Table 6.

Detailed illustration of the impact of different reference values on pairwise inequity comparisons: two examples

Panel A: Equation (12); variance; DU; standardization; education versus exercise
				r̃k=dF75m		r̃k=dF6074
circumstance	βj	$VAR\left(c_{ij}^{\mathit{\text{educ}}}\right)$	$VAR\left(c_{ij}^{\mathit{\text{exer}}}\right)$	${\sum }_{k=1}^K{\delta }_{jk}{\mathrm{r̃}}_k$	term 1μ	${\sum }_{k=1}^K{\delta }_{jk}{\mathrm{r̃}}_k$	term 1μ
lowedu	0.0141	0.0000	0.1904	0.0290	−0.0004	0.0733	−0.0015
smoke	0.0285	0.2079	0.2079	−0.0845	0	0.0711	0
underweight	0.0520	0.0120	0.0120	0.1048	0	0.1736	0
obese	0.0104	0.1082	0.1082	−0.0206	0	0.0369	0
nosport	0.0155	0.2481	0.0000	0.1451	0.0064	0.0393	0.0007
sum term 1					0.0060		−0.0007
sum term 2£					−0.0004		0.0001
diff var*					0.0056		−0.0006
Panel B: Equation (10); absolute Gini; DU; control; education versus exercise
		r̃k=smoke,underweight,nosport				r̃k=nosmoke,normal,sport
circumstance	βj	${\sum }_{k=1}^K{\delta }_{jk}{\mathrm{r̃}}_k$	ACeduc	ACexer	eq. (10)	${\sum }_{k=1}^K{\delta }_{jk}{\mathrm{r̃}}_k$	ACeduc	ACexer	eq. (10)
dM4059	0.0002	−0.0076	−0.2088	−0.1811	0.0002	0	−0.0186	−0.0510	0.0000
dM6074	0.1487	0.3152	0.0875	0.0875	0.0000	0	0.0875	0.0875	0.0000
dF6074	0.0471	0.2839	0.0520	0.0520	0.0000	0	0.0520	0.0520	0.0000
dM75m	0.6155	0.2600	0.0436	0.0436	0.0000	0	0.0436	0.0436	0.0000
dF75m	0.4625	0.1654	0.0531	0.0531	0.0000	0	0.0531	0.0531	0.0000
lowedu	0.0141		0	0.1157	−0.0016		0	0.1157	−0.0016
dM4059 * lowedu	0.0249			0.0083	−0.0002			0.0083	−0.0002
dM6074 * lowedu	0.0731			0.0255	−0.0019			0.0255	−0.0019
dF6074 * lowedu	0.0733			0.0275	−0.0020			0.0275	−0.0020
dM75 * lowmedu	0.0616			0.0171	−0.0011			0.0171	−0.0011
dF75 * lowedu	0.0290			0.0319	−0.0009			0.0319	−0.0009
sum eq. (10)					−0.0075				−0.0077

Note:

^μ: ${({\beta }_j+{\sum }_{k=1}^K{\delta }_{jk}{\mathrm{r̃}}_k)}^2\left[VAR\right(c_{ij}^{\mathit{\text{educ}}})-VAR(c_{ij}^{\mathit{\text{exer}}}\left)\right]$.

^£: $\text{sum term}2={\sum }_{j=1}^J\{2{\sum }_{l>j}^J({\beta }_j+{\sum }_{k=1}^K{\delta }_{jk}{\mathrm{r̃}}_k)({\beta }_l+{\sum }_{k=1}^K{\delta }_{lk}{\mathrm{r̃}}_k)[COV(c_{ij}^{\mathit{\text{educ}}},c_{il}^{\mathit{\text{educ}}})-COV(c_{ij}^{\mathit{\text{exer}}},c_{il}^{\mathit{\text{exer}}})\left]\right\}$.

^*: $\text{diff var}=VAR(d{u}_i^{\mathit{\text{educ}}})-VAR(d{u}_i^{\mathit{\text{exer}}})$.

$A{C}^x=AC(c_{ij}^x;d{u}_i^x({\mathrm{r̃}}_k))$