The Shape of the Student's t distribution is determined by the degrees of freedom. As shown in the animation above, its shape changes as the degrees of freedom increases. For more information on how this distribution is used in hypothesis testing, see t-test for independent samples and t-test for dependent samples in Basic Statistics and Tables. See also, Student's t Distribution. As indicated by the chart below, the areas given at the top of this table are the right tail areas for the t-value inside the table. To determine the 0.05 critical value from the t-distribution with 6 degrees of freedom, look in the 0.05 column at the 6 row: t(.05,6) = 1.943180.
t table with right tail probabilities
df\p
|
0.4
|
0.25
|
0.1
|
0.05
|
0.025
|
0.01
|
0.005
|
0.0005
|
1
|
0.32492
|
1
|
3.077684
|
6.313752
|
12.7062
|
31.82052
|
63.65674
|
636.6192
|
2
|
0.288675
|
0.816497
|
1.885618
|
2.919986
|
4.30265
|
6.96456
|
9.92484
|
31.5991
|
3
|
0.276671
|
0.764892
|
1.637744
|
2.353363
|
3.18245
|
4.5407
|
5.84091
|
12.924
|
4
|
0.270722
|
0.740697
|
1.533206
|
2.131847
|
2.77645
|
3.74695
|
4.60409
|
8.6103
|
5
|
0.267181
|
0.726687
|
1.475884
|
2.015048
|
2.57058
|
3.36493
|
4.03214
|
6.8688
|
6
|
0.264835
|
0.717558
|
1.439756
|
1.94318
|
2.44691
|
3.14267
|
3.70743
|
5.9588
|
7
|
0.263167
|
0.711142
|
1.414924
|
1.894579
|
2.36462
|
2.99795
|
3.49948
|
5.4079
|
8
|
0.261921
|
0.706387
|
1.396815
|
1.859548
|
2.306
|
2.89646
|
3.35539
|
5.0413
|
9
|
0.260955
|
0.702722
|
1.383029
|
1.833113
|
2.26216
|
2.82144
|
3.24984
|
4.7809
|
10
|
0.260185
|
0.699812
|
1.372184
|
1.812461
|
2.22814
|
2.76377
|
3.16927
|
4.5869
|
11
|
0.259556
|
0.697445
|
1.36343
|
1.795885
|
2.20099
|
2.71808
|
3.10581
|
4.437
|
12
|
0.259033
|
0.695483
|
1.356217
|
1.782288
|
2.17881
|
2.681
|
3.05454
|
4.3178
|
13
|
0.258591
|
0.693829
|
1.350171
|
1.770933
|
2.16037
|
2.65031
|
3.01228
|
4.2208
|
14
|
0.258213
|
0.692417
|
1.34503
|
1.76131
|
2.14479
|
2.62449
|
2.97684
|
4.1405
|
15
|
0.257885
|
0.691197
|
1.340606
|
1.75305
|
2.13145
|
2.60248
|
2.94671
|
4.0728
|
16
|
0.257599
|
0.690132
|
1.336757
|
1.745884
|
2.11991
|
2.58349
|
2.92078
|
4.015
|
17
|
0.257347
|
0.689195
|
1.333379
|
1.739607
|
2.10982
|
2.56693
|
2.89823
|
3.9651
|
18
|
0.257123
|
0.688364
|
1.330391
|
1.734064
|
2.10092
|
2.55238
|
2.87844
|
3.9216
|
19
|
0.256923
|
0.687621
|
1.327728
|
1.729133
|
2.09302
|
2.53948
|
2.86093
|
3.8834
|
20
|
0.256743
|
0.686954
|
1.325341
|
1.724718
|
2.08596
|
2.52798
|
2.84534
|
3.8495
|
21
|
0.25658
|
0.686352
|
1.323188
|
1.720743
|
2.07961
|
2.51765
|
2.83136
|
3.8193
|
22
|
0.256432
|
0.685805
|
1.321237
|
1.717144
|
2.07387
|
2.50832
|
2.81876
|
3.7921
|
23
|
0.256297
|
0.685306
|
1.31946
|
1.713872
|
2.06866
|
2.49987
|
2.80734
|
3.7676
|
24
|
0.256173
|
0.68485
|
1.317836
|
1.710882
|
2.0639
|
2.49216
|
2.79694
|
3.7454
|
25
|
0.25606
|
0.68443
|
1.316345
|
1.708141
|
2.05954
|
2.48511
|
2.78744
|
3.7251
|
26
|
0.255955
|
0.684043
|
1.314972
|
1.705618
|
2.05553
|
2.47863
|
2.77871
|
3.7066
|
27
|
0.255858
|
0.683685
|
1.313703
|
1.703288
|
2.05183
|
2.47266
|
2.77068
|
3.6896
|
28
|
0.255768
|
0.683353
|
1.312527
|
1.701131
|
2.04841
|
2.46714
|
2.76326
|
3.6739
|
29
|
0.255684
|
0.683044
|
1.311434
|
1.699127
|
2.04523
|
2.46202
|
2.75639
|
3.6594
|
30
|
0.255605
|
0.682756
|
1.310415
|
1.697261
|
2.04227
|
2.45726
|
2.75
|
3.646
|
inf
|
0.253347
|
0.67449
|
1.281552
|
1.644854
|
1.95996
|
2.32635
|
2.57583
|
3.2905
|
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