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

Having estimated the education indicators for each province, we transformed both indica- tors into normalized indices between 0 to 1 by the UNDP goalposts used since the 2014 Human Development Report: minimum of 0 years for both indicators, and maximum of 15 and 18 years for mean years of schooling and expected years of schooling, respectively [92]: MYSi ¼ MYi 0 15 0 EYSi ¼ EYi 0 18 0 where MYSi and EYSi are the mean years of schooling and the expected years of schooling nor- malized indices for province i, respectively. For each province, i, we calculated its PEIi as the arithmetic mean of the normalized education components (i.e., (MYSi + EYSi) / 2). This is the methodology used by UNDP to obtain the education index of the HDI since 2014 [92]. PEIi ranges from 0 (minimum level of educational development) to 1 (maximum level of educa- tional development). Applying the same method of estimating the PEI that the UNDP uses to construct the educational component of the HDI allowed us to “situate” the level of educa- tional development of Ecuadorian provinces in the international context. More specifically, it enabled us to compare Ecuador‘s educational well-being to that of LAC countries with similar socioeconomic characteristics. In this sense, to illustrate the spatial distribution of Ecuadorian educational development, we took as a reference the classification by quartiles corresponding to the PEI of Ecuadorian provinces in 2014. We used the quartile ranking because it is the procedure adopted by UNDP

to rank countries according to their level of human development based on their HDI values (low, medium, high, and very high) [93]. It should be mentioned that the HDI is meant to order geographic units, allowing comparisons between countries and between different time periods. Therefore, what is important is not so much the value of the HDI in a given country, but its rank or order number in relation to the rest of the countries. This is equally valid for each of the intermediate indexes that compose the HDI, such as the education index. To complete the above information, we determined the level of educational development of each province compared to that of the countries with available information for 2014 in the UNDP database [29] Thus, following the aforementioned UNDP methodology for its HDI, we calculated the first, second and third quartiles, respectively, of the HDI education index distri- bution for 2014. These quartiles are the thresholds that allowed each province to be classified according to its level of educational development. Statistical analysis of Ecuadorian educational inequality across provinces We explored whether the provinces with the lowest educational development in 2006 were the ones that grew the most between 2006 and 2014. To see whether this convergence process occurred, we estimated the Spearman‘s rank correlation coefficient, ρ, between the ranking of the provinces determined by their PEI in 2006 and that given by the annual mean variation of the PEI between 2006 and 2014 [94, 95], and we replicated this analysis for the two compo-

nents of the PEI. To analyze the significance of the results we used the statistic t ¼ r � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðN 2Þ= 1 r2 ð Þ p , where N is the number of provinces; assuming no concordance between rankings, this statistic follows a t-distribution with N—2 degrees of freedom. To quantify the inequality in Ecuador’s educational development across provinces and to gain an insight into its evolution over the period analyzed and the contribution of each compo- nent of the PEI makes to overall educational inequality, we used the square of the coefficient of PLOS ONE Education as a dimension of Human development PLOS ONE | https://doi.org/10.1371/journal.pone.0270932 July 8, 2022 9 / 27