Statistical Methods
Choose a distance metric with a documented unit convention
Define the task
Before computing a distance, align coordinate order and define the units. Euclidean distance gives squared deviations substantial influence, Manhattan distance sums absolute deviations, and maximum distance uses the largest absolute deviation. Mixing seconds and milligrams without a declared transformation can make any of these hard to interpret.
Carry out the check
For each pair of complete vectors, subtract coordinates in matching positions. Compute the selected aggregation and retain the coordinate differences for inspection. Use a fixed scaling rule when comparing multiple pairs. If values are missing, document whether the program omits coordinates, rescales a partial distance or excludes the pair. Those choices change the result.
Worked hypothetical example
For hypothetical vectors (1,2) and (4,6) on a common unitless scale, the coordinate differences are 3 and 4. Euclidean distance is 5, Manhattan distance is 7 and maximum distance is 4. These represent different definitions of separation. A distance is not a probability, and a cutoff needs justification for the downstream clustering or matching task. Use a synthetic pair with known differences as a regression test.
Method checked 12 November 2026 against R documentation: Distance Matrix Computation.