Education as a dimension of human development: A Provincial-level Education Index for Ecuador

schooling–, which allows us to understand the full meaning of the analysis. Table 4 shows the most common descriptive statistics in data analysis for these indicators. The mean value of the mean years of schooling indicator increases by slightly less than one year between 2006 and 2014 (0.885), while the increase is slightly more than one year for the mean of the expected years of schooling indicator (1.095). From the statistical point of view, normalization implies a change of scale in the variable: a transformation with respect to which CV2 is invariant, as shown in the table. However, it is worth noting the values taken by the coefficient of variation (square root of CV2) for each of the indicators. Thus, for the mean years of schooling indicator, the dispersion represents 10.8% of its mean value in 2014, while, in the case of the expected years of schooling indicator, the variability represents only 3.4%. Despite the reduction in educational inequality among Ecuadorian provinces, the range of the variable mean years of schooling in 2006 is around 3.4 years (from 5.902 in Bolivar to 9.285 in Pichincha), while, in 2014, this range reaches 4.1 years (from 6.144 in Chimborazo to 10.248 in Pichincha). However, when not considering Pichincha, the range is reduced to 3.1 years (from 6.144 in Chimborazo to 9.205 in Guayas). In the case of the expected years of schooling indicator, the range goes from 2.7 years in 2006 to 1.8 in 2014 (S5 Table). Data in Fig 4 show that the provinces with the greatest or lowest educational development

drive inequality the most, whereas the lowest weight corresponded to provinces whose PEI val- ues were closer to the mean value of the corresponding PEI distribution. Specifically, in 2006, the provinces of Pichincha and Guayas (with the highest PEI values) contributed most, in per- centage terms, to overall educational inequality in Ecuador (27% and 10.4%, respectively), fol- lowed by Bolivar, with 9%, and Cañar, with 7.3% (provinces that evidenced a lower level of educational well-being in said year). In 2014, Pichincha (32.1%) and Chimborazo (10.5%) were the provinces with the highest and lowest PEI value, respectively, and which contributed most to educational inequality in Ecuador. Table 2. Provincial-level Education Index and its components: Spearman´s rank correlation coefficient between the index in 2006 and its annual mean variation (2006–2014). ρ p PEI -0.493 0.011 � MYS -0.182 0.215 EYS -0.734 0.000 �� Notes: PEI = Provincial-level Education Index. MYS = mean years of schooling index; EYS = expected years of schooling index: ρ = Spearman’s rank correlation coefficient; p = p-value from the one-tailed t-test; � indicates statistical significance at the 5% level; �� indicates statistical significance at the 1% level. https://doi.org/10.1371/journal.pone.0270932.t002 Table 3. Inequality in educational development and contribution of education indicators. 2006 2014 MYS EYS PEI MYS EYS PEI CV2 0.013 0.002 0.004 0.012 0.001 0.003 % Contribution 63.18% 36.82% 77.31% 22.69%

Notes: MYS = mean years of schooling index; EYS = expected years of schooling index: PEI = Provincial-level Education Index: CV2 = squared of the coefficient of variation. https://doi.org/10.1371/journal.pone.0270932.t003 PLOS ONE Education as a dimension of Human development PLOS ONE | https://doi.org/10.1371/journal.pone.0270932 July 8, 2022 14 / 27