In the following, the results of the different methods used in this study are presented.
5.1. Implementation of the Average Nearest Neighbor and the Optimized Hot Spot Analysis
To investigate the overall distribution of the schools for years 2011, 2016, 2018, and 2021, the Average Nearest Neighbor was used. In this analysis, which does not include any variables, the Rate neighborhood (Rn) index is calculated throughout the city area based on the average distance of each point to its nearest neighbors. As previously mentioned, the closer the value of the Rate neighborhood (Rn) index is to zero, the more it represents a clustered pattern, and the closer it is to 2.15, the more it shows a scattered pattern. An index value of 1 also indicates a random pattern. Based on the results shown in
Table 1, because the Rate neighborhood (Rn) index is close to zero, the overall distributions of the schools in the years 2011, 2016, 2018, and 2021 are clustered.
The Average Nearest Neighbor was also analyzed separately for the boys’ and the girls’ primary schools, first high schools, and secondary high schools in the years 2011, 2016, and 2018. In this part of the analysis, the data for the year 2021 was excluded due to the uncertainty of the gender of the schools to be exploited by 2021. Based on the results of the analyses presented in
Table 2,
Table 3 and
Table 4, the overall distributions of the girls’ elementary and secondary schools for years 2011, 2016, and 2018 are clustered.
In the case of the girls’ secondary schools, the overall distribution of the schools is random in the years 2016 and 2018. However, for the year 2011, the distribution of the schools is clustered. In the case of boys’ schools, the overall distributions of the primary schools, first high schools, and secondary high schools for years 2011, 2016, and 2018 are clustered.
A subsequent analysis that was to investigate and show the overall distribution of the schools is the optimized hot spot analysis. As previously mentioned, the calculations of this analysis are based on the Getis Ord Gi* index and can be done in two ways. According to
Figure 3, the result of the school counting method per cell for the years 2011, 2016, 2018, and 2021 show the accumulation of hot spots in the central areas of the city and cold spots in the suburbs of the town and Golestan township.
By applying optimized hot spot analysis using the point count method within each polygon, which is the school counting method within each polygon, the autocorrelation of the schools at different levels, such as neighborhoods, statistical districts, and statistical blocks was investigated for the year 2018. The results indicate that the schools are generally more densely populated in the central areas of the city, but it was found that the location of the hot and the cold polygons differed. At the neighborhood level, the schools within the neighborhood of Ghiam, Nader, Amiriyeh, Berengy, Bargh, Enghelab, Vosogh, Daneshsara, Behzisti, Park Shahr, Madrese Ferdowsi, Sareban Mahale, Sfa, Mofkham, Padgan Artesh, North 17 Shahrivar, Jafar Abad, Mirzakuchek khan, Manba Ab, Sayyidi, Hosseini Masoum, and Koi Imam Reza were more dense, and the density of schools was lower in the neighborhoods of Malaksh, Halghe Sang, Shahrak Alghadir, Koi Janbazan, Ghale Aziz, and Ahmadabad. At the statistical districts level, the density of the schools in the districts located in Ghiam, Hosseini Masoum, Sayyidi, Manba Ab, Mirzakuchekkhan, Bargh, Berengy, Amiriyeh, Nader, Padegan Artesh, Enghelab, Vosough, Daneshsara, Madrese Ferdowsi, Sarban Mahale, Safa, Mokhofam, and Sharak Golestan neighborhoods was higher, and in the statistical districts located in Bagh Motahari, Shahrak Hekmat, Imam Khomeini township, Koi Sadeghiyeh, Bagher khan 1, Koi Azadegan, and Mohammadabad Korah, the school density was lower. However, at the level of statistical blocks, the density of the schools in the blocks located in the neighborhoods of Imam Reza, Koi Behdari, Ferdowsi, Mosalla, Nader, Amiriyeh, Berengy, Mirazkochekkhan, Manba Ab, Daneshsara, Park Shahr, Vosough, Enghelab, and Mokhofam was higher.
In the next step, the overall distribution of the schools at the spatial scales of neighborhoods, the statistical districts, and the statistical blocks was examined in different years. For the neighborhood spatial units, by comparing 2011, 2016, 2018, and 2021, it was found that the density of the schools was higher in the downtown neighborhoods, and these neighborhoods play the role of hot polygons. Neighborhoods in parts of the south of the city were also identified as cold polygons in terms of the school density.
At the level of statistical districts, the results indicate that the statistical districts in the downtown areas for the year 2011 are known as hot polygons in terms of the school density. The school density was also lower in the statistical districts of the western and the northeastern parts of the city. However, for the years 2016, 2018 and 2021, due to the addition of new schools in the Golestan Shahr township, the density of the schools in these areas has also increased, and the statistical district related to this township is also a hot polygon. Also, with the construction of the new schools on the outskirts of the city, the hot spots of the schools in the downtown area has been gradually reduced. However, the statistical districts within the neighborhoods of Bagh Motahari, Zir Bagh Motahhari, Hekmat townships, Imam Khomeini townships, Koi Sadeghiyeh, Koi Azadegan, Bagherkhan 1, and Mohammadabad Korah are cold polygons.
At the level of the statistical blocks, the results indicate that the statistical blocks located in parts of the city center in the year 2018 are known as hot polygons in terms of the school density. However, for years 2011, 2016, and 2021, some of the statistical blocks related to Golestan city are also among the high-density polygons. For the year 2021, there are cold polygons in parts of the south of the city, which include fewer schools than the other blocks. The results of these analyses are shown in
Figure 4.
5.2. Implementation of Moran’s I and Getis Ord General G
In this section, in order to investigate the spatial autocorrelation based on the substructure variable and to determine the random or clustered distribution of the schools, Moran’s I and Getis Ord General G indices were used. At first, Moran’s I statistic was used to check for the random or the clustered distributions of the girls’ primary schools, first high schools, and secondary high schools. It can be concluded that the overall distributions of the primary schools, first high schools, and the secondary high schools for girls based on the substructure variable in the years 2011, 2016, and 2018 are random, which is due to the closeness of the value of Moran’s coefficient to zero.
Then, in order to confirm the results of the Moran’s I analysis, the analysis of the Getis Ord General G statistic (which is in regard to the substructure variable) on the point layers of the girls’ primary schools, first high schools, and secondary high schools was performed for the years 2011, 2016 and 2018. According to
Table 5,
Table 6 and
Table 7, the results show that the overall distributions of the girls’ primary schools, first high schools, and secondary high schools based on the substructure variable for the years 2011, 2016, and 2018 are random, because the
z-score is close to zero.
The Moran’s I and Getis Ord General G analyses were conducted on the point data of the boys’ primary schools, first high schools, and secondary high schools. The results are shown in
Table 8,
Table 9 and
Table 10. For the boys’ primary schools, first high schools, and secondary high schools, because the coefficient of Moran is close to zero for the years 2011, 2016, and 2018, the overall distribution of the boys’ primary schools based on the substructure variable is random.
The result of the Getis Ord General G analysis on the boys’ primary schools confirms the Moran’s I analysis. This means that the Z-score is close to zero for the years 2011, 2016, and 2018, and the overall distribution of the boys’ primary schools based on the substructure variable is random. For the boys’ first high schools in the years 2011 and 2018, the distribution of the schools is random, because the Z-Score is close to zero. However, for the year 2016, the distribution of schools is clustered with a low concentration or cold spots, because the Z-score is below −1.65. The distributions of the boys’ secondary high schools for the years 2011, 2016, and 2018 are also random.
To investigate the spatio-temporal variations of the distribution pattern of the schools based on the net per capita variable, which includes the substructure area and the number of students, the differential Moran method was used. In the differential Moran analysis, which was performed using Geoda 1.10 software, the weight matrix was defined based on the existence of the common border method (0 and 1) according to the Equation (12). Also, in order to achieve a higher accuracy, 999 iterations were used for the simulation.
In this regard, using the calculations of the differential Moran index, the trend of the net per capita changes for all primary schools, first high schools, and secondary high schools were evaluated in the 2016–2017, 2017–2018, and 2016–2018 time intervals. The spatial-temporal autocorrelation results of the schools with respect to the net per capita variable are shown in the differential Moran scatter plot in
Figure 5, which illustrates the pattern of the net per capita changes of the schools in the desired time intervals.
The slope of the differential Moran scatter plot corresponds to the value of the Moran index. For all primary schools and first high schools, since the value of the Moran index is positive and tends to zero, the resulting pattern is random, and there is a weak positive autocorrelation between the net per capita in the 2016–2017, 2017–2018, and 2016–2018 time intervals, which reflects the positive and slight changes in the net per capita of the schools over time. For all the secondary high schools, the values of the Moran index are negative and tend to zero in the 2016–2017 and 2017–2018 time intervals, so the autocorrelation is negative and weak. That means that the net per capita of the secondary high schools in the 2016–2017 and the 2017–2018 time intervals has not only increased but has also shown a relative decline. However, due to the positive value of the Moran index, there is a weak and positive autocorrelation between the net per capita in the year 2016 and the net per capita in the year 2018.
5.3. Implementation of Anselin Local Moran’s I and Getis Ord Gi*
After confirming that the data distribution is clustered, the local indices were used to determine the location of the clusters. By performing the general autocorrelation analyses, it was found that in most cases the distribution pattern of the schools based on the substructure variable is random. However, with respect to the values of the Moran, the Getis Ord indices, and the value of Z-Score, there is a weak spatial autocorrelation among the data. In this regard, to show this kind of autocorrelation, Anselin Local Moran’s I and Getis Ord Gi* analyses were used in this study.
Anselin Local Moran’s I analysis was first performed given the substructure variable for the girls’ primary schools in 2011, 2016, and 2018. The results show that the substructure of the girls’ primary schools in the southwest of the city in the year 2018 was above average (high-high areas), and it was below average in a region of the downtown area (low-low areas), which indicates the presence of clusters in these areas. However, in another part of downtown, the high outliers that have a value higher than the neighbors were also found. In the year 2016, the high-high areas are seen in the southwestern part of the city. Furthermore, there are high outliers in another part of the city center. However, there are no clusters in the city for the year 2011, but there are high outliers in part of downtown.
Next, considering the substructure variable, a hot spot analysis was performed by calculating the Getis Ord Gi* index for the girls’ primary schools in 2011, 2016, and 2018. Then, in order to create a continuous raster surface, the Inverse Distance Weighting (IDW) interpolation method was applied to the results of the Getis Ord Gi* method. The results of applying this hybrid method are as follows. For the substructure variable, in the year 2018 in parts of downtown and south of the city in the neighborhoods of Koi Sadeghie, Shahed township, Koi Imam Hossein, Koi Behdari, Villashahr, and Tasfiekhane, the distribution of the schools are clustered with high values, and in parts of the northeast of the city in the neighborhoods of Safa, Mokhofam, Madrese Ferdowsi, and North 17 Shahrivar, the distribution of the schools is low-cluster. In the year 2016, in a part of the city center in the neighborhood of Koi Imam Reza, the distribution of the schools is clustered with high values, and in the Safa neighborhood, the distribution is clustered with low values. In the year 2011, in part of the downtown in the Berengi neighborhood, the distribution of the clusters with low values is observed.
For the boys’ primary schools, considering the substructure variable, the Anselin Local Moran’s I analysis was also performed for the years 2011, 2016, and 2018. The result is that the substructures of the boys’ primary schools in 2011, 2016, and 2018 do not have clusters in the city. However, there are high outliers in part of the city center in 2011.
Next, the inverse distance weighting interpolation method was used on the results of the Getis Ord Gi* analysis for the boys’ primary schools in 2011, 2016, and 2018. The results of applying this hybrid approach were that for the substructure variable, which was in a small area east of the city in the Taher Gholam neighborhood, the distribution of the schools is clustered with low values in 2011 and 2016. For the year 2018 in the southeast of the city in the Mirzakuchakkhan neighborhood, the distribution of the schools is clustered with high values, and in the Koi Sadeghiyeh neighborhood west of the city, the distribution of the schools is clustered with low values. The results of applying the inverse distance weighting interpolation on the results of the Getis Ord Gi* analysis for the girls’ and the boys’ primary schools are shown in
Figure 6.
Considering the substructure variable, the Anselin Local Moran’s I analysis for the girls’ first high schools in 2011, 2016, and 2018 was also performed. The result indicates that the substructure of the girls’ first high schools does not have any cluster in the city. However, in 2011 and 2016, there are high outliers in a small southeast part of the city. Also, for the year 2018, high outliers are seen in the downtown area. The results of the Getis Ord Gi* analysis for the girls’ first high schools also do not indicate significant statistical significance of the substructure variable in 2011, 2016, and 2018. Subsequently, considering the substructure variable, the Anselin local Moran’s I analysis was performed for the boys’ first high schools in 2011, 2016, and 2018. The result indicates that the substructure of the boys’ first high schools does not have any clusters in the city. However, in the year 2018, there are high outliers and low outliers in the southern parts of the city.
Then, the inverse distance weighting interpolation method was applied to the results of the Getis Ord Gi* analysis for the boys’ first high schools in 2011, 2016, and 2018. The results of applying this hybrid method for the substructure variable in the years 2016 and 2018 have no statistical significance in the city. However, in 2011, the distribution of the schools in part of downtown in the Madrese Ferdowsi neighborhood is clustered with high values, and in the Mirzakuchakkhan and Bargh neighborhoods, the distribution is clustered with low values. Due to the lack of significant statistical significance for the girls’ and the boys’ first high schools, the results of applying the local indexes to these schools have been ignored.
For the girls’ secondary high schools, considering the substructure variable, the Anselin Local Moran’s I was performed in the years 2011, 2016, and 2018. However, in parts of the downtown and the southern areas of the city in 2011, and in a small part of the city center, high outliers are seen. Also, for the year 2018, there are low outliers in a part of downtown.
The inverse distance weighting interpolation method was applied to the results of the Getis Ord Gi* analysis for the girls’ secondary high schools in the years 2011, 2016, and 2018. The results of applying this hybrid approach for the substructure variable are that for the years 2011 and 2016, the distribution of the schools in the southern part of the city in the Alghadir township neighborhood is clustered with high values, and in the northeast of the city in the Jafarabad neighborhood, distribution of schools is clustered with low values. Cold spots are also observed in the 17 Shahrivar and Safa neighborhoods in the year 2016. In the southern part of the city in a neighborhood in the Alghadir Township, the distribution of the schools is clustered with high values, and in the eastern part of the city in the Jafar Abad neighborhood, the distribution is clustered with low values in the year 2018.
For the boys’ secondary high schools in 2011, 2016, and 2018, considering the substructure variable, the Anselin Local Moran’s I analysis was also performed. The result is that the substructure of the boys’ secondary high schools in the west and southwest parts of the city is above average (high-high areas) in 2011 and 2016 and indicates the presence of clusters in these areas. However, there are also high outliers in some parts of downtown. There are no clusters in the city for the year 2018, but there are high outliers in parts of downtown and low outliers in the west part of town.
The results of applying the inverse distance weighting interpolation method on the results of Getis Ord Gi* analysis for the boys’ secondary high schools for the substructure variable for 2011 and 2016 years reveal that the distribution of schools in the west and the southwestern parts of the city in the Vilashahr and Polemantaghe neighborhoods is clustered with high values. Also, in the central districts in the North 17 Shahrivar, Mofkham, Safa, Daneshsara, Bargh, Berengi, and Amiriyeh neighborhoods are clustered with low values. In the southwest of the city in the Farrokhi and Polemantaghe neighborhoods, the distribution of schools is clustered with high values, and in the center and northeast of the city in the North 17 Shahrivar, Safa, Sareban Mahale, Berengi, and Koi Moallem neighborhoods, the distribution is clustered with low values. The results of the inverse distance weighting interpolation on the results of the Getis Ord Gi* analysis for the girls’ and the boys’ secondary high schools are shown in
Figure 7.