Correction to: Nature https://doi.org/10.1038/s41586-019-1846-3Published online 01 January 2020

In this Article, there were several minor errors to the main text and Supplementary Information, as detailed below. In the sentence “The change in SDG Index score among provinces from 2000 to 2015 ranged from a 11.1% increase (Shandong) to a 51.8% increase (Ningxia).”, ‘Shandong’ was incorrectly shown as ‘Shanghai’. In the sentence “The three SDGs that improved the most, in order of greatest to least improvement, were SDG 9 (industry, innovation and infrastructure), SDG 10 (reduced inequalities), and SDG 17 (partnerships for the goals).”, ‘partnerships for the goals’ was incorrectly shown as ‘affordable and clean energy’.

In the Methods, ‘for SDG scores’ should be removed from the heading ‘Uncertainty and sensitivity analysis for SDG scores’. In this paragraph, the asterisk should be removed from the following equation so it appears as:

$${C}_{n}^{m}=\frac{n!}{m!(n-m)!}$$

Instead of:

$${C}_{n}^{m}=\frac{n!}{m!\ast (n-m)!}$$

In the Methods paragraph starting “We also ran a sensitivity analysis37…”, seven occurrences of ‘SDG scores’ should have been ‘SDG Index scores’. Similarly, in the legend to Extended Data Fig. 3, four occurrences of ‘SDG scores’ should have been ‘SDG Index scores’. In the Supplementary Information, several minor changes have been made, including changing “smaller (larger)” to “larger (smaller)”; replacing “Shanxi” with “Jiangxi”; and replacing “the coefficients” with “the multiple regression coefficients”. The original Article has been corrected online.