Simpson’s paradox: a demographic case study of population dynamics, poverty, and inequality

Guimarães, Raphael Mendonça; Andrade, Flávia Cristina Drumond

doi:10.1590/1413-812320212610.10902021

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ARTICLE • Ciênc. saúde coletiva 26 (10) • Oct 2021 • https://doi.org/10.1590/1413-812320212610.10902021 copy

Simpson’s paradox: a demographic case study of population dynamics, poverty, and inequality

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Brazil is undergoing a demographic transition characterized by regional inequalities. It is reasonable to assume that aspects related to poverty, development and inequality might reverse the sign of the association of indicators of demographic transition, exemplifying a phenomenon known as Simpson’s Paradox. The aim of this study was to analyze the effect of inequality, poverty and social development on population dynamics in Brazil, verifying the occurrence of Simpson’s paradox in demographic transition. We used population data from the 1991, 2000 and 2010 national censuses, broken down by age and federative unit (FU). The correlation between demographic indicators was assessed by stratifying the FUs into groups according to their median social indicators. The findings show that all FUs have progressed against social indicators and are undergoing demographic transition; however, despite reductions in disparities over the study period, persistent gaps exist between regions. Simpson’s paradox was present when the analysis was carried out by census year and social indicators, and was particularly pronounced in 1991. The main challenge is to define how to analyze demographic dynamics in Brazil and understand how contextual factors alter the pace, quantum, and pattern of demographic transition.

Key words:
Demography; Demographic transition; Poverty; Inequality; Development

Dimension	Social Indicator	Indicator value	Correlation	1991			2000			2010
Dimension	Social Indicator	Indicator value	Correlation	Low	High	Total	Low	High	Total	Low	High	Total
Inequality	Gini coefficient	-	CBR x CMR	-0.547	-0.795	0.183 0.362	-0.420	-0.505	0.057 0.797	-0.464	-0.330	-0.289 0.144
Inequality	Gini coefficient	-	p-value	0.043	0.001		0.135	0.203		0.213	0.171
Development	HDI	+	CBR x CMR	-0.686	-0.775		-0.464	-0.456		-0.493	-0.448
Development	HDI	+	p-value	0.007	0.002		0.213	0.117		0.106	0.054
Poverty	% of pop living in extreme poverty	-	CBR x CMR	-0.768	-0.649		-0.420	-0.505		-0.458	-0.418
Poverty	% of pop living in extreme poverty	-	p-value	0.001	0.016		0.135	0.103		0.049	0.065
Income	Average income per capita	+	CBR x CMR	-0.686	-0.775		-0.363	-0.313		-0.481	-0.520
Income	Average income per capita	+	p-value	0.007	0.002		0.203	0.207		0.008	0.039

		Gini 1991	Gini 2000	Gini 2010	HDI 1991	HDI 2000	HDI 2010	% Poverty 1991	% Poverty 2000	% Poverty 2010	Income 1991	Income 2000	Income 2010	CBR 1991	CMR 1991	CBR 2000	CBR 2010	CMR 2000	CMR 2010
Gini 1991	r	1	0.829	0.681	-0.641	-0.661	-0.643	0.753	0.686	0.623	-0.548	-0.565	-0.521	0.246	0.609	0.102	0.138	0.453	0.400
Gini 1991	p		<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	0.001	0.003	0.002	0.005	0.216	0.001	0.613	0.492	0.018	0.039
Gini 2000	r	0.829	1	0.842	-0.700	-0.777	-0.736	0.737	0.839	0.781	-0.553	-0.634	-0.589	0.498	0.512	0.413	0.468	0.396	0.231
Gini 2000	p	<0.001		<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	0.003	<0.001	0.001	0.008	0.006	0.032	0.014	0.041	0.247
Gini 2010	r	0.681	0.842	1	-0.460	-0.583	-0.561	0.533	0.698	0.748	-0.259	-0.412	-0.394	0.562	0.332	0.571	0.612	0.313	0.071
Gini 2010	p	<0.001	<0.001		0.016	0.001	0.002	0.004	<0.001	<0.001	0.192	0.033	0.042	0.002	0.090	0.002	0.001	0.112	0.724
HDI 1991	r	-0.641	-0.700	-0.460	1	0.971	0.943	-0.915	-0.890	-0.838	0.932	0.946	0.914	-0.619	-0.484	-0.432	-0.478	-0.433	-0.333
HDI 1991	p	<0.001	<0.001	0.016		<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	0.001	0.011	0.024	0.012	0.024	0.089
IHDI 2000	r	-0.661	-0.777	-0.583	0.971	1	0.979	-0.910	-0.938	-0.892	0.898	0.937	0.908	-0.636	-0.523	-0.478	-0.529	-0.476	-0.348
IHDI 2000	p	<0.001	<0.001	0.001	<0.001		<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	0.005	0.012	0.005	0.012	0.075
HDI 2010	r	-0.643	-0.736	-0.561	0.943	0.979	1	-0.894	-0.920	-0.896	0.906	0.949	0.941	-0.593	-0.562	-0.457	-0.504	-0.528	-0.401
HDI 2010	p	<0.001	<0.001	0.002	<0.001	<0.001		<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	0.001	0.002	0.016	0.007	0.005	0.038
Poverty 1991	r	0.753	0.737	0.533	-0.915	-0.910	-0.894	1	0.936	0.864	-0.866	-0.867	-0.823	0.433	0.702	0.285	0.328	0.599	0.505
Poverty 1991	p	<0.001	<0.001	0.004	<0.001	<0.001	<0.001		<0.001	<0.001	<0.001	<0.001	<0.001	0.024	<0.001	0.149	0.095	0.001	0.007
Poverty 2000	r	0.686	0.839	0.698	-0.890	-0.938	-0.920	0.936	1	0.962	-0.803	-0.867	-0.831	0.610	0.592	0.497	0.547	0.525	0.357
Poverty 2000	p	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001		<0.001	<0.001	<0.001	<0.001	0.001	0.001	0.008	0.003	0.005	0.067
Poverty 2010	r	0.623	0.781	0.748	-0.838	-0.892	-0.896	0.864	0.962	1	-0.728	-0.827	-0.811	0.698	0.474	0.626	0.683	0.463	0.261
Poverty 2010	p	0.001	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001		<0.001	<0.001	<0.001	<0.001	0.013	<0.001	<0.001	0.015	0.188
Income 1991	r	-0.548	-0.553	-0.259	0.932	0.898	0.906	-0.866	-0.803	-0.728	1	0.972	0.949	-0.477	-0.547	-0.261	-0.301	-0.466	-0.396
Income 1991	p	0.003	0.003	0.192	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001		<0.001	<0.001	0.012	0.003	0.188	0.127	0.014	0.041
Income 2000	r	-0.565	-0.634	-0.412	0.946	0.937	0.949	-0.867	-0.867	-0.827	0.972	1	0.988	-0.605	-0.517	-0.434	-0.465	-0.465	-0.341
Income 2000	p	0.002	<0.001	0.033	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001		<0.001	0.001	0.006	0.024	0.015	0.015	0.081
Income 2010	r	-0.521	-0.589	-0.394	0.914	0.908	0.941	-0.823	-0.831	-0.811	0.949	0.988	1	-0.585	-0.515	-0.454	-0.476	-0.495	-0.376
Income 2010	p	0.005	0.001	0.042	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001		0.001	0.006	0.017	0.012	0.009	0.053
CBR 1991	r	0.246	0.498	0.562	-0.619	-0.636	-0.593	0.433	0.610	0.698	-0.477	-0.605	-0.585	1	-0.115	0.878	0.887	-0.098	-0.377
CBR 1991	p	0.216	0.008	0.002	0.001	<0.001	0.001	0.024	0.001	<0.001	0.012	0.001	0.001		0.569	<0.001	<0.001	0.627	0.052
CMR 1991	r	0.609	0.512	0.332	-0.484	-0.523	-0.562	0.702	0.592	0.474	-0.547	-0.517	-0.515	-0.115	1	-0.133	-0.143	0.877	0.828
CMR 1991	p	0.001	0.006	0.090	0.011	0.005	0.002	<0.001	0.001	0.013	0.003	0.006	0.006	0.569		0.510	0.477	<0.001	<0.001
CBR 2000	r	0.102	0.413	0.571	-0.432	-0.478	-0.457	0.285	0.497	0.626	-0.261	-0.434	-0.454	0.878	-0.133	1	0.970	-0.002	-0.312
CBR 2000	p	0.613	0.032	0.002	0.024	0.012	0.016	0.149	0.008	<0.001	0.188	0.024	0.017	<0.001	0.510		<0.001	0.992	0.113
CBR 2010	r	0.138	0.468	0.612	-0.478	-0.529	-0.504	0.328	0.547	0.683	-0.301	-0.465	-0.476	0.887	-0.143	0.970	1	0.013	-0.310
CBR 2010	p	0.492	0.014	0.001	0.012	0.005	0.007	0.095	0.003	<0.001	0.127	0.015	0.012	<0.001	0.477	<0.001		0.949	0.116
CMR 2000	r	0.453	0.396	0.313	-0.433	-0.476	-0.528	0.599	0.525	0.463	-0.466	-0.465	-0.495	-0.098	0.877	-0.002	0.013	1	0.865
CMR 2000	p	0.018	0.041	0.112	0.024	0.012	0.005	0.001	0.005	0.015	0.014	0.015	0.009	0.627	<0.001	0.992	0.949		<0.001
CMR 2010	r	0.400	0.231	0.071	-0.333	-0.348	-0.401	0.505	0.357	0.261	-0.396	-0.341	-0.376	-0.377	0.828	-0.312	-0.310	0.865	1
CMR 2010	p	0.039	0.247	0.724	0.089	0.075	0.038	0.007	0.067	0.188	0.041	0.081	0.053	0.052	<0.001	0.113	0.116	<0.001

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[1] Collaborations

All authors contributed to study conception, data collection and analysis, and writing and critically revising this manuscript.