A posteriori refers to the period of study after data have been collected and analyzed. A posteriori tests (also called post hoc tests) are statistical analyses performed after the initial analyses have been run, to explore the results in more depth.
For example, let’s say we conduct an experiment to examine the effects of background music on a short-term memory task. We use three different types of music: pop, rock, and country, and we have a no-music control group. We predict that background music will worsen performance, but we don’t make any specific predictions about music type.
We find that music did negatively impact performance. However, we can’t say for sure which groups performed worse than others without running additional tests to compare the groups to each other. A posteriori analyses such as these are useful in exploratory research, when researchers do not have enough information to make specific predictions ahead of time, but further analysis of results can yield new directions for future studies.