Someone told me to use a non-parametric test for non-parametric data. Is that right?

Data are not identified as non-parametric or parametric. Instead, “non-parametric” is used to describe the type of a significance test. A significance test is labeled as non-parametric if it does not bear any assumptions on the distribution of the underlying population. Therefore, 2 test, Mann-Whitney U test, and Kruskal-Wallis test are examples of a non-parametric test. On the other hand, t-test and ANOVA are examples of a parametric test, because they assume a Normal distribution.