Calculate your GPA/MCAT percentile at a candidate school

[aSagacious]

Before I post this, keep in mind:
A) Yes, I am very bored
B) This has very little practical use, however I found it interesting
C) This assumes that the accepted population exhibits a relatively normal distribution
D) inb4coolstorybro

So, without any further ado, here's how to calculate where you stand (as a percentile) at any given medical school for admissions purposes.

*1) Look up the MSAR 50th and 10th percentile values for either GPA or MCAT, I'll use GPA for the sake of this demonstration.

So at XYZ University, the mean GPA was a 3.65 and 10th percentile was a 3.25.

2) Using any old Z-score calculator, find the correlating Z value for the 10th percentile (http://www.measuringusability.com/zcalcp.php)

This turns out to be z = -1.28

*3) Using the equation: z = (x - u)/sd, where [(z=z score), (x = some GPA, we'll use the 10th percentile since that's what we were given), (u = school's average GPA), (sd = standard deviation, unknown)]

We'll use this to solve for the standard deviation:
-1.28 = (3.25 - 3.65) / sd
sd = 0.3125

4) Now, you can go back to z = (x - u)/sd and plug in your own GPA, the known standard deviation and mean, and calculate your personal z-score (and convert it to percentile: http://www.measuringusability.com/pcalcz.php)


So, let's try it out:

Student A --> 3.75 GPA
z = (3.75 - 3.65)/(0.3125) = 0.32
0.32 = 63rd percentile

Student B --> 3.4 GPA
z = (3.4 - 3.65)/(0.3125) = -0.8
-0.8 = 21st percentile

...enjoy!

*In order to attempt to deal with the skew:
- If you are above the mean, use the 90th percentile value to calculate standard deviation
- If you are below the mean, use the 10th percentile value to calculate standard deviation

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[FlowRate]

Assumption C is, sadly, invalid for most medical schools, since GPA caps at 4.0 and MCAT scores are on a skewed distribution.

 

[aSagacious]

Assumption C is, sadly, invalid for most medical schools, since GPA caps at 4.0 and MCAT scores are on a skewed distribution.

Very good point

 

[PressPforPi]

A) As am I. Welcome to the club
B) Helps people know where they stand so I'd say it's useful for people who don't know how to read percentiles I guess?
C) Area under the cover =
D) coolstorybraa. P.S. I like your monkey avatar better than I did the baby James Bond. I'd rather be associated with beastiality than pedophilia

 

[aSagacious]

I'd rather be associated with beastiality than pedophilia

Eh, matter of preference

 

[Catalystik]

here's how to calculate where you stand (as a percentile) at any given medical school for admissions purposes.

Where is apumic (oracle of the spreadsheet) when one needs an opinion?

 

[PressPforPi]

Eh, matter of preference

Point taken. Good luck on this cycle as well. You're on par with Cat as far as admissions advice goes IMHO.

 

[aSagacious]

You're on par with Cat as far as admissions advice goes IMHO.

That is both a flattering complement to me, as well as a slap in the face to Cat

 

[PressPforPi]

That is both a flattering complement to me, as well as a slap in the face to Cat

Lol I hope she/he doesn't take offense. Well, to make it a better analogy, let's say it's a baseball game. Cat's the head coach and you're in the outfield. Both necessary for the best outcome, but one is a little more important.

Screw the analogy. You're both frakin awesome.

 

[apumic]

Haha... I heard my name called so...

With some modifications to take account for some of the skew, this is essentially how the med school spreadsheet made its calculations. For most applicants (i.e., those w/ mid to high range GPA and MCAT scores -- around 3.4-4.0/28-40), the numbers fit the GPA/MCAT grid quite nicely, which gives at least some support to this theory. However, for low-end students (e.g., low 3s and below/low 20s), it's not as clear-cut. The ultimate determinant, though, in difficulty of acceptance is really the base acceptance rate. With a high base acceptance rate (small applicant pool), your chances are going to almost certainly be better.

 

[aSagacious]

Assumption C is, sadly, invalid for most medical schools, since GPA caps at 4.0 and MCAT scores are on a skewed distribution.

Though this is a sloppy approximation, here's what I suggest to deal with the skewed nature of the curve.

If you are above the mean, use the 90th percentile value to calculate standard deviation. If you are below the mean, use the 10th percentile value.

 

[apumic]

Though this is a sloppy approximation, here's what I suggest to deal with the skewed nature of the curve.

If you are above the mean, use the 90th percentile value to calculate standard deviation. If you are below the mean, use the 10th percentile value.

This works decently and I think it is largely what I used. I know I made some modifications to that, but I'd have to go back and look at the code to see what I did. The more accurate way of doing things would be to actually approximate the skew using the relationship of the median (which is what we're given, IIRC, not the mean) and the 10th and 90th percentiles. I'm not so sure, though, that, for instance, Excel has a simple way of doing this. I'm sure someone could find a way, though. It should be possible to at least closely approximate the skew. I simply don't have the time to spend working out the solution.

 

[Catalystik]

I simply don't have the time to spend working out the solution.

Perhaps aSagacious would be willing to step up to the plate?

 

[FlowRate]

Fit a model to the national/applicant MCAT distribution then cross-reference with 10th/50th/90th percentile scores. Wouldn't be difficult.

 

[apumic]

Fit a model to the national/applicant MCAT distribution then cross-reference with 10th/50th/90th percentile scores. Wouldn't be difficult.

Cool. Sounds good. You should try it...

 

[RogueUnicorn]

crunching admissions stats imo is not a particularly useful exercise

 

[aSagacious]

Perhaps aSagacious would be willing to step up to the plate?

Sure, I'll see what I can come up with.

 

[aSagacious]

crunching admissions stats imo is not a particularly useful exercise

Hence point B in my series of disclaimers

 

[RogueUnicorn]

Hence point B in my series of disclaimers

indeed. But it is worth repeating

 

[FlowRate]

Cool. Sounds good. You should try it...

crunching admissions stats imo is not a particularly useful exercise

 

[aSagacious]

Fit a model to the national/applicant MCAT distribution then cross-reference with 10th/50th/90th percentile scores.

I've employed this method in the attachment below. The source of my data is the 08-10 aggregate GPA/MCAT grid: https://www.aamc.org/download/157450/data/table24-mcatgpagridall2008-10.pdf.pdf

I tested it against a number of schools from this year's MSAR. As you would imagine, it is more accurate for schools that have averages closer to the national mean.

Customizing a percentile chart for a specific school using this fit turned out to be a bit more difficult than I had anticipated due to a small sample size (only 3 data points).

Anyway, this chart should suffice as a decent approximation for most schools.

 

[aSagacious]

... and those with a 40+ MCAT are a bit underrepresented according to this fit, but if an applicant is in that ballpark they shouldn't be worrying about their percentile anyway