Critical values for the \(t\)-distribution
Table B.1: Critical values for the \(t\)-distribution, given the degrees of freedom (rows)
and tail probability \(p\) (columns). These can be used for critical
values for a given confidence level.
|
|
Confidence level
|
|
|
80%
|
90%
|
95%
|
96%
|
98%
|
99%
|
99.5%
|
99.8%
|
99.9%
|
|
|
Right-tail probability p
|
|
df
|
0.1
|
0.05
|
0.025
|
0.02
|
0.01
|
0.005
|
0.0025
|
0.001
|
0.0005
|
|
1
|
3.078
|
6.314
|
12.706
|
15.895
|
31.821
|
63.657
|
127.321
|
318.309
|
636.619
|
|
2
|
1.886
|
2.920
|
4.303
|
4.849
|
6.965
|
9.925
|
14.089
|
22.327
|
31.599
|
|
3
|
1.638
|
2.353
|
3.182
|
3.482
|
4.541
|
5.841
|
7.453
|
10.215
|
12.924
|
|
4
|
1.533
|
2.132
|
2.776
|
2.999
|
3.747
|
4.604
|
5.598
|
7.173
|
8.610
|
|
5
|
1.476
|
2.015
|
2.571
|
2.757
|
3.365
|
4.032
|
4.773
|
5.893
|
6.869
|
|
6
|
1.440
|
1.943
|
2.447
|
2.612
|
3.143
|
3.707
|
4.317
|
5.208
|
5.959
|
|
7
|
1.415
|
1.895
|
2.365
|
2.517
|
2.998
|
3.499
|
4.029
|
4.785
|
5.408
|
|
8
|
1.397
|
1.860
|
2.306
|
2.449
|
2.896
|
3.355
|
3.833
|
4.501
|
5.041
|
|
9
|
1.383
|
1.833
|
2.262
|
2.398
|
2.821
|
3.250
|
3.690
|
4.297
|
4.781
|
|
10
|
1.372
|
1.812
|
2.228
|
2.359
|
2.764
|
3.169
|
3.581
|
4.144
|
4.587
|
|
11
|
1.363
|
1.796
|
2.201
|
2.328
|
2.718
|
3.106
|
3.497
|
4.025
|
4.437
|
|
12
|
1.356
|
1.782
|
2.179
|
2.303
|
2.681
|
3.055
|
3.428
|
3.930
|
4.318
|
|
13
|
1.350
|
1.771
|
2.160
|
2.282
|
2.650
|
3.012
|
3.372
|
3.852
|
4.221
|
|
14
|
1.345
|
1.761
|
2.145
|
2.264
|
2.624
|
2.977
|
3.326
|
3.787
|
4.140
|
|
15
|
1.341
|
1.753
|
2.131
|
2.249
|
2.602
|
2.947
|
3.286
|
3.733
|
4.073
|
|
16
|
1.337
|
1.746
|
2.120
|
2.235
|
2.583
|
2.921
|
3.252
|
3.686
|
4.015
|
|
17
|
1.333
|
1.740
|
2.110
|
2.224
|
2.567
|
2.898
|
3.222
|
3.646
|
3.965
|
|
18
|
1.330
|
1.734
|
2.101
|
2.214
|
2.552
|
2.878
|
3.197
|
3.610
|
3.922
|
|
19
|
1.328
|
1.729
|
2.093
|
2.205
|
2.539
|
2.861
|
3.174
|
3.579
|
3.883
|
|
20
|
1.325
|
1.725
|
2.086
|
2.197
|
2.528
|
2.845
|
3.153
|
3.552
|
3.850
|
|
21
|
1.323
|
1.721
|
2.080
|
2.189
|
2.518
|
2.831
|
3.135
|
3.527
|
3.819
|
|
22
|
1.321
|
1.717
|
2.074
|
2.183
|
2.508
|
2.819
|
3.119
|
3.505
|
3.792
|
|
23
|
1.319
|
1.714
|
2.069
|
2.177
|
2.500
|
2.807
|
3.104
|
3.485
|
3.768
|
|
24
|
1.318
|
1.711
|
2.064
|
2.172
|
2.492
|
2.797
|
3.091
|
3.467
|
3.745
|
|
25
|
1.316
|
1.708
|
2.060
|
2.167
|
2.485
|
2.787
|
3.078
|
3.450
|
3.725
|
|
26
|
1.315
|
1.706
|
2.056
|
2.162
|
2.479
|
2.779
|
3.067
|
3.435
|
3.707
|
|
27
|
1.314
|
1.703
|
2.052
|
2.158
|
2.473
|
2.771
|
3.057
|
3.421
|
3.690
|
|
28
|
1.313
|
1.701
|
2.048
|
2.154
|
2.467
|
2.763
|
3.047
|
3.408
|
3.674
|
|
29
|
1.311
|
1.699
|
2.045
|
2.150
|
2.462
|
2.756
|
3.038
|
3.396
|
3.659
|
|
30
|
1.310
|
1.697
|
2.042
|
2.147
|
2.457
|
2.750
|
3.030
|
3.385
|
3.646
|
|
40
|
1.303
|
1.684
|
2.021
|
2.123
|
2.423
|
2.704
|
2.971
|
3.307
|
3.551
|
|
50
|
1.299
|
1.676
|
2.009
|
2.109
|
2.403
|
2.678
|
2.937
|
3.261
|
3.496
|
|
60
|
1.296
|
1.671
|
2.000
|
2.099
|
2.390
|
2.660
|
2.915
|
3.232
|
3.460
|
|
120
|
1.289
|
1.658
|
1.980
|
2.076
|
2.358
|
2.617
|
2.860
|
3.160
|
3.373
|
|
10000
|
1.282
|
1.645
|
1.960
|
2.054
|
2.327
|
2.576
|
2.808
|
3.091
|
3.291
|