# What is the t-distribution

## T distribution

The following table shows selected values ​​of the inverse distribution function of the T-distribution: T (1- | df). For selected degrees of freedom (df) and probabilities (1-) the corresponding t-values ​​(t-quantiles) are shown, for which the following applies: W (Tt | df) = (1-). (1-) corresponds to the red (dark) area in the following figure (i.e. the integral of the density function from - to t). An exact calculation is possible with the statistical internet calculator.

Reading example: Find the t-value below which 95% of all possible values ​​of a T-distributed random variable T lie with df = 17 degrees of freedom. In the row for df = 17 you will find the value t = 1.740 you are looking for in column (1 -) = 0.95.

df(red / dark) area (1-)
0,650,70,750,80,850,90,950,9750,990,995
10,5100,7271,0001,3761,9633,0786,31412,70631,82163,656
20,4450,6170,8161,0611,3861,8862,9204,3036,9659,925
30,4240,5840,7650,9781,2501,6382,3533,1824,5415,841
40,4140,5690,7410,9411,1901,5332,1322,7763,7474,604
50,4080,5590,7270,9201,1561,4762,0152,5713,3654,032
60,4040,5530,7180,9061,1341,4401,9432,4473,1433,707
70,4020,5490,7110,8961,1191,4151,8952,3652,9983,499
80,3990,5460,7060,8891,1081,3971,8602,3062,8963,355
90,3980,5430,7030,8831,1001,3831,8332,2622,8213,250
100,3970,5420,7000,8791,0931,3721,8122,2282,7643,169
110,3960,5400,6970,8761,0881,3631,7962,2012,7183,106
120,3950,5390,6950,8731,0831,3561,7822,1792,6813,055
130,3940,5380,6940,8701,0791,3501,7712,1602,6503,012
140,3930,5370,6920,8681,0761,3451,7612,1452,6242,977
150,3930,5360,6910,8661,0741,3411,7532,1312,6022,947
160,3920,5350,6900,8651,0711,3371,7462,1202,5832,921
170,3920,5340,6890,8631,0691,3331,7402,1102,5672,898
180,3920,5340,6880,8621,0671,3301,7342,1012,5522,878
190,3910,5330,6880,8611,0661,3281,7292,0932,5392,861
200,3910,5330,6870,8601,0641,3251,7252,0862,5282,845
210,3910,5320,6860,8591,0631,3231,7212,0802,5182,831
220,3900,5320,6860,8581,0611,3211,7172,0742,5082,819
230,3900,5320,6850,8581,0601,3191,7142,0692,5002,807
240,3900,5310,6850,8571,0591,3181,7112,0642,4922,797
250,3900,5310,6840,8561,0581,3161,7082,0602,4852,787
300,3890,5300,6830,8541,0551,3101,6972,0422,4572,750
400,3880,5290,6810,8511,0501,3031,6842,0212,4232,704
500,3880,5280,6790,8491,0471,2991,6762,0092,4032,678
600,3870,5270,6790,8481,0451,2961,6712,0002,3902,660
700,3870,5270,6780,8471,0441,2941,6671,9942,3812,648
800,3870,5260,6780,8461,0431,2921,6641,9902,3742,639
900,3870,5260,6770,8461,0421,2911,6621,9872,3682,632
1000,3860,5260,6770,8451,0421,2901,6601,9842,3642,626
1500,3860,5260,6760,8441,0401,2871,6551,9762,3512,609
2000,3860,5250,6760,8431,0391,2861,6531,9722,3452,601
5000,3860,5250,6750,8421,0381,2831,6481,9652,3342,586
10000,3850,5250,6750,8421,0371,2821,6461,9622,3302,581