Table 1 Examples of weights on same-division states and other-division states

Example 1

Treatment 1

.24

2

.26

2

Treatment 2

.24

2

.26

2

Treatment 3

.24

2

.26

2

Treatment 4

.24

2

.26

2

Treatment 5

.02

2

.02

48

ADRZ calculation (equation (1))

$\frac{\left\{\frac{8\times 0.24+2\times 0.02}{5}\right\}/\left\{\frac{10}{5}\right\}}{\left\{\frac{8\times 0.26+48\times 0.02}{5}\right\}/\left\{\frac{56}{5}\right\}}=3.61$

Equation (2) calculation

$\frac{\left\{4\times \left(\frac{0.48}{2}\right)+1\times \left(\frac{0.04}{2}\right)\right\}/5}{\left\{4\times \left(\frac{0.52}{2}\right)+1\times \left(\frac{0.96}{48}\right)\right\}/5}=0.925$

Example 2

Treatment 1

.24

2

.26

2

Treatment 2

.24

2

.26

2

Treatment 3

.24

2

.26

2

Treatment 4

.24

2

.26

2

Treatment 5

.01

4

.01

96

ADRZ calculation (equation (1))

$\frac{\left\{\frac{8\times 0.24+4\times 0.01}{5}\right\}/\left\{\frac{12}{5}\right\}}{\left\{\frac{8\times 0.26+96\times 0.01}{5}\right\}/\left\{\frac{104}{5}\right\}}=5.59$

Equation (2) calculation

$\frac{\left\{4\times \left(\frac{0.48}{2}\right)+1\times \left(\frac{0.04}{4}\right)\right\}/5}{\left\{4\times \left(\frac{0.52}{2}\right)+1\times \left(\frac{0.96}{96}\right)\right\}/5}=0.924$