## 4 Results
### Improved Effectiveness of the MM-G2 SFCA Method  
Scatter plots were used to characterize the distribution of the accessibility results, and the normalized difference between the two results visually expresses the difference  
Figure 8: Scatterplots comparing the accessibility of the traditional gravity model MM-G2 SFCA with the standardized gravity model MM-G2 SFCA.  
Figure 7: One-hour accessibility of Shenzhen public hospitals for four methods: (**a**) MM-2 SFCA; (**b**) traditional gravity model MM-G2 SFCA; (**c**) traditional gravity model G2 SFCA; (**d**) standardized gravity model MM-G2 SFCA.  
in their spatial distribution. Local spatial autocorrelation analyses were conducted on the MM-2 SFCA and MM-G2 SFCA methods' accessibility using the Getis-Ord Gi* statistics to identify hot spot and cold spot areas. This was carried out to gain a deeper understanding of the spatial differences and clustering characteristics of the two accessibility results.  
As illustrated in Figure 9, the scatter density plot reveals that the accessibility results for the MM-G2 SFCA method exhibit a relatively higher degree of concentration and a lower overall level compared to the MM-2 SFCA method. This can be more clearly verified through the use of a difference plot of the normalized results of the two models, as illustrated in Figure 10. The red color in the plot represents a more prominent accessibility for the MM-G2 SFCA method, while the orange color and below represent a lower accessibility than the MM-2 SFCA method. It is evident that the number of areas with reduced levels of accessibility is significant and widespread.  
Figure 10: Difference between the normalized values in the standardized gravity model MM-G2 SFCA and the MM-2 SFCA in terms of accessibility.  
Figure 9: Scatterplots comparing the accessibility of MM-2 SFCA with MM-G2 SFCA.  
The difference between the normalized values reveals the accessibility differences between the MM-G2 SFCA method and the MM-2 SFCA method. The MM-G2 SFCA method increased the limitation of the time cost on the expression of accessibility, emphasizing the attraction of the supply points to the surrounding demand points, making the two high-accessibility centers in Luohu District and Nanshan District in the southwest of Shenzhen more prominent. Conversely, the accessibility in the central and western regions significantly declined. This is confirmed in Figure 11, where the MM-G2 SFCA method shows a slight reduction in the extent of the hot spot areas and that the cold spot areas are more prominent in the central and western regions. Combined with the distribution analysis of public hospitals, shown in Figure 12, the number of public hospitals in this region is relatively small, and the original high accessibility mainly comes from the complete radiation of a large number of public hospitals in the south. That is, once the hospital is accessible under a particular transportation mode, the MM-2 SFCA method will fully include the hospital's supply capacity under the corresponding transportation mode in the region's accessibility, while the MM-G2 SFCA method corrects this issue.  
Figure 11: Getis-Ord Gi* statistics of accessibility (**a**) the MM-2 SFCA method; (**b**) the MM-G2 SFCA method.  
Figure 12: Supply–demand ratio and regional accessibility of public hospitals in Shenzhen.  
At the same time, due to the reduction in the virtual high accessibility in these areas, the accessibility of remote areas relatively improved, such as Guangming District in the northwest and Dapeng New District in the east. Accordingly, the confidence level of these two areas as cold spots in the Gi* statistics results decreases.  
Therefore, the MM-G2 SFCA method helps to fix the impact of local neighboring areas, making the distribution of accessibility more reasonable.