1 × N $$C{D}_N={z}_{\alpha /{c}_1}\sqrt{nk\left( k+1\right)/6},\kern0.75em {c}_1= k-1$$ Demšar [2]
$$C{D}_M={m}_{\alpha, df= k-1,\rho ={\scriptscriptstyle \frac{1}{2}}}\sqrt{nk\left( k+1\right)/6}$$ Siegel and Castellan [18], Nemenyi [39], Miller [25], Hollander et al. [23], Zarr [20]
N × N $$C{D}_N={z}_{{\scriptscriptstyle \frac{1}{2}}\alpha /{c}_2}\sqrt{nk\left( k+1\right)/6},\kern0.5em {c}_2= k\left( k-1\right)/2$$ Siegel and Castellan [18], Gibbons and Chakraborti [21], Daniel [19], Hettmansperger [33], Sheskin [22]
$$\begin{array}{l} C{D}_Q = {q}_{\alpha, df= k,\infty}\sqrt{nk\left( k+1\right)/12}=\\ {}\kern3.25em \frac{q_{\alpha, df= k,\infty }}{\sqrt{2}}\sqrt{nk\left( k+1\right)/6}\end{array}$$ Nemenyi [39], Miller [25], Hollander et al. [23], Zarr [20], Desu and Raghavarao [40], Demšar [2]
$$C{D}_{\chi^2}=\sqrt{\chi_{\alpha, df= k-1}^2}\sqrt{nk\left( k+1\right)/6}$$ Miller [25], Bortz et al. [41], Wike [42]
1. Note: The constant $${m}_{\alpha, df= k-1,\rho ={\scriptscriptstyle \frac{1}{2}}}$$ is the upper αth percentile point for the distribution of the maximum of k − 1 equally correlated (ρ=.5) unit normal N(0, 1) random variables. The constant q α,df = k,∞ is the upper αth percentile point of the Studentized range (q) distribution with (k, ∞) degrees of freedom. The references in the right-most column are ordered by year of publication (of first edition).