SWDA Inequalities Dataset: Safe Water Drinking Water Access Indicator and Inequalities Indexes of Brazilian Municipalities

The SWDA Inequalities Dataset consist on results of Safe Drinking Water Access - SDWA indicators and inequalities indexes obtained by an adapted Lorenz Curve approach calculated for all Brazilian municipalities.The main datasource is the Brazillian 2010 Demographic Census, which is the last Population Census data publicaly available. The SDWA indicators are weighted by the SDWA values corresponding to census tracts considering permanent private household residents (Eq. 2). The safe drinking water sources are: (i) general water distribution network; (ii) well or spring located on the property; (iii) rainwater stored in a cistern, cement box, etc.; (iv) or well or spring outside the property, tank car, rainwater stored otherwise, river, dam, lake or stream, or another form of water supply. Considering that these drinking water sources differ in terms of accessibility, availability and water quality, the AHP Method was applied to obtain different weights for each form of water access (Eq. 1).

The Gini Index (G_water), Concentration Coefficient (C_water) and Dissimilarity Index (D_water), were adapted to analyze inequalities in SDWA. The Safe Drinking Water Concentration Index is obtained from the Lorenz Curve, with the percentage of residents in permanent households accumulated and ordered by per capita income in the abscissa of the graph (Eq. 3). The per capita income is obtained by the ratio between the total nominal monthly income and the number of residents of the permanent households of each census tract. The Safe Drinking Water Gini Index was similarly adapted, with the residents accumulated and ordered by the safe drinking water rate in the abscissa of the graph (Eq. 4).  The ratios between Upper and Lower Quintiles (R_8020) were obtained for each municipality, that is, the relationship between the rates of SDWA for permanent private households that represent 20% of the residents with the highest average per capita income (4th quintile represented by Q4) and the most economically unfavorable 20% (1st quintile represented by Q1) (Eq. 5). The Safe Drinking Water Dissimilarity Index is calculated by the weighted average of the absolute difference of the SDWA indicator of each quintile of the average per capita income and the average rate (Eq. 6). The inequalities indexes are also presented as normalized values (G_water_norm, C_water_norm, R_8020_norm, D_water_norm).

\(t_{water} = 0.376*t_{piped} + 0.309*t_{well} + 0.274*t_{cistern} + 0.041*t_{others} \;\;\;\;\;\;\;\;\;\; (Eq. 1) \)

\(0.041 \leq t_{water} \leq 0.368\)

\(t_{piped} + t_{well} + t_{cistern} + t_{others} = 1\)

t is the relationship between residents in permanent private households with access (piped, well, cistern and/or other) and the total number of residents in permanent private households.

\(SDWA = \frac{\sum_{i=1}^{n} (t_{water_{norm_i}}*p_i)}{\sum_{i=1}^{n}(p_i)} \;\;\;\;\;\;\;\;\;\; (Eq. 2)\)

considering the percentage of residents in permanent private households of each sector (pi) and the number of census tracts (n).

\(C_{water} = (p_{r_i}*t_{water_{norm_{i+1}}} - p_{r_{i+1}}*t_{water_{norm_{i}}}) + ... + (p_{r_{i-1}}*t_{water_{norm_{i}}} - p_{r_i}*t_{water_{norm_{i-1}}}) \;\;\;\;\;\;\;\;\;\; (Eq. 3)\)

where \(p_{r_i}\) stand for a percentage of residents in permanent private households ordered by average income per capita, with Cwater ranging between -1 and 1.

\(G_{water} = 1 - {\sum_{i=1}^{n}(p_{w_i}-p_{w_{i-1}})*(t_{water_{norm_i}} + t_{water_{norm_{i-1}}}}) \;\;\;\;\;\;\;\;\;\; (Eq. 4)\)

where \(p_{w_i}\)  is the percentage of residents in permanent private households ordered by the weighted water access rate ( \(t_{water_{norm}}\)), and Gwater ranging between 0 and 1.

\(R_{80/20} = \frac{t_{water_{norm_{Q_4}}}}{t_{water_{norm_{Q_1}}}} \;\;\;\;\;\;\;\;\;\; (Eq. 5)\)

with R80/20 ranging between 0 and ∞.

\(D_{water} = \frac{1}{2\overline t_{water_{norm}}} \times \sum_{i=1}^{n}\beta_i |t_{water_{norm_i}} - \overline t_{water_{norm}}| \{ \sum \beta_i = 1 \;\;\;\;\;\;\;\;\;\; (Eq. 6)\)

with βi standing for the proportion of group i in the sample, \(\overline t_{water_{norm}}\)  the normalized mean safe drinking water access rate of the municipality, \(t_{water_{norm_i}}\) the normalized safe drinking water access rate of group i, with a value between 0 and 1; and n the number of groups (n= 5); with Dwater presenting values between 0 and 1.