Table 2.

Components of age standardization and decomposition procedures

	NH–White	NH–Black	Hispanic
Age-standardization
Total population: Pa	76,371	12,690	16,863
Crude incarceration rate (CIR): ∑Eij/Pi	590.8	4413.65	1936.13
Difference in CIR: Ti − T1	–	3823.85	1345.33
% Difference in CIR: (Ti − T1)/T1	–	6.47	2.27
∑tijP1j	–	2,940,562	1,190,196
Age adjusted incarceration rate: ∑TijP1j/P1	590.8	3850.36	1558.44
Difference in adjusted rate	–	3260.26	967.64
% Difference in adjusted rate	–	5.51	1.63
Decomposition analyses
Difference due to rate: $\sum \frac{\text{Tij}+\text{T}1\text{j}}{2}\left(\frac{\text{Pij}}{\text{Pi}}-\frac{\text{P}1\text{j}}{\text{P}1}\right)$	–	3504.19	1082.79
Difference due to age: $\sum \frac{\frac{\text{Pij}}{\text{Pi}}+\frac{\text{P}1\text{j}}{\text{P}1}}{2}\left(\text{Tij}-\text{T}1\text{j}\right)$	–	318.66	262.54
Proportion of difference in CIR due to rateb	–	0.916	0.805
Proportion on difference in CIR due ageb	–	0.083	0.195

^aIn thousands

^bRelative to the non-Hispanic white male population