The main aim of this paper was to examine the relationship between the PISA (Programme for International Student Assessment) international study results of 15 and 16 years-old pupils from 2015 and a set of socio-economic indicators (on a national level) such as governments’ expenditures on primary education, gross domestic product per capita, the Democracy index compiled by the Economist Intelligence Unit, or primary teachers’ salaries. The study covered 71 countries or territories, including 34 OECD countries and their 37 non-OECD counterparts. The methods included multivariate linear models, models based on Törnquist functions, and cluster analysis. The main result of the study is that there exists a threshold in terms of GDP per capita and government expenditures on primary education per capita. Above the threshold, the higher GDP per capita or expenditures do not translate into the higher PISA scores. However, below this threshold, the opposite is true. Therefore, poorer and mainly non-OECD countries may achieve better student performances in PISA tests by increasing expenditures on primary education, while for student performances of the wealthy and mainly OECD countries expenditures are not a statistically significant factor. The division between OECD and non-OECD countries was also confirmed to be statistically significant by cluster analysis method. In addition, from linear multivariate models it was found that PISA scores were statistically significantly (and positively) related to the national GDP per capita, governments’ expenditures on primary education, and the Democracy index, while the influence of primary teachers’ salaries on PISA scores was found statistically insignificant.