Summary. We attempt to clarify, and suggest how to avoid, several serious misunderstandings about and fallacies of causal inference. These issues concern some of the most fundamental advantages and disadvantages of each basic research design. Problems include improper use of hypothesis tests for covariate balance between the treated and control groups, and the consequences of using randomization, blocking before randomization and matching after assignment of treatment to achieve covariate balance. Applied researchers in a wide range of scientific disciplines seem to fall prey to one or more of these fallacies and as a result make suboptimal design or analysis choices. To clarify these points, we derive a new four-part decomposition of the key estimation errors in making causal inferences. We then show how this decomposition can help scholars from different experimental and observational research traditions to understand better each other's inferential problems and attempted solutions.