Resolution
Resolution turns up in 2 fields: statistics, metrology. Here is what it means to the people in each one.
Resolution in statistics
Rating of a fractional factorial design, in Roman numerals, that states which effects are aliased with which.
Resolution is the length of the shortest word in a design's defining relation. In a resolution III design, main effects are aliased with two-factor interactions; resolution IV keeps main effects clear of two-factor interactions but aliases those interactions with each other; resolution V keeps both main effects and two-factor interactions clear. Higher resolution costs more runs, so screening work often accepts III or IV and follows up later.
"Res III is fine for screening twelve knobs, but don't publish an interaction from it. Fold it over first."
Resolution in metrology
The finest step an instrument can display, such as one count of the last digit on a digital readout.
The size of the smallest step an instrument can show: on a digital display it is one step of the last digit, on an analog dial it depends on scale spacing and pointer width. It enters the budget as a rectangular component with a half-width of half the resolution, giving a standard uncertainty of about 0.29 times the resolution. High resolution says nothing about accuracy: a 7-digit display can be wrong in the third digit.
"Gauge resolution is 0.01 mm and the tolerance is 0.02, you can't calibrate that meaningfully."