
1,68830
1,68709
1,68595
1,68488
1,68385
1,67591
1,67065
1,66692
1,66413
1,66196
1,66023
1,65882
1,65765
1,64485
t0,975
12,70615
4,30266
3,18245
2,77645
2,57058
2,44691
2,36462
2,30601
2,26216
2,22814
2,20099
2,17881
2,16037
2,14479
2,13145
2,11990
2,10982
2,10092
2,09302
2,08596
2,07961
2,07388
2,06865
2,06390
2,05954
2,05553
2,05183
2,04841
2,04523
2,04227
2,03951
2,03693
2,03452
2,03224
2,03011
2,02809
2,02619
2,02439
2,02269
2,02107
2,00856
2,00030
1,99444
1,99007
1,98667
1,98397
1,98177
1,97993
1,95996
t0,9875
25,45188
6,20537
4,17655
3,49541
3,16339
2,96868
2,84124
2,75153
2,68501
2,63377
2,59310
2,56003
2,53263
2,50957
2,48988
2,47288
2,45805
2,44500
2,43344
2,42311
2,41384
2,40547
2,39787
2,39095
2,38461
2,37878
2,37342
2,36845
2,36385
2,35957
2,35557
2,35184
2,34833
2,34506
2,34197
2,33906
2,33632
2,33372
2,33126
2,32893
2,31092
2,29905
2,29064
2,28437
2,27952
2,27566
2,27250
2,26987
2,24140
T0,99
31,82096
6,96455
4,54071
3,74694
3,36493
3,14267
2,99795
2,89647
2,82143
2,76377
2,71808
2,68099
2,65030
2,62449
2,60248
2,58349
2,56694
2,55238
2,53948
2,52798
2,51765
2,50832
2,49987
2,49216
2,48510
2,47863
2,47266
2,46714
2,46202
2,45726
2,45283
2,44868
2,44479
2,44115
2,43772
2,43450
2,43144
2,42857
2,42584
2,42326
2,40327
2,39012
2,38080
2,37387
2,36850
2,36421
2,36072
2,35783
2,32634
t0,995
63,65590
9,92499
5,84085
4,60408
4,03212
3,70743
3,49948
3,35538
3,24984
3,16926
3,10582
3,05454
3,01228
2,97685
2,94673
2,92079
2,89823
2,87844
2,86094
2,84534
2,83137
2,81876
2,80734
2,79695
2,78744
2,77872
2,77068
2,76326
2,75639
2,74998
2,74404
2,73849
2,73329
2,72839
2,72381
2,71948
2,71541
2,71157
2,70791
2,70446
2,67779
2,66027
2,64790
2,63870
2,63157
2,62589
2,62127
2,61742
2,57583
t0,999
318,28880
22,32846
10,21428
7,17293
5,89353
5,20755
4,78525
4,50076
4,29689
4,14366
4,02477
3,92960
3,85204
3,78743
3,73286
3,68615
3,64576
3,61048
3,57933
3,55183
3,52709
3,50497
3,48497
3,46678
3,45019
3,43498
3,42101
3,40820
3,39627
3,38521
3,37488
3,36528
3,35633
3,34796
3,34003
3,33261
3,32562
3,31900
3,31274
3,30692
3,26138
3,23169
3,21081
3,19524
3,18323
3,17377
3,16599
3,15951
3,09024
t0,9995
636,57761
31,59977
12,92443
8,61008
6,86850
5,95872
5,40807
5,04137
4,78089
4,58676
4,43688
4,31784
4,22093
4,14031
4,07279
4,01487
3,96511
3,92174
3,88332
3,84956
3,81930
3,79223
3,76764
3,74537
3,72514
3,70666
3,68949
3,67392
3,65952
3,64598
3,63347
3,62183
3,61091
3,60073
3,59112
3,58210
3,57366
3,56566
3,55809
3,55096
3,49595
3,46015
3,43498
3,41635
3,40195
3,39045
3,38114
3,37342
3,29048
CMM
4/26
TABELAS DE ESTATÍSTICA
Valores da Função Distribuição de Qui - Quadrado
G.l.
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
50
60
zp
0,001
0,0000
0,0020
0,0243
0,0908
0,2102
0,3810
0,5985
0,8571
1,1519
1,4787
1,8338
2,2141
2,6172
3,0407
3,4825
3,9417
4,4162
4,9048
5,4067
5,9210
6,4467
6,9829
7,5291
8,0847
8,6494
9,2222
9,8029
10,3907
10,9861
11,5876
17,9166
24,6736
31,7381
-3,0902
0,005
0,0000
0,0100
0,0717
0,2070
0,4118
0,6757
0,9893
1,3444
1,7349
2,1558
2,6032
3,0738
3,5650
4,0747
4,6009
5,1422
5,6973
6,2648
6,8439
7,4338
8,0336
8,6427
9,2604
9,8862
10,5196
11,1602
11,8077
12,4613
13,1211
13,7867
20,7066
27,9908
35,5344
-2,5758
0,01
0,0002
0,0201
0,1148
0,2971
0,5543
0,8721
1,2390
1,6465
2,0879
2,5582
3,0535
3,5706
4,1069
4,6604
5,2294
5,8122
6,4077
7,0149
7,6327
8,2604
8,8972
9,5425
10,1957
10,8563
11,5240
12,1982
12,8785
13,5647
14,2564
14,9535
22,1642
29,7067
37,4848
-2,3263
0,025
0,0010
0,0506
0,2158
0,4844
0,8312
1,2373
1,6899
2,1797
2,7004
3,2470
3,8157
4,4038
5,0087
5,6287
6,2621
6,9077
7,5642
8,2307
8,9065
9,5908
10,2829
10,9823
11,6885
12,4011
13,1197
13,8439
14,5734
15,3079
16,0471
16,7908
24,4331
32,3574
40,4817
-1,9600
Nota : Para graus de liberdade k > 30 use : χ 2k ; p =
0,05
0,0039
0,1026
0,3518
0,7107
1,1455
1,6354
2,1673
2,7326
3,3251
3,9403
4,5748
5,2260
5,8919
6,5706
7,2609
7,9616
8,6718
9,3904
10,1170
10,8508
11,5913
12,3380
13,0905
13,8484
14,6114
15,3792
16,1514
16,9279
17,7084
18,4927
26,5093
34,7642
43,1880
-1,6449
(
0,1
0,0158
0,2107
0,5844
1,0636
1,6103
2,2041
2,8331
3,4895
4,1682
4,8652
5,5778
6,3038
7,0415
7,7895
8,5468
9,3122
10,0852
10,8649
11,6509
12,4426
13,2396
14,0415
14,8480
15,6587
16,4734
17,2919
18,1139
18,9392
19,7677
20,5992
29,0505
37,6886
46,4589
-1,2816
1
z + 2 k −1
2 p
)
0,2
0,0642
0,4463
1,0052
1,6488
2,3425
3,0701
3,8223
4,5936
5,3801
6,1791
6,9887
7,8073
8,6339
9,4673
10,3070
11,1521
12,0023
12,8570
13,7158
14,5784
15,4446
16,3140
17,1865
18,0618
18,9397
19,8202
20,7030
21,5880
22,4751
23,3641
32,3449
41,4492
50,6406
-0,8416
0,3
0,1485
0,7133
1,4237
2,1947
2,9999
3,8276
4,6713
5,5274
6,3933
7,2672
8,1479
9,0343
9,9257
10,8215
11,7212
12,6243
13,5307
14,4399
15,3517
16,2659
17,1823
18,1007
19,0211
19,9432
20,8670
21,7924
22,7192
23,6475
24,5770
25,5078
34,8719
44,3133
53,8091
-0,5244
0,5
0,4549
1,3863
2,3660
3,3567
4,3515
5,3481
6,3458
7,3441
8,3428
9,3418
10,3410
11,3403
12,3398
13,3393
14,3389
15,3385
16,3382
17,3379
18,3376
19,3374
20,3372
21,3370
22,3369
23,3367
24,3366
25,3365
26,3363
27,3362
28,3361
29,3360
39,3353
49,3349
59,3347
0,0000
2
onde z p é um valor da
distribuição Normal Reduzida
UA 2003/2004
CMM
5/26
TABELAS DE ESTATÍSTICA
Valores da Função Distribuição de Qui - Quadrado - Continuação
G.l.
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
50
60
zp
0,7
1,0742
2,4079
3,6649
4,8784
6,0644
7,2311
8,3834
9,5245
10,6564
11,7807
12,8987
14,0111
15,1187
16,2221
17,3217
18,4179
19,5110
20,6014
21,6891
22,7745
23,8578
24,9390
26,0184
27,0960
28,1719
29,2463
30,3193
31,3909
32,4612
33,5302
44,1649
54,7228
65,2265
0,5244
0,8
1,6424
3,2189
4,6416
5,9886
7,2893
8,5581
9,8032
11,0301
12,2421
13,4420
14,6314
15,8120
16,9848
18,1508
19,3107
20,4651
21,6146
22,7595
23,9004
25,0375
26,1711
27,3015
28,4288
29,5533
30,6752
31,7946
32,9117
34,0266
35,1394
36,2502
47,2685
58,1638
68,9721
0,8416
0,9
2,7055
4,6052
6,2514
7,7794
9,2363
10,6446
12,0170
13,3616
14,6837
15,9872
17,2750
18,5493
19,8119
21,0641
22,3071
23,5418
24,7690
25,9894
27,2036
28,4120
29,6151
30,8133
32,0069
33,1962
34,3816
35,5632
36,7412
37,9159
39,0875
40,2560
51,8050
63,1671
74,3970
1,2816
0,95
3,8415
5,9915
7,8147
9,4877
11,0705
12,5916
14,0671
15,5073
16,9190
18,3070
19,6752
21,0261
22,3620
23,6848
24,9958
26,2962
27,5871
28,8693
30,1435
31,4104
32,6706
33,9245
35,1725
36,4150
37,6525
38,8851
40,1133
41,3372
42,5569
43,7730
55,7585
67,5048
79,0820
1,6449
Nota : Para graus de liberdade k > 30 use : χ 2k ; p =
0,975
5,0239
7,3778
9,3484
11,1433
12,8325
14,4494
16,0128
17,5345
19,0228
20,4832
21,9200
23,3367
24,7356
26,1189
27,4884
28,8453
30,1910
31,5264
32,8523
34,1696
35,4789
36,7807
38,0756
39,3641
40,6465
41,9231
43,1945
44,4608
45,7223
46,9792
59,3417
71,4202
83,2977
1,9600
(
0,99
6,6349
9,2104
11,3449
13,2767
15,0863
16,8119
18,4753
20,0902
21,6660
23,2093
24,7250
26,2170
27,6882
29,1412
30,5780
31,9999
33,4087
34,8052
36,1908
37,5663
38,9322
40,2894
41,6383
42,9798
44,3140
45,6416
46,9628
48,2782
49,5878
50,8922
63,6908
76,1538
88,3794
2,3263
1
z + 2 k −1
2 p
)
0,995
7,8794
10,5965
12,8381
14,8602
16,7496
18,5475
20,2777
21,9549
23,5893
25,1881
26,7569
28,2997
29,8193
31,3194
32,8015
34,2671
35,7184
37,1564
38,5821
39,9969
41,4009
42,7957
44,1814
45,5584
46,9280
48,2898
49,6450
50,9936
52,3355
53,6719
66,7660
79,4898
91,9518
2,5758
0,999
10,8274
13,8150
16,2660
18,4662
20,5147
22,4575
24,3213
26,1239
27,8767
29,5879
31,2635
32,9092
34,5274
36,1239
37,6978
39,2518
40,7911
42,3119
43,8194
45,3142
46,7963
48,2676
49,7276
51,1790
52,6187
54,0511
55,4751
56,8918
58,3006
59,7022
73,4029
86,6603
99,6078
3,0902
2
onde z p é um valor da
distribuição Normal Reduzida
UA 2003/2004
CMM
6/26
TABELAS DE ESTATÍSTICA
Quantis da Estatística de Teste de Kolmogorov (Tabela A14)
n
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0,80
0,900
0,684
0,565
0,493
0,447
0,410
0,381
0,358
0,339
0,323
0,308
0,296
0,285
0,275
0,266
0,258
0,250
0,244
0,237
0,232
0,90
0,950
0,776
0,636
0,565
0,509
0,468
0,436
0,410
0,387
0,369
0,352
0,338
0,325
0,314
0,304
0,295
0,286
0,279
0,271
0,265
p
0,95
0,975
0,842
0,708
0,624
0,563
0,519
0,483
0,454
0,430
0,409
0,391
0,375
0,361
0,349
0,338
0,327
0,318
0,309
0,301
0,294
0,98
0,990
0,900
0,785
0,689
0,627
0,577
0,538
0,507
0,480
0,457
0,437
0,419
0,404
0,390
0,377
0,366
0,355
0,346
0,337
0,329
0,99
0,995
0,929
0,829
0,734
0,669
0,617
0,576
0,542
0,513
0,489
0,468
0,449
0,432
0,418
0,404
0,392
0,381
0,371
0,361
0,352
n
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
0,80
0,226
0,221
0,216
0,212
0,208
0,204
0,200
0,197
0,193
0,190
0,187
0,184
0,182
0,179
0,177
0,174
0,172
0,170
0,168
0,165
1,07
> 40
n
0,90
0,259
0,253
0,247
0,242
0,238
0,233
0,229
0,225
0,221
0,218
0,214
0,211
0,208
0,205
0,202
0,199
0,196
0,194
0,191
0,189
1,22
n
p
0,95
0,287
0,281
0,275
0,269
0,264
0,259
0,254
0,250
0,246
0,242
0,238
0,234
0,231
0,227
0,224
0,221
0,218
0,215
0,130
0,210
1,36
n
0,98
0,321
0,314
0,307
0,301
0,295
0,290
0,284
0,279
0,275
0,270
0,266
0,262
0,258
0,254
0,251
0,247
0,244
0,241
0,238
0,235
1,52
n
0,99
0,344
0,337
0,330
0,323
0,317
0,311
0,305
0,300
0,295
0,290
0,285
0,281
0,277
0,273
0,269
0,265
0,262
0,258
0,255
0,252
1,63
n
Fonte : Adaptada da Tabela de Miller (1956)

n 
Nota : Uma melhor aproximação para n > 40 resulta se  n +

10 

UA 2003/2004
12
for usada em vez de
n
CMM
7/26
TABELAS DE ESTATÍSTICA
Quantis da Estatística de Teste de Lilliefors para a Normal (Tabela A15)
n
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25
30
> 30
0,80
0,300
0,285
0,265
0,247
0,233
0,223
0,215
0,206
0,199
0,190
0,183
0,177
0,173
0,169
0,166
0,163
0,160
0,142
0,131
0,736
n
0,85
0,319
0,299
0,277
0,258
0,244
0,233
0,224
0,217
0,212
0,202
0,194
0,187
0,182
0,177
0,173
0,169
0,166
0,147
0,136
0,768
n
p
0,90
0,352
0,315
0,294
0,276
0,261
0,249
0,239
0,230
0,223
0,214
0,207
0,201
0,195
0,189
0,184
0,179
0,174
0,158
0,144
0,805
n
0,95
0,381
0,337
0,319
0,300
0,285
0,271
0,258
0,249
0,242
0,234
0,227
0,220
0,213
0,206
0,200
0,195
0,190
0,173
0,161
0,886
n
0,99
0,417
0,405
0,364
0,348
0,331
0,311
0,294
0,284
0,275
0,268
0,261
0,257
0,250
0,245
0,239
0,235
0,231
0,200
0,187
1,031
n
Fonte : Adaptada da Tabela I de Lilliefors (1967), com correcções.
UA 2003/2004
CMM
8/26
TABELAS DE ESTATÍSTICA
Quantis da Estatística de Teste de Lilliefors para a Exponencial (Tabela A16)
n
2
3
4
5
6
7
8
9
10
12
14
16
18
20
22
24
26
28
30
35
40
45
50
60
70
80
90
100
> 100
0,80
0,5507
0,4508
0,4007
0,3603
0,3320
0,3098
0,2914
0,2758
0,2626
0,2411
0,2242
0,2105
0,1990
0,1893
0,1809
0,1735
0,1670
0,1611
0,1559
0,1447
0,1356
0,1281
0,1217
0,1114
0,1033
0,0968
0,0914
0,0868
0,8678
n
0,90
0,5934
0,5111
0,4442
0,4045
0,3732
0,3481
0,3274
0,3101
0,2955
0,2714
0,2525
0,2371
0,2242
0,2132
0,2038
0,1954
0,1881
0,1815
0,1756
0,1630
0,1528
0,1443
0,1371
0,1255
0,1164
0,1090
0,1029
0,0977
0,9773
n
p
0,95
0,6133
0,5508
0,4844
0,4420
0,4080
0,3811
0,3590
0,3404
0,3244
0,2681
0,2774
0,2606
0,2465
0,2345
0,2241
0,2150
0,2069
0,1997
0,1932
0,1793
0,1681
0,1588
0,1509
0,1381
0,1281
0,1200
0,1132
0,1075
1,0753
n
0,99
0,6284
0,6003
0,5574
0,5127
0,4746
0,4459
0,4208
0,3995
0,3813
0,3511
0,3272
0,3076
0,2911
0,2771
0,2649
0,2542
0,2447
0,2362
0,2286
0,2123
0,1990
0,1880
0,1787
0,1635
0,1517
0,1421
0,1341
0,1274
1,2743
n
0,999
0,6317
0,6296
0,6215
0,5811
0,5497
0,5181
0,4913
0,4679
0,4473
0,4132
0,3858
0,3632
0,3441
0,3277
0,3135
0,3010
0,2899
0,2799
0,2709
0,2517
0,2361
0,2231
0,2121
0,1943
b
b
b
b
b
Fonte : Adaptada de Durbin (1975)
b - Estes quantis não estão disponíveis presentemente
UA 2003/2004
CMM
9/26
TABELAS DE ESTATÍSTICA
Valores Críticos das Distribuição Fmáx
α = 5%
n0-1
2
3
4
5
6
7
8
9
10
12
15
20
30
60
∞
2
39,00
15,40
9,60
7,15
5,82
4,99
4,43
4,03
3,72
3,28
2,86
2,46
2,07
1,67
1,00
3
4
5
87,50 142,00 202,00
27,80 39,20 50,70
15,50 20,60 25,20
10,80 13,70 16,30
8,38 10,40 12,10
6,94
8,44
9,70
6,00
7,18
8,12
5,34
6,31
7,11
4,85
5,67
6,34
4,16
4,79
5,30
3,54
4,01
4,37
2,95
3,29
3,54
2,40
2,61
2,78
1,85
1,96
2,04
1,00
1,00
1,00
6
266,00
62,00
25,50
18,70
13,70
10,80
9,03
7,80
6,92
5,72
4,68
3,76
2,91
2,11
1,00
k
7
333,00
72,90
33,60
20,80
15,00
11,80
9,78
8,41
7,42
6,09
4,95
3,94
3,02
2,17
1,00
8
407,00
83,50
37,50
22,90
16,30
12,70
10,50
8,95
7,87
6,42
5,19
4,10
3,12
2,22
1,00
9
407,00
93,60
41,10
24,70
17,50
13,50
11,10
9,45
8,28
6,72
5,40
4,24
3,21
2,26
1,00
10
550,00
104,00
44,60
26,50
18,60
14,30
11,70
9,91
8,66
7,00
5,59
4,37
3,29
2,30
1,00
11
626,00
114,00
48,00
28,20
19,70
15,10
12,20
10,30
9,01
7,25
5,77
4,49
3,36
2,33
1,00
12
704,00
124,00
51,40
29,90
10,70
15,80
12,70
10,70
9,34
7,48
5,93
4,59
3,39
2,36
1,00
α = 1%
k
n0-1
2
3
4
5
6
7
8
9
10
11
12
199
448
729
1036
1362
1705
2063
2432
2813
3204
3605
2
3 47,50 85,00 120,00 151,00 184,00 216,00 249,00 281,00 310,00 337,00 361,00
4 23,20 37,00 49,00 59,00 69,00 79,00 89,00 97,00 106,00 113,00 120,00
5 14,90 22,00 28,00 33,00 38,00 42,00 46,00 50,00 54,00 57,00 60,00
6 11,10 15,50 19,10 22,00 25,00 27,00 30,00 32,00 34,00 36,00 37,00
8,89 12,10 14,50 16,50 18,40 20,00 22,00 23,00 24,00 26,00 27,00
7
7,50 9,90 11,70 13,20 14,50 15,80 16,90 17,90 18,90 19,90 21,00
8
6,54 8,50
9,90
11,10 12,10 13,10 13,90 14,70 15,30 16,00 16,60
9
8,60
9,60
10,40 11,10 11,80 12,40 12,90 13,40 13,90
10 5,85 7,40
6,90
7,60
8,20
8,70
9,10
9,50
9,90
10,20 10,60
12 4,91 6,10
5,50
6,00
6,40
6,70
7,10
7,30
7,50
7,80
8,00
15 4,07 4,90
4,30
4,60
4,90
5,10
5,30
5,50
5,60
5,80
5,90
20 3,32 3,80
3,30
3,40
3,60
3,70
3,80
3,90
4,00
4,10
4,20
30 2,63 3,00
2,30
2,40
2,40
2,50
2,50
2,60
2,60
2,70
2,70
60 1,96 2,20
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
∞ 1,00 1,00
UA 2003/2004
CMM
10/26
TABELAS DE ESTATÍSTICA
Valores Críticos da Distribuição de Fisher - Snedecor
α = 5%
G
r
a
u
s
d
e
L
i
b
e
r
d
a
d
e
d
o
D
e
n
o
m
i
n
a
d
o
r
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
50
60
70
80
90
100
110
120
∞
1
161,446
18,513
10,128
7,709
6,608
5,987
5,591
5,318
5,117
4,965
4,844
4,747
4,667
4,600
4,543
4,494
4,451
4,414
4,381
4,351
4,325
4,301
4,279
4,260
4,242
4,225
4,210
4,196
4,183
4,171
4,085
4,034
4,001
3,978
3,960
3,947
3,936
3,927
3,920
3,842
UA 2003/2004
2
199,499
19,000
9,552
6,944
5,786
5,143
4,737
4,459
4,256
4,103
3,982
3,885
3,806
3,739
3,682
3,634
3,592
3,555
3,522
3,493
3,467
3,443
3,422
3,403
3,385
3,369
3,354
3,340
3,328
3,316
3,232
3,183
3,150
3,128
3,111
3,098
3,087
3,079
3,072
2,997
Graus de Liberdade do Numerador
3
4
5
6
7
8
215,707 224,583 230,160 233,988 236,767 238,884
19,164 19,247 19,296 19,329 19,353 19,371
9,277 9,117 9,013 8,941 8,887 8,845
6,591 6,388 6,256 6,163 6,094 6,041
5,409 5,192 5,050 4,950 4,876 4,818
4,757 4,534 4,387 4,284 4,207 4,147
4,347 4,120 3,972 3,866 3,787 3,726
4,066 3,838 3,688 3,581 3,500 3,438
3,863 3,633 3,482 3,374 3,293 3,230
3,708 3,478 3,326 3,217 3,135 3,072
3,587 3,357 3,204 3,095 3,012 2,948
3,490 3,259 3,106 2,996 2,913 2,849
3,411 3,179 3,025 2,915 2,832 2,767
3,344 3,112 2,958 2,848 2,764 2,699
3,287 3,056 2,901 2,790 2,707 2,641
3,239 3,007 2,852 2,741 2,657 2,591
3,197 2,965 2,810 2,699 2,614 2,548
3,160 2,928 2,773 2,661 2,577 2,510
3,127 2,895 2,740 2,628 2,544 2,477
3,098 2,866 2,711 2,599 2,514 2,447
3,072 2,840 2,685 2,573 2,488 2,420
3,049 2,817 2,661 2,549 2,464 2,397
3,028 2,796 2,640 2,528 2,442 2,375
3,009 2,776 2,621 2,508 2,423 2,355
2,991 2,759 2,603 2,490 2,405 2,337
2,975 2,743 2,587 2,474 2,388 2,321
2,960 2,728 2,572 2,459 2,373 2,305
2,947 2,714 2,558 2,445 2,359 2,291
2,934 2,701 2,545 2,432 2,346 2,278
2,922 2,690 2,534 2,421 2,334 2,266
2,839 2,606 2,449 2,336 2,249 2,180
2,790 2,557 2,400 2,286 2,199 2,130
2,758 2,525 2,368 2,254 2,167 2,097
2,736 2,503 2,346 2,231 2,143 2,074
2,719 2,486 2,329 2,214 2,126 2,056
2,706 2,473 2,316 2,201 2,113 2,043
2,696 2,463 2,305 2,191 2,103 2,032
2,687 2,454 2,297 2,182 2,094 2,024
2,680 2,447 2,290 2,175 2,087 2,016
2,606 2,373 2,215 2,099 2,011 1,939
9
240,543
19,385
8,812
5,999
4,772
4,099
3,677
3,388
3,179
3,020
2,896
2,796
2,714
2,646
2,588
2,538
2,494
2,456
2,423
2,393
2,366
2,342
2,320
2,300
2,282
2,265
2,250
2,236
2,223
2,211
2,124
2,073
2,040
2,017
1,999
1,986
1,975
1,966
1,959
1,881
10
241,882
19,396
8,785
5,964
4,735
4,060
3,637
3,347
3,137
2,978
2,854
2,753
2,671
2,602
2,544
2,494
2,450
2,412
2,378
2,348
2,321
2,297
2,275
2,255
2,236
2,220
2,204
2,190
2,177
2,165
2,077
2,026
1,993
1,969
1,951
1,938
1,927
1,918
1,910
1,832
CMM
11/26
TABELAS DE ESTATÍSTICA
Valores Críticos da Distribuição de Fisher - Snedecor - Continuação
G
r
A
u
s
D
E
L
I
B
E
r
D
A
D
E
D
O
D
E
n
O
M
I
n
A
D
O
r
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
50
60
70
80
90
100
110
120
∞
11
242,981
19,405
8,763
5,936
4,704
4,027
3,603
3,313
3,102
2,943
2,818
2,717
2,635
2,565
2,507
2,456
2,413
2,374
2,340
2,310
2,283
2,259
2,236
2,216
2,198
2,181
2,166
2,151
2,138
2,126
2,038
1,986
1,952
1,928
1,910
1,897
1,886
1,877
1,869
1,790
UA 2003/2004
12
243,905
19,412
8,745
5,912
4,678
4,000
3,575
3,284
3,073
2,913
2,788
2,687
2,604
2,534
2,475
2,425
2,381
2,342
2,308
2,278
2,250
2,226
2,204
2,183
2,165
2,148
2,132
2,118
2,104
2,092
2,003
1,952
1,917
1,893
1,875
1,861
1,850
1,841
1,834
1,753
Graus de Liberdade do Numerador
13
14
15
16
17
18
244,690 245,363 245,949 246,466 246,917 247,324
19,419 19,424 19,429 19,433 19,437 19,440
8,729 8,715 8,703 8,692 8,683 8,675
5,891 5,873 5,858 5,844 5,832 5,821
4,655 4,636 4,619 4,604 4,590 4,579
3,976 3,956 3,938 3,922 3,908 3,896
3,550 3,529 3,511 3,494 3,480 3,467
3,259 3,237 3,218 3,202 3,187 3,173
3,048 3,025 3,006 2,989 2,974 2,960
2,887 2,865 2,845 2,828 2,812 2,798
2,761 2,739 2,719 2,701 2,685 2,671
2,660 2,637 2,617 2,599 2,583 2,568
2,577 2,554 2,533 2,515 2,499 2,484
2,507 2,484 2,463 2,445 2,428 2,413
2,448 2,424 2,403 2,385 2,368 2,353
2,397 2,373 2,352 2,333 2,317 2,302
2,353 2,329 2,308 2,289 2,272 2,257
2,314 2,290 2,269 2,250 2,233 2,217
2,280 2,256 2,234 2,215 2,198 2,182
2,250 2,225 2,203 2,184 2,167 2,151
2,222 2,197 2,176 2,156 2,139 2,123
2,198 2,173 2,151 2,131 2,114 2,098
2,175 2,150 2,128 2,109 2,091 2,075
2,155 2,130 2,108 2,088 2,070 2,054
2,136 2,111 2,089 2,069 2,051 2,035
2,119 2,094 2,072 2,052 2,034 2,018
2,103 2,078 2,056 2,036 2,018 2,002
2,089 2,064 2,041 2,021 2,003 1,987
2,075 2,050 2,027 2,007 1,989 1,973
2,063 2,037 2,015 1,995 1,976 1,960
1,974 1,948 1,924 1,904 1,885 1,868
1,921 1,895 1,871 1,850 1,831 1,814
1,887 1,860 1,836 1,815 1,796 1,778
1,863 1,836 1,812 1,790 1,771 1,753
1,845 1,817 1,793 1,772 1,752 1,734
1,830 1,803 1,779 1,757 1,737 1,720
1,819 1,792 1,768 1,746 1,726 1,708
1,810 1,783 1,758 1,736 1,716 1,698
1,803 1,775 1,750 1,728 1,709 1,690
1,721 1,693 1,667 1,645 1,624 1,605
19
247,688
19,443
8,667
5,811
4,568
3,884
3,455
3,161
2,948
2,785
2,658
2,555
2,471
2,400
2,340
2,288
2,243
2,203
2,168
2,137
2,109
2,084
2,061
2,040
2,021
2,003
1,987
1,972
1,958
1,945
1,853
1,798
1,763
1,737
1,718
1,703
1,691
1,682
1,674
1,588
α = 5%
20
248,016
19,446
8,660
5,803
4,558
3,874
3,445
3,150
2,936
2,774
2,646
2,544
2,459
2,388
2,328
2,276
2,230
2,191
2,155
2,124
2,096
2,071
2,048
2,027
2,007
1,990
1,974
1,959
1,945
1,932
1,839
1,784
1,748
1,722
1,703
1,688
1,676
1,667
1,659
1,572
CMM
12/26
TABELAS DE ESTATÍSTICA
Valores Críticos da Distribuição de Fisher - Snedecor - Continuação
α = 5%
G
r
a
u
s
d
e
L
i
b
e
r
d
a
d
e
d
o
D
e
n
o
m
i
n
a
d
o
r
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
50
60
70
80
90
100
110
120
∞
21
248,307
19,448
8,654
5,795
4,549
3,865
3,435
3,140
2,926
2,764
2,636
2,533
2,448
2,377
2,316
2,264
2,219
2,179
2,144
2,112
2,084
2,059
2,036
2,015
1,995
1,978
1,961
1,946
1,932
1,919
1,826
1,771
1,735
1,709
1,689
1,675
1,663
1,653
1,645
1,557
UA 2003/2004
22
248,579
19,450
8,648
5,787
4,541
3,856
3,426
3,131
2,917
2,754
2,626
2,523
2,438
2,367
2,306
2,254
2,208
2,168
2,133
2,102
2,073
2,048
2,025
2,003
1,984
1,966
1,950
1,935
1,921
1,908
1,814
1,759
1,722
1,696
1,677
1,662
1,650
1,640
1,632
1,543
Graus de Liberdade do Numerador
23
24
25
26
27
28
248,823 249,052 249,260 249,453 249,631 249,798
19,452 19,454 19,456 19,457 19,459 19,460
8,643 8,638 8,634 8,630 8,626 8,623
5,781 5,774 5,769 5,763 5,759 5,754
4,534 4,527 4,521 4,515 4,510 4,505
3,849 3,841 3,835 3,829 3,823 3,818
3,418 3,410 3,404 3,397 3,391 3,386
3,123 3,115 3,108 3,102 3,095 3,090
2,908 2,900 2,893 2,886 2,880 2,874
2,745 2,737 2,730 2,723 2,716 2,710
2,617 2,609 2,601 2,594 2,588 2,582
2,514 2,505 2,498 2,491 2,484 2,478
2,429 2,420 2,412 2,405 2,398 2,392
2,357 2,349 2,341 2,333 2,326 2,320
2,297 2,288 2,280 2,272 2,265 2,259
2,244 2,235 2,227 2,220 2,212 2,206
2,199 2,190 2,181 2,174 2,167 2,160
2,159 2,150 2,141 2,134 2,126 2,119
2,123 2,114 2,106 2,098 2,090 2,084
2,092 2,082 2,074 2,066 2,059 2,052
2,063 2,054 2,045 2,037 2,030 2,023
2,038 2,028 2,020 2,012 2,004 1,997
2,014 2,005 1,996 1,988 1,981 1,973
1,993 1,984 1,975 1,967 1,959 1,952
1,974 1,964 1,955 1,947 1,939 1,932
1,956 1,946 1,938 1,929 1,921 1,914
1,940 1,930 1,921 1,913 1,905 1,898
1,924 1,915 1,906 1,897 1,889 1,882
1,910 1,901 1,891 1,883 1,875 1,868
1,897 1,887 1,878 1,870 1,862 1,854
1,803 1,793 1,783 1,775 1,766 1,759
1,748 1,737 1,727 1,718 1,710 1,702
1,711 1,700 1,690 1,681 1,672 1,664
1,685 1,674 1,664 1,654 1,646 1,637
1,665 1,654 1,644 1,634 1,626 1,617
1,650 1,639 1,629 1,619 1,610 1,601
1,638 1,627 1,616 1,607 1,598 1,589
1,628 1,617 1,606 1,597 1,587 1,579
1,620 1,608 1,598 1,588 1,579 1,570
1,530 1,518 1,507 1,497 1,487 1,477
29
249,951
19,461
8,620
5,750
4,500
3,813
3,381
3,084
2,869
2,705
2,576
2,472
2,386
2,314
2,253
2,200
2,154
2,113
2,077
2,045
2,016
1,990
1,967
1,945
1,926
1,907
1,891
1,875
1,861
1,847
1,751
1,694
1,656
1,629
1,609
1,593
1,581
1,571
1,562
1,469
30
250,096
19,463
8,617
5,746
4,496
3,808
3,376
3,079
2,864
2,700
2,570
2,466
2,380
2,308
2,247
2,194
2,148
2,107
2,071
2,039
2,010
1,984
1,961
1,939
1,919
1,901
1,884
1,869
1,854
1,841
1,744
1,687
1,649
1,622
1,602
1,586
1,573
1,563
1,554
1,460
CMM
13/26
TABELAS DE ESTATÍSTICA
Valores Críticos da Distribuição de Fisher - Snedecor - Conclusão
α = 5%
G
r
a
u
s
d
e
L
i
b
e
r
d
a
d
e
d
o
D
e
n
o
m
i
n
a
d
o
r
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
50
60
70
80
90
100
110
120
∞
40
251,144
19,471
8,594
5,717
4,464
3,774
3,340
3,043
2,826
2,661
2,531
2,426
2,339
2,266
2,204
2,151
2,104
2,063
2,026
1,994
1,965
1,938
1,914
1,892
1,872
1,853
1,836
1,820
1,806
1,792
1,693
1,634
1,594
1,566
1,545
1,528
1,515
1,504
1,495
1,395
UA 2003/2004
50
251,774
19,476
8,581
5,699
4,444
3,754
3,319
3,020
2,803
2,637
2,507
2,401
2,314
2,241
2,178
2,124
2,077
2,035
1,999
1,966
1,936
1,909
1,885
1,863
1,842
1,823
1,806
1,790
1,775
1,761
1,660
1,599
1,559
1,530
1,508
1,491
1,477
1,466
1,457
1,351
Graus de Liberdade do Numerador
60
70
80
90
100
110
252,196 252,498 252,723 252,898 253,043 253,156
19,479 19,481 19,483 19,485 19,486 19,487
8,572 8,566 8,561 8,557 8,554 8,551
5,688 5,679 5,673 5,668 5,664 5,661
4,431 4,422 4,415 4,409 4,405 4,401
3,740 3,730 3,722 3,716 3,712 3,708
3,304 3,294 3,286 3,280 3,275 3,271
3,005 2,994 2,986 2,980 2,975 2,970
2,787 2,776 2,768 2,761 2,756 2,751
2,621 2,609 2,601 2,594 2,588 2,584
2,490 2,478 2,469 2,462 2,457 2,452
2,384 2,372 2,363 2,356 2,350 2,345
2,297 2,284 2,275 2,267 2,261 2,256
2,223 2,210 2,201 2,193 2,187 2,182
2,160 2,147 2,137 2,130 2,123 2,118
2,106 2,093 2,083 2,075 2,068 2,063
2,058 2,045 2,035 2,027 2,020 2,015
2,017 2,003 1,993 1,985 1,978 1,973
1,980 1,966 1,955 1,947 1,940 1,935
1,946 1,932 1,922 1,913 1,907 1,901
1,916 1,902 1,891 1,883 1,876 1,870
1,889 1,875 1,864 1,856 1,849 1,843
1,865 1,850 1,839 1,830 1,823 1,818
1,842 1,828 1,816 1,808 1,800 1,795
1,822 1,807 1,796 1,787 1,779 1,773
1,803 1,788 1,776 1,767 1,760 1,754
1,785 1,770 1,758 1,749 1,742 1,736
1,769 1,754 1,742 1,733 1,725 1,719
1,754 1,738 1,726 1,717 1,710 1,703
1,740 1,724 1,712 1,703 1,695 1,689
1,637 1,621 1,608 1,597 1,589 1,582
1,576 1,558 1,544 1,534 1,525 1,518
1,534 1,516 1,502 1,491 1,481 1,474
1,505 1,486 1,471 1,459 1,450 1,442
1,482 1,463 1,448 1,436 1,426 1,418
1,465 1,445 1,429 1,417 1,407 1,399
1,450 1,430 1,415 1,402 1,392 1,383
1,439 1,418 1,402 1,390 1,379 1,370
1,429 1,408 1,392 1,379 1,369 1,360
1,319 1,295 1,275 1,259 1,245 1,233
120
253,254
19,487
8,549
5,658
4,398
3,705
3,267
2,967
2,748
2,580
2,448
2,341
2,252
2,178
2,114
2,059
2,011
1,968
1,930
1,896
1,866
1,838
1,813
1,790
1,768
1,749
1,731
1,714
1,698
1,683
1,577
1,511
1,467
1,435
1,411
1,391
1,376
1,363
1,352
1,223
∞
254,302
19,496
8,527
5,628
4,365
3,669
3,230
2,928
2,707
2,538
2,405
2,297
2,207
2,131
2,066
2,010
1,961
1,917
1,879
1,844
1,812
1,784
1,758
1,734
1,712
1,691
1,672
1,655
1,638
1,623
1,510
1,439
1,390
1,354
1,326
1,303
1,284
1,269
1,255
1,033
CMM
14/26
TABELAS DE ESTATÍSTICA
Valores Críticos da Distribuição de Fisher - Snedecor
α = 1%
G
r
a
u
s
d
e
L
i
b
e
r
d
a
d
e
d
o
D
e
n
o
m
i
n
a
d
o
r
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
50
60
70
80
90
100
110
120
∞
1
4052,19
98,502
34,116
21,198
16,258
13,745
12,246
11,259
10,562
10,044
9,646
9,330
9,074
8,862
8,683
8,531
8,400
8,285
8,185
8,096
8,017
7,945
7,881
7,823
7,770
7,721
7,677
7,636
7,598
7,562
7,314
7,171
7,077
7,011
6,963
6,925
6,895
6,871
6,851
6,637
UA 2003/2004
2
4999,34
99,000
30,816
18,000
13,274
10,925
9,547
8,649
8,022
7,559
7,206
6,927
6,701
6,515
6,359
6,226
6,112
6,013
5,926
5,849
5,780
5,719
5,664
5,614
5,568
5,526
5,488
5,453
5,420
5,390
5,178
5,057
4,977
4,922
4,881
4,849
4,824
4,803
4,787
4,607
Graus de Liberdade do Numerador
3
4
5
6
7
8
5403,53 5624,26 5763,96 5858,95 5928,33 5980,95
99,164 99,251 99,302 99,331 99,357 99,375
29,457 28,710 28,237 27,911 27,671 27,489
16,694 15,977 15,522 15,207 14,976 14,799
12,060 11,392 10,967 10,672 10,456 10,289
9,780 9,148 8,746 8,466 8,260 8,102
8,451 7,847 7,460 7,191 6,993 6,840
7,591 7,006 6,632 6,371 6,178 6,029
6,992 6,422 6,057 5,802 5,613 5,467
6,552 5,994 5,636 5,386 5,200 5,057
6,217 5,668 5,316 5,069 4,886 4,744
5,953 5,412 5,064 4,821 4,640 4,499
5,739 5,205 4,862 4,620 4,441 4,302
5,564 5,035 4,695 4,456 4,278 4,140
5,417 4,893 4,556 4,318 4,142 4,004
5,292 4,773 4,437 4,202 4,026 3,890
5,185 4,669 4,336 4,101 3,927 3,791
5,092 4,579 4,248 4,015 3,841 3,705
5,010 4,500 4,171 3,939 3,765 3,631
4,938 4,431 4,103 3,871 3,699 3,564
4,874 4,369 4,042 3,812 3,640 3,506
4,817 4,313 3,988 3,758 3,587 3,453
4,765 4,264 3,939 3,710 3,539 3,406
4,718 4,218 3,895 3,667 3,496 3,363
4,675 4,177 3,855 3,627 3,457 3,324
4,637 4,140 3,818 3,591 3,421 3,288
4,601 4,106 3,785 3,558 3,388 3,256
4,568 4,074 3,754 3,528 3,358 3,226
4,538 4,045 3,725 3,499 3,330 3,198
4,510 4,018 3,699 3,473 3,305 3,173
4,313 3,828 3,514 3,291 3,124 2,993
4,199 3,720 3,408 3,186 3,020 2,890
4,126 3,649 3,339 3,119 2,953 2,823
4,074 3,600 3,291 3,071 2,906 2,777
4,036 3,563 3,255 3,036 2,871 2,742
4,007 3,535 3,228 3,009 2,845 2,715
3,984 3,513 3,206 2,988 2,823 2,694
3,965 3,495 3,188 2,970 2,806 2,677
3,949 3,480 3,174 2,956 2,792 2,663
3,784 3,321 3,019 2,804 2,641 2,513
9
6022,40
99,390
27,345
14,659
10,158
7,976
6,719
5,911
5,351
4,942
4,632
4,388
4,191
4,030
3,895
3,780
3,682
3,597
3,523
3,457
3,398
3,346
3,299
3,256
3,217
3,182
3,149
3,120
3,092
3,067
2,888
2,785
2,718
2,672
2,637
2,611
2,590
2,573
2,559
2,409
10
6055,93
99,397
27,228
14,546
10,051
7,874
6,620
5,814
5,257
4,849
4,539
4,296
4,100
3,939
3,805
3,691
3,593
3,508
3,434
3,368
3,310
3,258
3,211
3,168
3,129
3,094
3,062
3,032
3,005
2,979
2,801
2,698
2,632
2,585
2,551
2,524
2,503
2,486
2,472
2,323
CMM
15/26
TABELAS DE ESTATÍSTICA
Valores Críticos da Distribuição de Fisher - Snedecor - Continuação
α = 1%
G
R
A
U
S
D
E
L
I
B
E
R
D
A
D
E
D
O
D
E
N
O
M
I
N
A
D
O
R
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
50
60
70
80
90
100
110
120
∞
11
6083,40
99,408
27,132
14,452
9,963
7,790
6,538
5,734
5,178
4,772
4,462
4,220
4,025
3,864
3,730
3,616
3,518
3,434
3,360
3,294
3,236
3,184
3,137
3,094
3,056
3,021
2,988
2,959
2,931
2,906
2,727
2,625
2,559
2,512
2,478
2,451
2,430
2,413
2,399
2,249
UA 2003/2004
12
6106,68
99,419
27,052
14,374
9,888
7,718
6,469
5,667
5,111
4,706
4,397
4,155
3,960
3,800
3,666
3,553
3,455
3,371
3,297
3,231
3,173
3,121
3,074
3,032
2,993
2,958
2,926
2,896
2,868
2,843
2,665
2,563
2,496
2,450
2,415
2,389
2,368
2,350
2,336
2,187
Graus de Liberdade do Numerador
13
14
15
16
17
18
6125,77 6143,00 6156,97 6170,01 6181,19 6191,43
99,422 99,426 99,433 99,437 99,441 99,444
26,983 26,924 26,872 26,826 26,786 26,751
14,306 14,249 14,198 14,154 14,114 14,079
9,825 9,770 9,722 9,680 9,643 9,609
7,657 7,605 7,559 7,519 7,483 7,451
6,410 6,359 6,314 6,275 6,240 6,209
5,609 5,559 5,515 5,477 5,442 5,412
5,055 5,005 4,962 4,924 4,890 4,860
4,650 4,601 4,558 4,520 4,487 4,457
4,342 4,293 4,251 4,213 4,180 4,150
4,100 4,052 4,010 3,972 3,939 3,910
3,905 3,857 3,815 3,778 3,745 3,716
3,745 3,698 3,656 3,619 3,586 3,556
3,612 3,564 3,522 3,485 3,452 3,423
3,498 3,451 3,409 3,372 3,339 3,310
3,401 3,353 3,312 3,275 3,242 3,212
3,316 3,269 3,227 3,190 3,158 3,128
3,242 3,195 3,153 3,116 3,084 3,054
3,177 3,130 3,088 3,051 3,018 2,989
3,119 3,072 3,030 2,993 2,960 2,931
3,067 3,019 2,978 2,941 2,908 2,879
3,020 2,973 2,931 2,894 2,861 2,832
2,977 2,930 2,889 2,852 2,819 2,789
2,939 2,892 2,850 2,813 2,780 2,751
2,904 2,857 2,815 2,778 2,745 2,715
2,872 2,824 2,783 2,746 2,713 2,683
2,842 2,795 2,753 2,716 2,683 2,653
2,814 2,767 2,726 2,689 2,656 2,626
2,789 2,742 2,700 2,663 2,630 2,600
2,611 2,563 2,522 2,484 2,451 2,421
2,508 2,461 2,419 2,382 2,348 2,318
2,442 2,394 2,352 2,315 2,281 2,251
2,395 2,348 2,306 2,268 2,234 2,204
2,361 2,313 2,271 2,233 2,199 2,169
2,334 2,286 2,244 2,206 2,172 2,142
2,313 2,265 2,223 2,185 2,151 2,120
2,296 2,248 2,206 2,168 2,134 2,103
2,282 2,234 2,191 2,154 2,119 2,089
2,132 2,083 2,040 2,002 1,967 1,935
19
6200,75
99,448
26,719
14,048
9,580
7,422
6,181
5,384
4,833
4,430
4,123
3,883
3,689
3,529
3,396
3,283
3,186
3,101
3,027
2,962
2,904
2,852
2,805
2,762
2,724
2,688
2,656
2,626
2,599
2,573
2,394
2,290
2,223
2,176
2,141
2,114
2,092
2,075
2,060
1,907
20
6208,66
99,448
26,690
14,019
9,553
7,396
6,155
5,359
4,808
4,405
4,099
3,858
3,665
3,505
3,372
3,259
3,162
3,077
3,003
2,938
2,880
2,827
2,780
2,738
2,699
2,664
2,632
2,602
2,574
2,549
2,369
2,265
2,198
2,150
2,115
2,088
2,067
2,049
2,035
1,880
CMM
16/26
TABELAS DE ESTATÍSTICA
Valores Críticos da Distribuição de Fisher - Snedecor - Continuação
α = 1%
G
R
A
U
S
D
E
L
I
B
E
R
D
A
D
E
D
O
D
E
N
O
M
I
N
A
D
O
R
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
50
60
70
80
90
100
110
120
∞
21
6216,11
99,451
26,664
13,994
9,528
7,372
6,132
5,336
4,786
4,383
4,077
3,836
3,643
3,483
3,350
3,237
3,139
3,055
2,981
2,916
2,857
2,805
2,758
2,716
2,677
2,642
2,609
2,579
2,552
2,526
2,346
2,242
2,175
2,127
2,092
2,065
2,043
2,026
2,011
1,856
UA 2003/2004
22
6223,10
99,455
26,639
13,970
9,506
7,351
6,111
5,316
4,765
4,363
4,057
3,816
3,622
3,463
3,330
3,216
3,119
3,035
2,961
2,895
2,837
2,785
2,738
2,695
2,657
2,621
2,589
2,559
2,531
2,506
2,325
2,221
2,153
2,106
2,070
2,043
2,021
2,004
1,989
1,833
Graus de Liberdade do Numerador
23
24
25
26
27
28
6228,69 6234,27 6239,86 6244,52 6249,14 6252,90
99,455 99,455 99,459 99,462 99,462 99,462
26,617 26,597 26,579 26,562 26,546 26,531
13,949 13,929 13,911 13,894 13,878 13,864
9,485 9,466 9,449 9,433 9,418 9,404
7,331 7,313 7,296 7,281 7,266 7,253
6,092 6,074 6,058 6,043 6,029 6,016
5,297 5,279 5,263 5,248 5,234 5,221
4,746 4,729 4,713 4,698 4,684 4,672
4,344 4,327 4,311 4,296 4,283 4,270
4,038 4,021 4,005 3,990 3,977 3,964
3,798 3,780 3,765 3,750 3,736 3,724
3,604 3,587 3,571 3,556 3,543 3,530
3,444 3,427 3,412 3,397 3,383 3,371
3,311 3,294 3,278 3,264 3,250 3,237
3,198 3,181 3,165 3,150 3,137 3,124
3,101 3,083 3,068 3,053 3,039 3,026
3,016 2,999 2,983 2,968 2,955 2,942
2,942 2,925 2,909 2,894 2,880 2,868
2,877 2,859 2,843 2,829 2,815 2,802
2,818 2,801 2,785 2,770 2,756 2,743
2,766 2,749 2,733 2,718 2,704 2,691
2,719 2,702 2,686 2,671 2,657 2,644
2,676 2,659 2,643 2,628 2,614 2,601
2,638 2,620 2,604 2,589 2,575 2,562
2,602 2,585 2,569 2,554 2,540 2,526
2,570 2,552 2,536 2,521 2,507 2,494
2,540 2,522 2,506 2,491 2,477 2,464
2,512 2,495 2,478 2,463 2,449 2,436
2,487 2,469 2,453 2,437 2,423 2,410
2,306 2,288 2,271 2,256 2,241 2,228
2,202 2,183 2,167 2,151 2,136 2,123
2,134 2,115 2,098 2,083 2,068 2,054
2,086 2,067 2,050 2,034 2,019 2,005
2,050 2,032 2,015 1,999 1,983 1,969
2,023 2,004 1,987 1,971 1,956 1,942
2,001 1,983 1,965 1,949 1,934 1,919
1,984 1,965 1,947 1,931 1,916 1,901
1,969 1,950 1,932 1,916 1,901 1,886
1,812 1,793 1,774 1,757 1,741 1,726
29
6257,09
99,462
26,517
13,850
9,391
7,240
6,003
5,209
4,660
4,258
3,952
3,712
3,518
3,359
3,225
3,112
3,014
2,930
2,855
2,790
2,731
2,679
2,632
2,589
2,550
2,514
2,481
2,451
2,423
2,398
2,215
2,110
2,041
1,992
1,956
1,928
1,906
1,888
1,873
1,712
30
6260,35
99,466
26,504
13,838
9,379
7,229
5,992
5,198
4,649
4,247
3,941
3,701
3,507
3,348
3,214
3,101
3,003
2,919
2,844
2,778
2,720
2,667
2,620
2,577
2,538
2,503
2,470
2,440
2,412
2,386
2,203
2,098
2,028
1,980
1,944
1,916
1,893
1,875
1,860
1,698
CMM
17/26
TABELAS DE ESTATÍSTICA
Valores Críticos da Distribuição de Fisher - Snedecor - Conclusão
α = 1%
G
R
A
u
s
d
e
L
i
b
e
r
d
a
d
e
d
o
D
e
n
o
m
i
n
a
d
o
r
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
50
60
70
80
90
100
110
120
∞
40
6286,43
99,477
26,411
13,745
9,291
7,143
5,908
5,116
4,567
4,165
3,860
3,619
3,425
3,266
3,132
3,018
2,920
2,835
2,761
2,695
2,636
2,583
2,536
2,492
2,453
2,417
2,384
2,354
2,325
2,299
2,114
2,007
1,936
1,886
1,849
1,820
1,797
1,778
1,763
1,594
UA 2003/2004
50
6302,26
99,477
26,354
13,690
9,238
7,091
5,858
5,065
4,517
4,115
3,810
3,569
3,375
3,215
3,081
2,967
2,869
2,784
2,709
2,643
2,584
2,531
2,483
2,440
2,400
2,364
2,330
2,300
2,271
2,245
2,058
1,949
1,877
1,826
1,788
1,759
1,735
1,716
1,700
1,525
Graus de Liberdade do Numerador
60
70
80
90
100
110
6312,97 6320,89 6326,47 6330,66 6333,92 6336,72
99,484 99,484 99,484 99,488 99,491 99,491
26,316 26,289 26,269 26,253 26,241 26,230
13,652 13,626 13,605 13,590 13,577 13,566
9,202 9,176 9,157 9,142 9,130 9,120
7,057 7,032 7,013 6,998 6,987 6,977
5,824 5,799 5,781 5,766 5,755 5,745
5,032 5,007 4,989 4,975 4,963 4,954
4,483 4,459 4,441 4,426 4,415 4,406
4,082 4,058 4,039 4,025 4,014 4,004
3,776 3,752 3,734 3,719 3,708 3,698
3,535 3,511 3,493 3,478 3,467 3,457
3,341 3,317 3,298 3,284 3,272 3,263
3,181 3,157 3,138 3,124 3,112 3,102
3,047 3,022 3,004 2,989 2,977 2,968
2,933 2,908 2,889 2,875 2,863 2,853
2,835 2,810 2,791 2,776 2,764 2,754
2,749 2,724 2,705 2,690 2,678 2,668
2,674 2,649 2,630 2,614 2,602 2,592
2,608 2,582 2,563 2,548 2,535 2,525
2,548 2,523 2,503 2,488 2,476 2,465
2,495 2,469 2,450 2,434 2,422 2,411
2,447 2,421 2,401 2,386 2,373 2,363
2,403 2,377 2,357 2,342 2,329 2,319
2,364 2,337 2,317 2,302 2,289 2,278
2,327 2,301 2,281 2,265 2,252 2,241
2,294 2,267 2,247 2,231 2,218 2,207
2,263 2,236 2,216 2,200 2,187 2,176
2,234 2,207 2,187 2,171 2,158 2,147
2,208 2,181 2,160 2,144 2,131 2,120
2,019 1,991 1,969 1,952 1,938 1,927
1,909 1,880 1,857 1,839 1,825 1,813
1,836 1,806 1,783 1,764 1,749 1,737
1,785 1,754 1,730 1,711 1,695 1,683
1,746 1,714 1,690 1,671 1,655 1,642
1,716 1,684 1,659 1,639 1,623 1,610
1,692 1,659 1,634 1,614 1,598 1,584
1,672 1,639 1,614 1,593 1,577 1,563
1,656 1,623 1,597 1,576 1,559 1,545
1,475 1,437 1,407 1,382 1,361 1,343
120
6339,51
99,491
26,221
13,558
9,112
6,969
5,737
4,946
4,398
3,996
3,690
3,449
3,255
3,094
2,959
2,845
2,746
2,660
2,584
2,517
2,457
2,403
2,354
2,310
2,270
2,233
2,198
2,167
2,138
2,111
1,917
1,803
1,726
1,672
1,630
1,598
1,572
1,551
1,533
1,327
∞
6365,59
99,499
26,126
13,464
9,022
6,881
5,651
4,860
4,312
3,910
3,604
3,362
3,166
3,005
2,870
2,754
2,654
2,567
2,490
2,422
2,361
2,307
2,257
2,212
2,171
2,133
2,098
2,065
2,035
2,008
1,806
1,685
1,602
1,542
1,496
1,459
1,429
1,404
1,383
1,048
CMM
18/26
TABELAS DE ESTATÍSTICA
Valores Críticos da Studentized Range
α = 5%
v\k
2
3
1
17,970
26,980
32,820 37,080
40,410 43,120
45,400 47,360
49,070
2
6,085
8,331
9,798
10,880
11,750 12,440
13,030 13,540
13,990
3
4,501
5,910
6,825
7,502
8,037
8,478
8,853
9,177
9,462
4
3,927
5,040
5,757
6,287
6,707
7,053
7,347
7,602
7,826
5
3,635
4,602
5,218
5,673
6,033
6,330
6,582
6,802
6,995
6
3,461
4,339
4,896
5,305
5,628
5,895
6,122
6,319
6,493
7
3,344
4,165
4,681
5,060
5,359
5,606
5,815
5,998
6,158
8
3,261
4,041
4,529
4,886
5,167
5,399
5,597
5,767
5,918
9
3,199
3,949
4,415
4,756
5,024
5,244
5,432
5,595
5,739
10
3,151
3,877
4,327
4,654
4,912
5,124
5,305
5,461
5,599
11
3,113
3,820
4,256
4,574
4,823
5,028
5,202
5,353
5,487
12
3,000
3,773
4,199
4,508
4,751
4,950
5,119
5,265
5,395
13
3,055
3,735
4,151
4,453
4,690
4,885
5,049
5,192
5,318
14
3,033
3,702
4,111
4,407
4,639
4,829
4,990
5,131
5,254
15
3,014
3,674
4,076
4,367
4,595
4,782
4,940
5,077
5,198
16
2,998
3,649
4,046
4,333
4,557
4,741
4,897
5,031
5,150
17
2,984
3,628
4,020
4,303
4,524
4,705
4,858
4,991
5,108
18
2,971
3,609
3,997
4,277
4,495
4,673
4,824
4,956
5,071
19
2,960
3,593
3,977
4,253
4,469
4,645
4,794
4,924
5,038
20
2,950
3,578
3,958
4,232
4,445
4,200
4,768
4,896
5,008
24
2,919
3,532
3,901
4,166
4,373
4,541
4,684
4,807
4,915
30
2,888
3,486
3,845
4,102
4,302
4,464
4,602
4,720
4,824
40
2,858
3,442
3,791
4,039
4,232
4,389
4,521
4,635
4,735
60
2,829
3,399
3,737
3,977
4,163
4,314
4,441
4,550
4,646
120
2,800
3,356
3,685
3,917
4,096
4,241
4,363
4,468
4,560
∞
2,772
3,314
3,633
3,858
4,030
4,170
4,286
4,387
4,474
UA 2003/2004
4
5
6
7
8
9
10
CMM
19/26
TABELAS DE ESTATÍSTICA
Valores Críticos da Studentized Range - Continuação
α = 5%
v\k
11
12
1
50,590
51,960
53,200 54,330
55,360 56,320
57,220 58,040
58,830
2
14,390
14,750
15,080 15,380
15,650 15,910
16,140 16,370
16,570
3
9,717
9,946
10,150 10,350
10,530 10,690
10,840 10,980
11,110
4
8,027
8,208
8,373
8,525
8,664
8,794
8,914
9,028
9,134
5
7,168
7,324
7,466
7,596
7,717
7,828
7,932
8,030
8,122
6
6,649
6,789
6,917
7,034
7,143
7,244
7,338
7,426
7,508
7
6,302
6,431
6,550
6,658
6,759
6,852
6,939
7,020
7,097
8
6,054
6,175
6,287
6,389
6,483
6,571
6,653
6,729
6,802
9
5,867
5,983
6,089
6,186
6,276
6,359
6,437
6,510
6,579
10
5,722
5,833
5,935
6,028
6,114
6,194
6,269
6,339
6,405
11
5,605
5,713
5,811
5,901
5,984
6,062
6,134
6,202
6,265
12
5,511
5,615
5,710
5,798
5,878
5,953
6,023
6,089
6,151
13
5,431
5,533
5,625
5,711
5,789
5,862
5,931
5,995
6,055
14
5,364
5,463
5,554
5,637
5,714
5,786
5,852
5,915
5,974
15
5,306
5,404
5,493
5,574
5,649
5,720
5,785
5,846
5,904
16
5,256
5,352
5,439
5,520
5,593
5,662
5,727
5,786
5,843
17
5,212
5,307
5,392
5,471
5,544
5,612
5,675
5,734
5,790
18
5,174
5,267
5,352
5,429
5,501
5,568
5,630
5,688
5,743
19
5,140
5,231
5,315
5,391
5,402
5,528
5,589
5,647
5,701
20
5,108
5,199
5,282
5,357
5,427
5,493
5,553
5,610
5,663
24
5,012
5,099
5,179
5,251
5,319
5,381
5,439
5,494
5,545
30
4,917
5,001
5,077
5,147
5,211
5,271
5,327
5,379
5,429
40
4,824
4,904
4,977
5,077
5,106
5,163
5,216
5,266
5,313
60
4,732
4,808
4,878
4,942
5,001
5,056
5,107
5,154
5,199
120
4,641
4,714
4,781
4,842
4,898
4,950
4,998
5,044
5,086
∞
4,552
4,622
4,685
4,743
4,796
4,845
4,891
4,934
4,974
UA 2003/2004
13
14
15
16
17
18
19
CMM
20/26
TABELAS DE ESTATÍSTICA
Valores Críticos da Studentized Range Continuação
α = 5%
v\k
20
22
1
56,560
60,910
62,120 63,220
64,230 65,150
66,010 66,810
67,560
2
16,770
17,130
17,450 17,750
18,020 18,270
18,500 18,720
18,920
3
11,240
11,470
11,680 11,870
12,050 12,210
12,360 12,500
12,630
4
9,233
9,418
9,584
9,735
9,875
10,000
10,120 10,230
10,340
5
8,208
8,368
8,512
8,643
8,764
8,875
8,979
9,075
9,165
6
7,587
7,730
7,861
7,979
8,088
8,189
8,283
8,370
8,452
7
7,170
7,303
7,423
7,533
7,634
7,728
7,814
7,895
7,972
8
6,870
6,995
7,109
7,212
7,307
7,395
7,477
7,554
7,625
9
6,644
6,763
6,871
6,970
7,061
7,145
7,222
7,295
7,363
10
6,467
6,582
6,686
6,781
6,868
6,948
7,023
7,093
7,159
11
6,326
6,436
6,536
6,628
6,712
6,790
6,863
6,930
6,994
12
6,209
6,317
6,414
6,503
6,585
6,660
6,731
6,796
6,858
13
6,112
6,217
6,312
6,398
6,478
6,551
6,620
6,684
6,744
14
6,029
6,132
6,224
6,309
6,387
6,459
6,526
6,588
6,647
15
5,958
6,059
6,149
6,233
6,309
6,379
6,445
6,506
6,564
16
5,897
5,995
6,084
6,166
6,241
6,310
6,374
6,434
6,491
17
5,842
5,940
6,027
6,107
6,181
6,249
6,313
6,372
6,427
18
5,794
5,890
5,977
6,055
6,128
6,195
6,258
6,316
6,371
19
5,752
5,846
5,932
6,009
6,081
6,147
6,209
6,267
6,321
20
5,714
5,807
5,891
5,680
6,039
6,104
6,165
6,222
6,275
24
5,594
5,683
5,764
5,838
5,906
5,968
6,027
6,081
6,132
30
5,475
5,561
5,638
5,709
5,774
5,833
5,889
5,941
5,990
40
5,358
5,439
5,513
5,581
5,642
5,700
5,753
5,803
5,849
60
5,241
5,319
5,389
5,453
5,512
5,566
5,617
5,664
5,708
120
5,126
5,200
5,266
5,327
5,388
5,434
5,481
5,526
5,568
∞
5,012
5,081
5,144
5,201
5,253
5,301
5,346
5,388
5,427
UA 2003/2004
24
26
28
30
32
34
36
CMM
21/26
TABELAS DE ESTATÍSTICA
Valores Críticos da Studentized Range - Conclusão
α = 5%
UA 2003/2004
v\k
38
40
50
60
1
68,260
68,920
71,730 73,970
2
19,110
19,280
3
12,750
4
70
80
90
100
75,820 77,400
78,770
79,980
20,050 20,660
21,160 21,590
21,960
22,290
12,870
13,360 13,760
14,800 14,360
14,610
14,820
10,440
10,530
10,930 11,240
11,510 11,730
11,920
12,090
5
9,250
9,330
9,647
9,949
10,180 10,380
10,540
10,690
6
8,529
8,601
8,913
9,163
9,370
9,548
9,702
9,839
7
8,043
8,110
8,400
8,632
8,824
8,989
9,133
9,261
8
7,693
7,756
8,029
8,248
8,430
8,586
8,722
8,843
9
7,428
7,488
7,749
7,958
8,132
8,281
8,410
8,526
10
7,220
7,279
7,529
7,730
7,897
8,041
8,166
8,276
11
7,053
7,110
7,352
7,546
7,708
7,847
7,968
8,075
12
6,916
6,970
7,205
7,394
7,552
7,687
7,804
7,909
13
6,800
6,854
7,083
7,267
7,421
7,552
7,667
7,769
14
6,702
6,754
6,979
7,159
7,309
7,438
7,550
7,650
15
6,618
6,669
6,888
7,065
7,212
7,339
7,449
7,546
16
6,544
6,594
6,810
6,984
7,128
7,252
7,360
7,457
17
6,479
6,529
6,741
6,912
7,054
7,176
7,283
7,377
18
6,422
6,471
6,680
6,848
6,989
7,109
7,213
7,307
19
6,371
6,419
6,626
6,792
6,930
7,048
7,152
7,244
20
6,325
6,373
6,576
6,740
6,887
6,994
7,097
7,187
24
6,182
6,226
6,421
6,579
6,710
6,822
6,920
7,008
30
6,037
6,080
6,267
6,417
6,543
6,650
6,744
6,827
40
5,893
5,934
6,112
6,255
6,375
6,477
6,566
6,645
60
5,750
5,789
5,958
6,093
6,206
6,303
6,387
6,642
120
5,607
5,644
5,802
5,929
6,035
6,126
6,205
6,275
∞
5,463
5,498
5,646
5,764
5,863
5,947
6,020
6,085
CMM
22/26
TABELAS DE ESTATÍSTICA
Valores Críticos da Studentized Range
α = 1%
v\k
2
3
4
5
6
7
8
9
10
1
90,030 135,000 164,300 185,600 202,200 215,800 227,200 237,000 245,600
2
14,040
19,020
22,290
24,720
26,630
28,200
29,530
30,680
31,690
3
8,261
10,620
12,170
13,330
14,240
15,000
15,640
16,200
16,690
4
6,512
8,120
9,173
9,958
10,580
11,100
11,550
11,930
12,270
5
5,702
6,976
7,804
8,421
8,913
9,321
9,669
9,972
10,240
6
5,243
6,331
7,033
7,556
7,973
8,318
8,613
8,869
9,097
7
4,949
5,919
6,543
7,005
7,373
7,679
7,939
8,166
8,368
8
4,746
5,635
6,204
6,625
6,960
7,237
7,474
7,681
7,863
9
4,596
5,428
5,957
6,348
6,658
6,915
7,134
7,325
7,495
10
4,482
5,270
5,769
6,136
6,428
6,669
6,875
7,055
7,213
11
4,392
5,146
5,621
5,970
6,247
6,476
6,672
6,842
6,992
12
4,320
5,046
5,502
5,836
6,101
6,321
6,507
6,670
6,814
13
4,260
4,964
5,404
5,727
5,981
6,192
6,372
6,528
6,667
14
4,210
4,895
5,322
5,634
5,881
6,685
6,258
6,409
6,543
15
4,168
4,836
5,252
5,556
5,796
5,994
6,162
6,309
6,439
16
4,131
4,786
5,192
5,489
5,722
5,915
6,079
6,222
6,349
17
4,099
4,742
5,140
5,430
5,659
5,847
6,007
6,147
6,270
18
4,071
4,703
5,094
5,379
5,603
5,788
5,944
6,081
6,201
19
4,046
4,670
5,054
5,334
5,554
5,735
5,889
6,022
6,141
20
4,024
4,639
5,018
5,294
5,510
5,688
5,839
5,970
6,087
24
3,956
4,546
4,907
5,168
5,374
5,542
5,685
5,809
5,919
30
3,889
4,455
4,799
5,018
5,242
5,401
5,536
5,653
5,756
40
3,825
4,367
4,969
4,931
5,114
5,265
5,392
5,502
5,599
60
3,762
4,282
4,595
4,818
4,991
5,133
5,253
5,356
5,447
120
3,702
4,200
4,497
4,709
4,872
5,005
5,118
5,214
5,299
∞
3,643
4,120
4,403
4,603
4,757
4,882
4,987
5,078
5,157
Valores Críticos da Studentized Range - Continuação
UA 2003/2004
CMM
23/26
TABELAS DE ESTATÍSTICA
α = 1%
v\k
11
12
13
14
15
16
17
18
19
1
253,200 260,000 266,200 271,800 277,000 281,800 286,300 290,400 294,300
2
32,590
33,400
34,130
34,810
35,430
36,000
36,530
37,030
37,500
3
17,130
17,530
17,890
18,220
18,520
18,810
19,070
19,320
19,550
4
12,570
12,840
13,090
13,320
13,530
13,730
13,910
14,080
14,240
5
10,480
10,700
10,890
11,080
11,240
11,400
11,550
11,680
11,810
6
9,301
9,485
9,653
9,808
9,951
10,080
10,210
10,320
10,430
7
8,548
8,711
8,860
8,997
9,124
9,242
9,353
9,456
9,554
8
8,027
8,176
8,312
8,436
8,552
8,659
8,760
8,854
8,943
9
7,647
7,784
7,910
8,025
8,132
8,232
8,325
8,412
8,495
10
7,356
7,485
7,603
7,712
7,812
7,906
7,993
8,076
8,153
11
7,128
7,250
7,362
7,465
7,560
7,649
7,732
7,809
7,883
12
6,943
7,060
7,167
7,265
7,356
7,441
7,520
7,594
7,665
13
6,791
6,903
7,006
7,101
7,188
7,269
7,345
7,417
7,485
14
6,664
6,772
6,871
6,962
7,047
7,126
7,190
7,268
7,333
15
6,555
6,660
6,757
6,845
6,927
7,003
7,074
7,142
7,204
16
6,462
6,564
6,658
6,744
6,823
6,898
6,967
7,032
7,093
17
6,381
6,480
6,572
6,656
6,734
6,806
6,873
6,937
6,997
18
6,310
6,407
6,497
6,579
6,655
6,725
6,792
6,854
6,912
19
6,247
6,342
6,430
6,510
6,585
6,651
6,719
6,780
6,837
20
6,191
6,285
6,371
6,450
6,523
6,591
6,654
6,714
6,771
24
6,017
6,106
6,186
6,261
6,330
6,394
6,453
6,510
6,563
30
5,849
5,932
6,008
6,078
6,143
6,203
6,259
6,311
6,361
40
5,686
5,776
5,835
5,900
5,961
6,017
6,069
6,119
6,165
60
5,528
5,601
5,667
5,728
5,785
5,837
5,886
5,931
5,974
120
5,375
5,443
5,505
5,562
5,614
5,662
5,708
5,750
5,790
∞
5,227
5,290
5,348
5,400
5,458
5,493
5,535
5,574
5,611
Valores Críticos da Studentized Range - Continuação
UA 2003/2004
CMM
24/26
TABELAS DE ESTATÍSTICA
α = 1%
v\k
20
22
24
26
28
30
32
34
36
1
298,000 304,700 310,800 316,300 321,300 326,000 330,300 334,300 338,000
2
37,950
38,760
39,490
40,150
40,760
41,320
41,840
42,330
42,780
3
19,770
20,170
20,530
20,860
21,160
21,440
21,700
21,950
22,170
4
14,400
14,680
14,630
15,160
15,370
15,570
15,750
15,920
16,080
5
11,930
12,160
12,360
12,540
12,710
12,870
13,020
13,150
13,280
6
10,540
10,730
10,910
11,060
11,210
11,340
11,470
11,580
11,690
7
9,646
9,815
9,970
10,110
10,240
10,360
10,470
10,580
10,670
8
9,027
9,182
9,322
9,450
9,569
9,678
9,779
9,874
9,964
9
8,573
8,717
8,847
8,966
9,075
9,177
9,271
9,360
9,443
10
8,226
8,361
8,483
8,595
8,698
8,794
8,883
8,966
9,044
11
7,952
8,080
8,196
8,303
8,400
8,491
88,640
8,654
8,728
12
7,731
7,853
7,964
8,066
8,159
8,246
8,327
8,402
8,473
13
7,548
7,665
7,772
7,870
7,960
8,043
8,121
8,193
8,262
14
7,395
7,508
7,611
7,705
7,792
7,873
7,948
8,018
8,080
15
7,264
7,374
7,474
7,566
7,650
7,728
7,800
7,869
7,932
16
7,152
7,258
7,356
7,445
7,527
7,602
7,673
7,739
7,802
17
7,053
7,158
7,253
7,340
7,420
7,493
7,563
7,627
7,687
18
6,968
7,070
7,163
7,247
7,325
7,398
7,465
7,528
7,587
19
6,891
6,992
7,082
7,166
7,242
7,313
7,379
7,440
7,498
20
6,823
6,922
7,011
7,092
7,168
7,237
7,302
7,362
7,419
24
6,612
6,705
6,789
6,865
6,936
7,001
7,062
7,119
7,173
30
6,407
6,494
6,572
6,644
6,710
6,772
6,828
6,881
6,932
40
6,209
6,289
6,362
6,429
6,490
6,547
6,600
6,650
6,697
60
6,015
6,090
6,158
6,220
6,277
6,330
6,378
6,424
6,467
120
5,827
5,897
5,959
6,016
6,069
6,117
6,162
6,204
6,244
∞
5,645
5,709
5,766
5,818
5,866
5,911
5,952
5,990
6,026
UA 2003/2004
CMM
25/26
TABELAS DE ESTATÍSTICA
Valores Críticos da Studentized Range Conclusão
α = 1%
v\k
38
40
50
60
70
80
90
100
1
341,500 344,800 358,900 370,100 379,400 387,300 394,100 400,100
2
43,210
43,610
45,330
46,700
47,830
48,800
49,640
50,380
3
22,390
22,590
23,450
24,130
24,710
25,190
25,620
25,990
4
16,230
16,370
16,980
17,460
17,860
18,200
18,500
18,770
5
13,400
13,520
14,000
14,390
14,720
14,990
15,230
15,450
6
11,800
11,900
12,310
12,650
12,920
13,160
13,370
13,550
7
10,770
10,850
11,230
11,520
11,770
11,990
12,170
12,340
8
10,050
10,130
10,470
10,750
10,970
11,170
11,340
11,490
9
9,521
9,594
9,912
10,170
10,380
10,570
10,730
10,870
10
9,117
9,187
9,486
9,726
9,927
10,100
10,250
10,390
11
8,798
8,864
9,148
9,377
9,568
9,732
9,875
10,000
12
8,539
8,603
8,875
9,094
9,277
9,434
9,571
9,693
13
8,326
8,387
8,648
8,859
9,035
9,187
9,318
9,436
14
8,146
8,204
8,457
8,861
8,832
8,978
9,106
9,219
15
7,992
8,049
8,295
8,492
8,658
8,800
8,924
9,035
16
7,860
7,916
8,154
8,347
8,507
8,646
8,767
8,874
17
7,745
7,799
8,031
8,219
8,377
8,511
8,630
8,735
18
7,643
7,696
7,924
8,107
8,261
8,393
8,508
8,611
19
7,553
7,605
7,828
8,008
8,159
8,288
8,401
8,502
20
7,473
7,523
7,742
7,919
8,067
8,194
8,305
8,404
24
7,223
7,270
7,476
7,642
7,780
7,900
8,004
8,097
30
6,978
7,023
7,215
7,370
7,500
7,611
7,709
7,796
40
6,740
6,782
6,960
7,104
7,225
7,328
7,419
7,500
60
6,507
6,546
6,710
6,843
6,954
7,050
7,133
7,207
120
6,281
6,316
6,467
6,588
6,689
6,776
6,852
6,919
∞
6,060
6,092
6,228
6,338
6,429
6,507
6,575
6,636
Tabela dos Factores de Correcção para σ e para µR (d2 e d3)
UA 2003/2004
CMM
26/26
TABELAS DE ESTATÍSTICA
Constantes para as Cartas X e R (A2, D3 e D4)
Números de
Observações
no subgrupo
n
2
3
4
5
6
7
8
9
10
Factor d2
d2 =
R
σ
Factor d3
d3 =
1,128
1,693
2,059
2,326
2,534
2,704
2,847
2,970
3,078
σR
σ
0,8525
0,8884
0,8798
0,8641
0,848
0,8332
0,8198
0,8078
0,7971
Carta - R
Carta - X
A2
D3
D4
1,8806
1,0231
0,7285
0,5768
0,4833
0,4193
0,3726
0,3367
0,3082
0
0
0
0
0
0,0756
0,1361
0,1840
0,2231
3,2673
2,5742
2,2819
2,1145
2,0039
1,9244
1,8639
1,8160
1,7769
µ,σ
σ) - Quantis Qn;αα
Pontos Percentuais de Wn, em modelos Normais (µ
α
0,001
0,005
0,01
0,025
0,05
0,95
0,975
0,99
0,995
0,999
UA 2003/2004
2
0
0,01
0,02
0,04
0,09
2,77
3,17
3,64
3,97
4,65
3
0,06
0,13
0,19
0,30
0,43
3,31
3,68
4,12
4,42
5,06
4
0,20
0,34
0,43
0,59
0,76
3,63
3,98
4,40
4,96
5,31
5
0,37
0,55
0,66
0,85
1,03
3,86
4,20
4,60
4,89
5,48
n
6
0,54
0,75
0,87
1,06
1,25
4,03
4,36
4,76
5,03
5,62
7
0,69
0,92
1,05
1,25
1,44
4,17
4,49
4,88
5,15
5,73
8
0,83
1,08
1,20
1,41
1,60
4,29
4,61
4,99
5,26
5,28
9
0,96
1,21
1,34
1,55
1,74
4,39
4,70
5,08
5,34
5,90
10
1,08
1,33
1,47
1,67
1,86
4,47
4,79
5,16
5,42
5,97
CMM