I want to run a statistical analysis on the gender pay gap data published by EU (https://ec.europa.eu/eurostat/databrowser/product/page/SDG_05_20) at a specific year, this data have the following form: for each country they provide the difference between the average gross hourly earnings of male paid employees and of female paid employees as a percentage of average gross hourly earnings of male paid employees. I am looking whether there exist a correlation between someone's gender and its earnings. I could not find which statistical test I should use to do that.
Secondary question: I then need to use more data to check whether the gander pay gap is correlated to other discrete variables, such as whether the employee works in the pubic or private sector (https://ec.europa.eu/eurostat/databrowser/product/page/EARN_GR_GPGR2CT). The data are split in groups, again giving the same information per country. think that I should use ANOVA, my problem is that earnings' information is given as a percentage difference. Should I use ANOVA, Kruskal-Wallis, or something different? (I am going to run both tests to see whether there exist a significant different on their results).
My problem-concern for both questions are the form of the earnings' data, I have never dealt with such data before. Please note that I am not supposed to use any additional data.