Table 1 Sample from \(\hat{R_{\mathbbm{T}}\ }\) and \(\hat{H_{\mathbbm{T}}\ }\) (panel a), ranking matrix (panel b) and hierarchy matrix (panel c) of the hypothetical network of three treatments t₁, t₂ and t₃ of Fig. 1

\({{r}_{{t}_{1}}}^{\ast}={3}\)

\({{r}_{{t}_{2}}}^{\ast}={2}\)

\({{r}_{{t}_{3}}}^{\ast}={1}\)

t₃

t₂

t₁

1st

2nd

3rd

h_l

\({p}_{{h}_{l}}\)

\({{r}_{{t}_{1}}}^{\ast}={2}\)

\({{r}_{{t}_{2}}}^{\ast}={1}\)

\({{r}_{{t}_{3}}}^{\ast}={3}\)

t₂

t₁

t₃

t₁

25%

50%

25%

{t₃, t₁, t₂} (h₁)

25%

\({{r}_{{t}_{1}}}^{\ast}={1}\)

\({{r}_{{t}_{3}}}^{\ast}={2}\)

\({{r}_{{t}_{2}}}^{\ast}={3}\)

t₁

t₃

t₂

t₂

30%

40%

30%

{t₂, t₁, t₃} (h₂)

25%

\({{r}_{{t}_{1}}}^{\ast}={2}\)

\({{r}_{{t}_{2}}}^{\ast}={3}\)

\({{r}_{{t}_{3}}}^{\ast}={1}\)

t₃

t₁

t₂

t₃

45%

10%

45%

{t₃, t₂, t₁} (h₃)

20%

\({{r}_{{t}_{1}}}^{\ast}={1}\)

\({{r}_{{t}_{2}}}^{\ast}={2}\)

\({{r}_{{t}_{3}}}^{\ast}={3}\)

t₁

t₂

t₃

{t₁, t₂, t₃} (h₄)

20%

\({{r}_{{t}_{1}}}^{\ast}={2}\)

\({{r}_{{t}_{2}}}^{\ast}={1}\)

\({{r}_{{t}_{3}}}^{\ast}={3}\)

t₂

t₁

t₃

{t₂, t₃, t₁} (h₅)

5%

\({{r}_{{t}_{1}}}^{\ast}={2}\)

\({{r}_{{t}_{2}}}^{\ast}={3}\)

\({{r}_{{t}_{3}}}^{\ast}={1}\)

t₃

t₁

t₂

{t₁, t₃, t₂} (h₆)

5%

\({{r}_{{t}_{1}}}^{\ast}={1}\)

\({{r}_{{t}_{2}}}^{\ast}={2}\)

\({{r}_{{t}_{3}}}^{\ast}={3}\)

t₁

t₂

t₃

\({{r}_{{t}_{1}}}^{\ast}={2}\)

\({{r}_{{t}_{2}}}^{\ast}={1}\)

\({{r}_{{t}_{3}}}^{\ast}={3}\)

t₂

t₁

t₃

\({{r}_{{t}_{1}}}^{\ast}={3}\)

\({{r}_{{t}_{2}}}^{\ast}={2}\)

\({{r}_{{t}_{3}}}^{\ast}={1}\)

t₃

t₂

t₁

…

…

…