48  \(t\) table

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The entries of the \(t\) table give upper quantiles of several \(t\) distributions. The entry in the row for degrees of freedom \(k\) and tail probability \(\alpha\) is equal to \(t_{k,\alpha}\), which is the value such that \(P(T > t_{k,\alpha}) = \alpha\), where \(T \sim t_k\). For example, \(t_{26,0.025} = 2.0555\).

# t-table
df <- c(1:35,40,50,60,120,Inf)
a <- c(0.200,0.100,0.050,0.025,0.010,0.005,0.001)

ndf <- length(df)
na <- length(a)
tab <- matrix(NA,ndf,na)
for(i in 1:ndf)
  for(j in 1:na){
    
    tab[i,j] <- round(qt(1-a[j],df[i]),4)
    
  }

rownames(tab) <- df
colnames(tab) <- a

tab

       0.2   0.1  0.05  0.025   0.01  0.005   0.001
1   1.3764 3.078 6.314 12.706 31.820 63.657 318.309
2   1.0607 1.886 2.920  4.303  6.965  9.925  22.327
3   0.9785 1.638 2.353  3.182  4.541  5.841  10.214
4   0.9410 1.533 2.132  2.776  3.747  4.604   7.173
5   0.9195 1.476 2.015  2.571  3.365  4.032   5.893
6   0.9057 1.440 1.943  2.447  3.143  3.707   5.208
7   0.8960 1.415 1.895  2.365  2.998  3.499   4.785
8   0.8889 1.397 1.859  2.306  2.897  3.355   4.501
9   0.8834 1.383 1.833  2.262  2.821  3.250   4.297
10  0.8791 1.372 1.812  2.228  2.764  3.169   4.144
11  0.8755 1.363 1.796  2.201  2.718  3.106   4.025
12  0.8726 1.356 1.782  2.179  2.681  3.054   3.930
13  0.8702 1.350 1.771  2.160  2.650  3.012   3.852
14  0.8681 1.345 1.761  2.145  2.624  2.977   3.787
15  0.8662 1.341 1.753  2.131  2.603  2.947   3.733
16  0.8647 1.337 1.746  2.120  2.583  2.921   3.686
17  0.8633 1.333 1.740  2.110  2.567  2.898   3.646
18  0.8620 1.330 1.734  2.101  2.552  2.878   3.611
19  0.8610 1.328 1.729  2.093  2.539  2.861   3.579
20  0.8600 1.325 1.725  2.086  2.528  2.845   3.552
21  0.8591 1.323 1.721  2.080  2.518  2.831   3.527
22  0.8583 1.321 1.717  2.074  2.508  2.819   3.505
23  0.8575 1.319 1.714  2.069  2.500  2.807   3.485
24  0.8569 1.318 1.711  2.064  2.492  2.797   3.467
25  0.8562 1.316 1.708  2.059  2.485  2.787   3.450
26  0.8557 1.315 1.706  2.055  2.479  2.779   3.435
27  0.8551 1.314 1.703  2.052  2.473  2.771   3.421
28  0.8546 1.312 1.701  2.048  2.467  2.763   3.408
29  0.8542 1.311 1.699  2.045  2.462  2.756   3.396
30  0.8538 1.310 1.697  2.042  2.457  2.750   3.385
31  0.8534 1.310 1.696  2.039  2.453  2.744   3.375
32  0.8530 1.309 1.694  2.037  2.449  2.739   3.365
33  0.8526 1.308 1.692  2.034  2.445  2.733   3.356
34  0.8523 1.307 1.691  2.032  2.441  2.728   3.348
35  0.8520 1.306 1.690  2.030  2.438  2.724   3.340
40  0.8507 1.303 1.684  2.021  2.423  2.704   3.307
50  0.8489 1.299 1.676  2.009  2.403  2.678   3.261
60  0.8477 1.296 1.671  2.000  2.390  2.660   3.232
120 0.8446 1.289 1.658  1.980  2.358  2.617   3.159
Inf 0.8416 1.282 1.645  1.960  2.326  2.576   3.090