Originally posted by doc05
I have to disagree. The fact is that we (as medical students) don't know how the thing is scored. But if ~60% is a passing score, why isn't an 80%=95th percentile? Maybe the Kaplan guy was wrong, but the thing is that Kaplan knows the USMLE inside-out, almost as well as the people at the NBME.
Okay, I did the math and Kaplan does overestimate a bit (provided I didn't bastardize some of the calculations). These are all estimations based on the 1999 data in the front of my edition of First Aid. I think that you
can assume that it's a normal distribution.
Passing is a 3-digit score of 180. If we assume that 60% is passing (most cite 55-65% as passing), this makes the highest attainable 3-digit score 300. [180/0.6=300]
80% of 300 = 240
In 1999, the mean for Step 1 was 215 with a s.d. of 20. Assume a Gaussian distribution and that the mean score is the 50th percentile.
One s.d. above the mean is 235. This corresponds to the 84th percentile. [Scores of 185-235 encompass 68% of all the scores in a normal distribution (1 s.d below and above the mean). 100%-68%=32% "remaining" scores. That means 16% of the scores are higher 1 s.d. above the mean and 16% of the scores are lower than 1 s.d. below the mean. For a score of 235 (1 s.d. above the mean), 100%-16%=84%.]
Two s.d. above the mean is 255. Since 2 s.d. around the mean encompasses 95% of all the scores, this corresponds to the 97.5th percentile in a normal distribution. [Similar calculation as above.]
The difference between a score of 235 and 255 is 13.5 percentiles. [97.5-84=13.5] Within that range, that's a change of 0.675 percentiles per point. [13.5/20=0.675]
A score of 240 (which we determined above to be an 80%) is 5 points above 235. This is roughly the same as 3.375 percentiles above the 84th = 87.375th percentile. [5x0.675=3.375]
Thus, a score of 240 (80% correct) is approximately an 87th percentile score, not the 95th percentile that Kaplan claims.
If you assume a negative skew to the distribution (median > mean), it would tend to drive the percentiles even higher, requiring you to score even better to reach a certain percentile than in a normal distribution.
Okay, that's way too much statistics for my liking. Someone who knows what they are talking above can go ahead and rip apart the numbers now.
😎