percentage vs proficiency level you get after the exam
Lots have already been said on this..Make it simple. It was not possible to associate a percentage to the pass/not pass and proficiency/below proficiency level except from the 61% passing level that was reported or the 58/65% threshold level that is "observed" elsewhere (by experienced observers, let's say) due to the modified angoff evaluation model used by pmi.
That said, let's try another approach: top down approach to understand "roughly" but more accurate than ever, the proficiency level you get in each knowledge area after the exam.
The idea will be the same for one knowledge area than for the whole exam, but you can considere that the average rating score may be slightly different between knowledge areas.
Consider the whole community of exam takers. Their rating (in percentage) can be accurately represented with a normal distribution.
Here comes the assumptions: 1) I have read that around 30-40% of exam takers don't pass the exam (the first time): let's say 30% gets a percentage lower than 61%. 2) I have seen a lot of people claiming their score around 80% in standard practice tests..but couldn't find one that claims to reach easily 90% while practicing. This said, we can assume that only around 1% gets a rating higher than 89% in the exam. Sounds crazy? you can still adjust the number to what you believe more accurate.
In a normal curve, 30% not passing corresponds to a score lower than 0.5 sigma (standard deviation) and the 1% higher ranked correspond to scoring higher than 2.3 sigma. Processing this(89-61=(2.3+0.5) sigma), we have a sigma=10 (in the unit of the percentage of exam questions), which makes the average scoring number to 66%. Change the number as you wish, you will never fall far from this value.
Now, let's link it to the proficiency level.
I ASSUME the way PMI looks at it is the same than every statistician will do. So, proficiency shall be related to the standard deviation this way:
average more or less sigma= moderate proficiency
higher than one sigma=proficiency
lower than one sigma= below proficiency
Does it make sense to you?
Below 56%, your fit in "below proficency"
Between 56% and 76% you fit in "moderate proficiency"
above 76%, you fit in "proficiency" level.
This said, you can have 5 moderate and one below and still pass (or not) the exam like we can read in this forum both cases. But in principle, you could be all moderate and not pass the exam, unless PMI has selected the lower limit to 0.5sigma instead of 1 sigma which does not change the reasoning.
So now, I am curious if anyone has received full moderate eficiency but still did not succeed in passing the exam. I guess this would be sadism from PMI to allow this. so the lower level in the proficiency rating may be 61% instead of 56%. And in practice, every questions are weighted so you may have to add a +/-2.5% on these numbers.