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

level that was above the distribution mean (equal to 0.599, in 2006, and 0.659, in 2014). It is also worth highlighting the different behavior of the distributions of the PEI components. The slight bias to the right of the 2006 MYS distribution virtually disappeared in 2014 and with it so did the number of provinces displaying MYS values below the respective mean value (equal to 0.482, in 2006, and 0.541, in 2014). Regarding the EYS distribution, Fig 2 indicates that most provinces were concentrated around the mean value (equal to 0.715, in 2006, and 0.776, in 2014) for both years of the study. It can also be seen that the density linked to lower values of this indicator tended to decrease in 2014. Despite this, there was a second mode for this indicator in said year, which is related to a group of provinces with below mean values. The graphs above reflect the general time evolution of the PEI distributions and their com- ponents, and, therefore, do not show any changes that have occurred at a provincial level between the years in the study. Any change in the general distribution of a variable may be the consequence of multiple combinations of changes at a provincial level [98]. As a result, it is necessary to look at the annual mean variations distribution for each index. The mean values of the distributions (0.0074, for MYS and 0.0076, for EYS) as well as the standard deviations (0.0044, for MYS and 0.0041, for EYS) were virtually the same in both distributions. However, Fig 3 shows that the growth patterns differed by index, being more moderate in the case of

MYS. There was also a group of provinces with a negative mean variation in the distribution of this component. Despite there was an overall improvement in PEI values between 2006 and 2014, certain provinces which had a poorer educational development in 2006, such as Cañar or Bolı´var and, particularly, Esmeraldas, were seen to be those which had improved most (annual mean varia- tion [AMV] equal to 0.0099, 0.0108, and 0.0112, respectively), whereas others who exhibited greater initial educational development, such as El Oro or Guayas, had made less progress (respective AMV values equal to 0.0052 and 0.0041) (Fig 1). In this regard, our estimation of the Spearman’s rank correlation coefficient between the classification of Ecuadorian provinces as determined by the PEI in 2006 and the other defined by the AMV of the PEI was negative (-0.493). This fact indicated that the provinces which most increased their values between 2006 and 2014 were those that lagged furthest behind in 2006 with a lower PEI. This therefore pointed to a process of convergence in education amongst Ecuadorian provinces. Based on the provincial estimations of the education components of the PEI (S6 Table), the convergence between provinces was greater for the EYS index, since the absolute value of the Spearman’s rank correlation coefficient was closer to one (-0.734) and was extremely weak for the MYS index (-0.182) (Table 2). Table 3 provides the CV2 values of the PEI and of its components for 2006 and 2014. These values give useful information on the degree of educational inequality among Ecuadorian

Fig 2. Distribution of the Provincial-level Education Index and its components. Notes: Each line represents the density function of the corresponding distribution. MYS = mean years of schooling index; EYS = expected years of schooling index: PEI = Provincial-level Education Index. https://doi.org/10.1371/journal.pone.0270932.g002 PLOS ONE Education as a dimension of Human development PLOS ONE | https://doi.org/10.1371/journal.pone.0270932 July 8, 2022 12 / 27