Shortage and inequalities in the distribution of specialists across community health centres in Uttar Pradesh, 2002–2012

Singh, Aditya

doi:10.1186/s12913-019-4134-x

Table 8 Computing Decomposable Theil ‘T’: An Example

From: Shortage and inequalities in the distribution of specialists across community health centres in Uttar Pradesh, 2002–2012

CHC S.N.	District	# of specialists (y_i)	Share of specialists (s_i)	Average # of specialists in district (\( {\overline{y}}_i\Big) \)	\( \frac{{\overline{y}}_i}{\overline{y}} \)	\( \ln \left(\frac{{\overline{y}}_i}{\overline{y}}\right) \)	Between-district inequality values for districts \( {s}_i\ln \left(\frac{{\overline{y}}_i}{\overline{y}}\right) \)	\( \frac{y_i}{{\overline{y}}_i} \)	\( \ln \left(\frac{y_i}{{\overline{y}}_i}\right) \)	\( \frac{y_i}{{\overline{y}}_i}\ln \left(\frac{y_i}{{\overline{y}}_i}\right) \)	District Theil T T_i	Within-district inequality value for districts s_iT_i
1	South	3						0.68	−0.38	−0.26
2	South	4						0.91	−0.10	−0.09
3	South	5						1.14	0.13	0.15
4	South	6						1.36	0.31	0.42
5	South	4						0.91	−0.10	−0.09
	Total South	22	0.36 (22/61)	4.4 (22/5)	1.15	0.14	0.05			\( \sum \limits_{i=1}^N\frac{y_i}{{\overline{y}}_i}\ln \left(\frac{y_i}{{\overline{y}}_i}\right)= \)0.13	0.03	0.01
6	North	3						1.25	0.22	0.28
7	North	1						0.42	−0.88	−0.36
8	North	2						0.83	−0.18	− 0.15
9	North	1						0.42	−0.88	−0.36
10	North	5						2.08	0.73	1.53
	Total North	12	0.20 (12/61)	2.4 (12/5)	0.63	−0.46	−0.09			\( \sum \limits_{i=1}^N\frac{y_i}{{\overline{y}}_i}\ln \left(\frac{y_i}{{\overline{y}}_i}\right)= \)0.93	0.19	0.04
11	West	3						0.67	−0.41	−0.27
12	West	5						1.11	0.11	0.12
13	West	2						0.44	−0.81	−0.36
14	West	7						1.56	0.44	0.69
15	West	9						2.00	0.69	1.39
16	West	1						0.22	−1.50	−0.33
	Total West	27	0.44(27/61)	4.5 (27/6)	1.18	0.17	0.07			1.23	0.20	0.09
	Total All CHCs	61
Average number of specialist per CHC in the province		3.81 \( \Big(\overline{y} \))	Overall between-district inequality \( \sum \limits_{i=0}^m{s}_i\ln \left(\frac{{\overline{y}}_i}{\overline{y}}\right) \) 0.03			Overall within-district inequality \( \sum \limits_{i=0}^m{s}_i{T}_i \) 0.14		Overall Theil T \( \sum \limits_{i=0}^m{s}_i{T}_i+\sum \limits_{i=0}^m{s}_i\ln \left(\frac{{\overline{y}}_i}{\overline{y}}\right) \) 0.17

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ISSN: 1472-6963

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