*2.3. Comparison of Sodium Content over the Years*

The two versions of the database described in Section 2.1 were used. Since some items were present in both versions, duplicates were removed prior to the analysis. For the matching comparison, identical products were chosen in different years (2–6 years gap). Small differences were permitted, given that the product didn't undergo major changes.

#### *2.4. Statistics*

The Kruskal-Wallis test is useful as a general nonparametric test for comparing more than two independent samples. It can be used to test whether such samples come from the same distribution. This test is a powerful alternative to the one-way analysis of variance. Nonparametric ANOVA has no assumption of normality of random error but the independence of random error is required. If the Kruskal-Wallis statistic is significant, the nonparametric multiple comparison tests are useful methods for further analysis.

Pairwise agreement between both NPMs in the proportions of foods classified as "high in sodium" was assessed across all foods using the κ statistics, as follows: 0.01–0.20 'slight'; 0.21–0.40 'fair'; 0.41–0.60 'moderate'; 0.61–0.80 'substantial'; 0.81–0.99 'near perfect'. When agreement is high, the κ statistics either cannot be calculated or provides inconsistent values. Therefore, for some groups the agreement was assessed by using the disagreement probability (0 to 1). When this parameter was >0.1, it was considered 'substantial'; <0.1 'near perfect' and 0 'perfect'. The statistical analysis of the application data in this work was performed with Microsoft Excel and Google Colab with Jupyter Notebooks, libraries scikit-learn 0.22.2.post1, Pandas v0.25.3, and Matplotlib Python v3.2.0. The significance level was set as *p* < 0.05 in all statistical analyses.
