47  \(\chi^2\) table

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The table below gives certain upper quantiles of chi-squared distributions with degrees of freedom parameters \(k =1,\dots,29\). The entry in row \(k\) in the column corresponding to probability \(\alpha\) gives the value of \(\chi^2_{k,\alpha}\), which is the value such that \(P(W > \chi^2_{k,\alpha}) = \alpha\), where \(W \sim \chi^2_{k,\alpha}\). For example, \(\chi^2_{26,0.10} = 35.563\) is the upper \(0.10\) quantile of the \(\chi^2_{26}\) distribution.

df <- c(1:29)
a <- c(0.990,0.975,0.950,0.900,0.750,0.250,0.100,0.050,0.025,0.010)

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(qchisq(1-a[j],df=df[i]),3)
    
  }

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

tab

     0.99  0.975   0.95    0.9   0.75  0.25   0.1  0.05 0.025  0.01
1   0.000  0.001  0.004  0.016  0.102  1.32  2.71  3.84  5.02  6.63
2   0.020  0.051  0.103  0.211  0.575  2.77  4.61  5.99  7.38  9.21
3   0.115  0.216  0.352  0.584  1.213  4.11  6.25  7.82  9.35 11.35
4   0.297  0.484  0.711  1.064  1.923  5.38  7.78  9.49 11.14 13.28
5   0.554  0.831  1.145  1.610  2.675  6.63  9.24 11.07 12.83 15.09
6   0.872  1.237  1.635  2.204  3.455  7.84 10.64 12.59 14.45 16.81
7   1.239  1.690  2.167  2.833  4.255  9.04 12.02 14.07 16.01 18.48
8   1.646  2.180  2.733  3.490  5.071 10.22 13.36 15.51 17.54 20.09
9   2.088  2.700  3.325  4.168  5.899 11.39 14.68 16.92 19.02 21.67
10  2.558  3.247  3.940  4.865  6.737 12.55 15.99 18.31 20.48 23.21
11  3.053  3.816  4.575  5.578  7.584 13.70 17.27 19.68 21.92 24.73
12  3.571  4.404  5.226  6.304  8.438 14.85 18.55 21.03 23.34 26.22
13  4.107  5.009  5.892  7.042  9.299 15.98 19.81 22.36 24.74 27.69
14  4.660  5.629  6.571  7.790 10.165 17.12 21.06 23.68 26.12 29.14
15  5.229  6.262  7.261  8.547 11.037 18.25 22.31 25.00 27.49 30.58
16  5.812  6.908  7.962  9.312 11.912 19.37 23.54 26.30 28.84 32.00
17  6.408  7.564  8.672 10.085 12.792 20.49 24.77 27.59 30.19 33.41
18  7.015  8.231  9.390 10.865 13.675 21.61 25.99 28.87 31.53 34.80
19  7.633  8.907 10.117 11.651 14.562 22.72 27.20 30.14 32.85 36.19
20  8.260  9.591 10.851 12.443 15.452 23.83 28.41 31.41 34.17 37.57
21  8.897 10.283 11.591 13.240 16.344 24.93 29.61 32.67 35.48 38.93
22  9.542 10.982 12.338 14.041 17.240 26.04 30.81 33.92 36.78 40.29
23 10.196 11.689 13.091 14.848 18.137 27.14 32.01 35.17 38.08 41.64
24 10.856 12.401 13.848 15.659 19.037 28.24 33.20 36.41 39.36 42.98
25 11.524 13.120 14.611 16.473 19.939 29.34 34.38 37.65 40.65 44.31
26 12.198 13.844 15.379 17.292 20.843 30.43 35.56 38.88 41.92 45.64
27 12.879 14.573 16.151 18.114 21.749 31.53 36.74 40.11 43.20 46.96
28 13.565 15.308 16.928 18.939 22.657 32.62 37.92 41.34 44.46 48.28
29 14.256 16.047 17.708 19.768 23.567 33.71 39.09 42.56 45.72 49.59