If you were to enter the projected raw mean for Version 6 Emergency Medicine (mean of V6.1= 77.41 and V6.2= 77.11) to determine a mean scale score, it would be different than the mean scale score that is currently displayed on the website.
Likewise, in reverse, if you were to enter the projected scale score mean for Version 6 Emergency Medicine (mean V6 = 406) to determine a mean raw score, it would also be different than the current mean raw scores that are displayed on the website. You might also get an error message stating that the tool "Can't find scale score on the lookup table."
While this may seem confusing, this is not a flaw in the tool; the tool is actually working correctly. The tool is meant to convert a single student’s scores and subscores, not average scores. Converting a program’s average raw score would tell us what scale score a student who had attained that average raw score would receive. It would not tell us the average scale score for the program. The best way to compute an average scale score is to average the scale scores of the students in a given cohort.
This happens for a few reasons: raw scores are on a normal distribution, but not around the midpoint; in the case of PAEA End of Rotation exams, there are 100 questions and most students score between 50–90. Scale scores try to eliminate this shift by stretching the range of scores that students achieve over 200 integers. Since the scale score metric ranges from 300–500 (200 points) and test forms only contain 100 items, there will not be a raw score for each possible scale score. There will be exactly one scale score for each individual raw score. This means that there is a scale score for score a student can achieve, but not for averages, which could calculate to a half point.