Let's say an individual gets a score (between 1 and 6) on different pieces of equipment in their department. For example, if I'm proficient at repairing a particular piece of equipment I will score higher, say a 5 or 6. If you then take the average score I get across all the equipment (upwards of 50-100 pieces) in the department in which I work...you get my overall average score. The more effective I am, the more pay I can take home as a result.
The problem I face is that each department has different equipment, so the average is unfair. It may be simpler to gain proficiency (and thus a promotion) in one department simply because they have less equipment. I don't have to improve proficiency on as much equipment so it is mathematically easier. I'd like to include some 'bias' in order to correct for this but I don't know how to do so.
How can you normalize the data despite the difference in sample size?
Seems like an easy question but I'm having difficulty finding the right statistical tool to correct for it. Also, hopefully this is the right place to answer this question.