Critical Values for F, p = .001
There are three separate charts of critical values for F, the outcome of the analysis of
variance (ANOVA) statistic, a chart of critical values for α = .05, a chart for α = .01, and a
chart for α = .001. Select the appropriate chart and note the degrees of freedom (df) for the
between-groups comparison across the top of the chart. For a 1-way, between-groups
ANOVA, the df between is the number of levels of the independent variable minus 1. The df
within is the number of participants minus the number of levels of the independent
variable. To find the critical value, locate the appropriate column and read down to the
appropriate df within. This chart should be used when the level of probability for
interpreting the study is set at p = .001.
◄df between ►
α = .001
df within
▼
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1
21.03960
19.68679
18.64332
17.81542
17.14336
16.58742
16.12020
15.72223
15.37931
15.08084
14.81878
14.58688
14.38026
14.19501
14.02801
13.87670
13.73897
13.61309
13.49759
13.39125
13.29301
13.20201
13.11745
13.03869
12.96515
12.89634
12.83180
12.77115
12.71406
12.66022
12.60936
12.56124
2
14.90536
13.81155
12.97367
12.31273
11.77887
11.33915
10.97099
10.65844
10.38991
10.15681
9.95262
9.77233
9.61199
9.46850
9.33935
9.22251
9.11631
9.01936
8.93051
8.84880
8.77340
8.70361
8.63882
8.57853
8.52228
8.46968
8.42039
8.37410
8.33055
8.28950
8.25075
8.21411
3
12.55275
11.56113
10.80420
10.20894
9.72937
9.33525
9.00594
8.72685
8.48745
8.27993
8.09838
7.93826
7.79601
7.66883
7.55446
7.45107
7.35717
7.27151
7.19306
7.12096
7.05446
6.99294
6.93586
6.88277
6.83325
6.78697
6.74361
6.70292
6.66464
6.62858
6.59454
6.56236
4
11.28275
10.34612
9.63273
9.07274
8.62232
8.25268
7.94420
7.68306
7.45928
7.26546
7.09603
6.94671
6.81415
6.69570
6.58924
6.49306
6.40574
6.32612
6.25323
6.18626
6.12452
6.06742
6.01447
5.96522
5.91931
5.87640
5.83622
5.79851
5.76305
5.72965
5.69813
5.66835
5
10.48072
9.57838
8.89211
8.35409
7.92181
7.56739
7.27186
7.02187
6.80778
6.62247
6.46056
6.31794
6.19138
6.07835
5.97679
5.88507
5.80182
5.72594
5.65650
5.59271
5.53391
5.47955
5.42915
5.38228
5.33859
5.29778
5.25956
5.22369
5.18998
5.15822
5.12826
5.09995
6
9.92561
9.04662
8.37881
7.85573
7.43577
7.09168
6.80493
6.56250
6.35497
6.17542
6.01861
5.88052
5.75802
5.64864
5.55040
5.46168
5.38119
5.30783
5.24071
5.17906
5.12226
5.06974
5.02105
4.97579
4.93360
4.89419
4.85729
4.82267
4.79013
4.75948
4.73057
4.70325
7
9.51745
8.65535
8.00087
7.48855
7.07747
6.74082
6.46039
6.22338
6.02057
5.84515
5.69199
5.55714
5.43755
5.33079
5.23491
5.14835
5.06982
4.99827
4.93280
4.87269
4.81729
4.76609
4.71863
4.67450
4.63339
4.59498
4.55902
4.52528
4.49357
4.46371
4.43555
4.40893
© Taylor & Francis 2014
8
9.20415
8.35479
7.71035
7.20615
6.80174
6.47068
6.19498
5.96204
5.76276
5.59043
5.43999
5.30757
5.19015
5.08533
4.99122
4.90626
4.82920
4.75898
4.69475
4.63577
4.58142
4.53120
4.48464
4.44136
4.40104
4.36337
4.32810
4.29502
4.26393
4.23465
4.20704
4.18094
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12.51564
12.47238
12.43127
12.39217
12.35492
12.31941
12.28550
12.25310
12.22211
12.19243
12.16399
12.13670
12.11051
12.08535
12.06115
12.03786
12.01544
11.99383
11.97299
11.95288
11.93347
11.91471
11.89658
11.87904
11.86207
11.84564
11.82972
11.81429
11.79932
11.78481
11.77072
11.75704
11.74375
11.73084
11.71828
11.70607
11.69419
11.68262
11.67136
11.66039
11.64971
11.63929
11.62914
11.61923
11.60957
11.60014
11.59093
11.58194
8.17941
8.14649
8.11524
8.08552
8.05722
8.03025
8.00451
7.97993
7.95642
7.93392
7.91236
7.89168
7.87184
7.85278
7.83446
7.81684
7.79987
7.78352
7.76776
7.75256
7.73788
7.72371
7.71001
7.69676
7.68394
7.67153
7.65952
7.64787
7.63658
7.62562
7.61500
7.60468
7.59465
7.58492
7.57545
7.56624
7.55729
7.54857
7.54009
7.53183
7.52378
7.51593
7.50828
7.50082
7.49355
7.48645
7.47952
7.47276
6.53190
6.50302
6.47560
6.44953
6.42472
6.40107
6.37851
6.35697
6.33637
6.31666
6.29778
6.27967
6.26230
6.24562
6.22959
6.21416
6.19932
6.18502
6.17123
6.15793
6.14510
6.13271
6.12073
6.10915
6.09795
6.08710
6.07660
6.06642
6.05656
6.04699
6.03771
6.02870
6.01994
6.01144
6.00317
5.99514
5.98732
5.97971
5.97230
5.96509
5.95807
5.95122
5.94455
5.93804
5.93169
5.92550
5.91945
5.91355
5.64015
5.61342
5.58805
5.56393
5.54098
5.51911
5.49825
5.47833
5.45928
5.44106
5.42361
5.40688
5.39083
5.37541
5.36060
5.34635
5.33264
5.31943
5.30670
5.29442
5.28257
5.27113
5.26007
5.24938
5.23904
5.22903
5.21934
5.20995
5.20085
5.19202
5.18345
5.17514
5.16706
5.15922
5.15159
5.14418
5.13697
5.12995
5.12312
5.11647
5.10999
5.10368
5.09753
5.09153
5.08567
5.07996
5.07439
5.06895
5.07315
5.04776
5.02365
5.00074
4.97893
4.95816
4.93835
4.91943
4.90135
4.88405
4.86748
4.85160
4.83636
4.82173
4.80767
4.79415
4.78113
4.76860
4.75652
4.74487
4.73363
4.72277
4.71228
4.70214
4.69233
4.68284
4.67365
4.66474
4.65611
4.64774
4.63961
4.63173
4.62407
4.61663
4.60940
4.60238
4.59554
4.58889
4.58241
4.57611
4.56997
4.56398
4.55815
4.55246
4.54692
4.54150
4.53622
4.53107
4.67739
4.65289
4.62963
4.60753
4.58650
4.56647
4.54736
4.52911
4.51168
4.49499
4.47902
4.46370
4.44901
4.43491
4.42136
4.40832
4.39578
4.38370
4.37205
4.36083
4.34999
4.33953
4.32942
4.31965
4.31020
4.30105
4.29219
4.28361
4.27529
4.26723
4.25940
4.25180
4.24443
4.23726
4.23030
4.22353
4.21694
4.21054
4.20430
4.19823
4.19231
4.18655
4.18093
4.17545
4.17011
4.16490
4.15981
4.15485
4.38375
4.35988
4.33722
4.31570
4.29522
4.27570
4.25710
4.23933
4.22235
4.20611
4.19055
4.17564
4.16134
4.14761
4.13441
4.12172
4.10951
4.09775
4.08642
4.07549
4.06494
4.05476
4.04492
4.03541
4.02621
4.01731
4.00869
4.00034
3.99224
3.98439
3.97678
3.96939
3.96221
3.95523
3.94846
3.94187
3.93546
3.92923
3.92316
3.91725
3.91150
3.90589
3.90042
3.89509
3.88990
3.88482
3.87988
3.87505
© Taylor & Francis 2014
4.15625
4.13285
4.11064
4.08954
4.06946
4.05034
4.03210
4.01469
3.99804
3.98212
3.96688
3.95226
3.93825
3.92479
3.91186
3.89942
3.88746
3.87593
3.86483
3.85412
3.84378
3.83381
3.82417
3.81485
3.80583
3.79711
3.78866
3.78048
3.77255
3.76486
3.75740
3.75016
3.74312
3.73629
3.72965
3.72320
3.71692
3.71081
3.70487
3.69908
3.69344
3.68795
3.68259
3.67737
3.67228
3.66731
3.66247
3.65773
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11.57316
11.56459
11.55620
11.54801
11.54000
11.53216
11.52450
11.51699
11.50965
11.50247
11.49543
7.46615
7.45969
7.45339
7.44722
7.44119
7.43530
7.42954
7.42389
7.41837
7.41297
7.40768
5.90779
5.90216
5.89666
5.89128
5.88603
5.88089
5.87586
5.87094
5.86613
5.86142
5.85681
5.06364
5.05845
5.05338
5.04842
5.04358
5.03884
5.03421
5.02968
5.02524
5.02090
5.01665
4.52603
4.52111
4.51631
4.51161
4.50702
4.50253
4.49814
4.49385
4.48965
4.48553
4.48151
4.15000
4.14526
4.14063
4.13611
4.13169
4.12737
4.12314
4.11901
4.11496
4.11100
4.10712
3.87033
3.86572
3.86122
3.85682
3.85252
3.84832
3.84420
3.84018
3.83624
3.83239
3.82862
© Taylor & Francis 2014
3.65311
3.64860
3.64419
3.63988
3.63567
3.63155
3.62752
3.62358
3.61973
3.61595
3.61226