This thesis proposes a way to look beyond mean balance tests. Balance tests are a key component for plausible causal identification. Both in experimental designs and natural experiments, the standard practice is to use statistical tests with the null hypothesis of no difference between the pre-treatment covariates across treatment and control groups. The main idea is that the distributions of pretreatment variables should be roughly balanced between treatment and control groups. In recent decades, presenting evidence for the quality of the causal research designs became standard in social science. While observational researchers normally focus on evidence of balance for the covariates included in their model, experimental researchers provide randomization tests for balance on pretreatment covariates.