McCrary Density Test
Also known as · McCrary test · density test · sorting test
The McCrary density test (McCrary 2008) checks whether units can manipulate their position on the Running Variable to land on a preferred side of the Cutoff. If sorting is occurring, the density of the running variable will be discontinuous at the cutoff — visibly bunched on the side that yields the desirable treatment status. A smooth density supports the Continuity Assumption and the RDD design; a sharp jump in density signals manipulation and invalidates the design.
When to use
Run the McCrary test as a routine sanity check before reporting any RDD result. R: rddensity::rddensity(running, c = cutoff) returns the test statistic and a p-value. Examples of likely manipulation: standardised-test scores near scholarship cutoffs (students retake), income near means-test eligibility thresholds (households underreport). Examples where manipulation is implausible: vote shares in elections (no individual can move the aggregate count), birth dates near a school-cutoff date.