I contest the value of the median MCAT score

[mmmcdowe]

---

Members don't see this ad.

Hey guys,

I read alot around here about schools who's median is this or that, but I think people are under a afalse assumption. This assumption is that median scores of, say, 12, 11, 12 result in a total median of 35. THIS IS NOT TRUE! This reasoning in under the assumption that the same half of the class is getting all the grades above or equal to 12, 11, 12. Case in point, me. My BS score is above this median, where as my PS is not. The actual median scores, I would assert, are actually lower than 35. Look at the percentile rankings of the MCAT. 12s and 11s are in the low 90th percentile or less, where as 35 is in the top 5 percent. The average tells you two things. Having a lower average than your 35 "median" suggests that either people are getting in with lower scores relative to the median compared to higher scores relative to the median, causing a shift in the curve, OR that the true median is actually below what the sum total of three medians is. I'm pretty sure that the "median" of NYU is 35, but the average is several points lower. I bet the true median is around 33-34.

 

[RoadRunner17]

Hey guys,

I read alot around here about schools who's median is this or that, but I think people are under a afalse assumption. This assumption is that median scores of, say, 12, 11, 12 result in a total median of 35. THIS IS NOT TRUE! This reasoning in under the assumption that the same half of the class is getting all the grades above or equal to 12, 11, 12. Case in point, me. My BS score is above this median, where as my PS is not. The actual median scores, I would assert, are actually lower than 35. Look at the percentile rankings of the MCAT. 12s and 11s are in the low 90th percentile or less, where as 35 is in the top 5 percent. The average tells you two things. Having a lower average than your 35 "median" suggests that either people are getting in with lower scores relative to the median compared to higher scores relative to the median, causing a shift in the curve, OR that the true median is actually below what the sum total of three medians is. I'm pretty sure that the "median" of NYU is 35, but the average is several points lower. I bet the true median is around 33-34.

Thanks for bringing up a pet peeve of mine. 👍

 

[mmmcdowe]

Thanks for bringing up a pet peeve of mine. 👍

Seriously, this is what happens when math is downplayed for pre-meds! LOL 😎

 

[LizzyM]

Hmmm... I just pulled a dozen applications at random from those I'm about to review.

The range of scores are (8-12), (10-13) and (11-15). The total MCAT is in the range of 31-35

The median scores are 10.5 , 11 , 11 . The median of the total MCAT is 33.

The average scores are 10.3, 11.1 and 11.8. The average total MCAT is 33.1

Not sure I see your point.

 

[mfrizzo3]

Hey guys,

I read alot around here about schools who's median is this or that, but I think people are under a afalse assumption. This assumption is that median scores of, say, 12, 11, 12 result in a total median of 35. THIS IS NOT TRUE! This reasoning in under the assumption that the same half of the class is getting all the grades above or equal to 12, 11, 12. Case in point, me. My BS score is above this median, where as my PS is not. The actual median scores, I would assert, are actually lower than 35. Look at the percentile rankings of the MCAT. 12s and 11s are in the low 90th percentile or less, where as 35 is in the top 5 percent. The average tells you two things. Having a lower average than your 35 "median" suggests that either people are getting in with lower scores relative to the median compared to higher scores relative to the median, causing a shift in the curve, OR that the true median is actually below what the sum total of three medians is. I'm pretty sure that the "median" of NYU is 35, but the average is several points lower. I bet the true median is around 33-34.

Hmmmmm.

Median 12 11 12
#1 11 12 12
#2 10 10 15
#3 13 13 9
#4 12 13 10

I can go for days..

 

[mmmcdowe]

Hmmm... I just pulled a dozen applications at random from those I'm about to review.

The range of scores are (8-12), (10-13) and (11-15). The total MCAT is in the range of 31-35

The median scores are 10.5 , 11 , 11 . The median of the total MCAT is 33.

The average scores are 10.3, 11.1 and 11.8. The average total MCAT is 33.1

Not sure I see your point.

Hello LizzyM, loved your spreadsheet. So first of all, I think you misunderstand what I am saying. I wasn't saying so much that the average and the median were the same, as that the PERCEIVED median (the one you get on the MSAR by adding the three different median scores) tends to be inflated when compared to the real. Now I see that you have picked applications at random, but what I would be more interested is if you could pick a few from the accepted pile of applications, or better yet students who matriculated last year since there is no garuntee that students will matriculate, and repeat what you just did. My arguement is that the median that you get from the MSAR tends to be higher because of the fact that some students will have, say 11, 14, 11, while others might have 12, 8, 12, and others might have 10, 11, 10. In this case, the median score is a 32. The median score when you take each individually, however, is a 33 (11, 11, 11). While this is opposite of my contention that median totals tend to be higher, it still shows how there can be a difference.

 

[MrAgreeable]

Hey guys,

I read alot around here about schools who's median is this or that, but I think people are under a afalse assumption. This assumption is that median scores of, say, 12, 11, 12 result in a total median of 35. THIS IS NOT TRUE! This reasoning in under the assumption that the same half of the class is getting all the grades above or equal to 12, 11, 12. Case in point, me. My BS score is above this median, where as my PS is not. The actual median scores, I would assert, are actually lower than 35. Look at the percentile rankings of the MCAT. 12s and 11s are in the low 90th percentile or less, where as 35 is in the top 5 percent. The average tells you two things. Having a lower average than your 35 "median" suggests that either people are getting in with lower scores relative to the median compared to higher scores relative to the median, causing a shift in the curve, OR that the true median is actually below what the sum total of three medians is. I'm pretty sure that the "median" of NYU is 35, but the average is several points lower. I bet the true median is around 33-34.

I believe (in the MSAR) that they average the numbers of all they ACCEPT not those who matriculate (~1/2 accepted), so John Q. Overachiever gets accepted to 12 schools with his 3.9/40S, well Johnny is bringing up the stats at all 12 schools (Exept Wash U. probably. Funny story, we played a team in their football conference and watched Wash U on film. My coach starts laughing at a play they bungled and said "What idiots" I laughed in my head and thought "This guy doesn't know that these are the smartest kids in the nation"). Anyway, point is that the average matriculant score is usually lower than the average accepted score. This thinking works for median scores, as well. Just my one quid and six six-pence.

 

[LizzyM]

OK, I thought you might ask so I picked 110 applications of people who did matriculate over the past few years.

means: 11.2 10.4 11.3 33.0
medians: 11 11 11 33

the range is from 22 to 41, btw.

 

[RoadRunner17]

Seems like people are missing the point. You can't just add up the 3 median scores for the subsections and automatically get the median total score. Sometimes you can get away with it, sometimes you can't; the point is that the scores come in bundles of 3, not individually, to generate the total score.

 

[mmmcdowe]

OK, I thought you might ask so I picked 110 applications of people who did matriculate over the past few years.

means: 11.2 10.4 11.3 33.0
medians: 11 11 11 33

the range is from 22 to 41, btw.

LizzyM, so are you saying that the 33 is the median when you just sum them up? Or are you adding up 11, 11, 11 to get 33? Is that the median at your school?

 

[mmmcdowe]

I believe (in the MSAR) that they average the numbers of all they ACCEPT not those who matriculate (~1/2 accepted), so John Q. Overachiever gets accepted to 12 schools with his 3.9/40S, well Johnny is bringing up the stats at all 12 schools (Exept Wash U. probably. Funny story, we played a team in their football conference and watched Wash U on film. My coach starts laughing at a play they bungled and said "What idiots" I laughed in my head and thought "This guy doesn't know that these are the smartest kids in the nation"). Anyway, point is that the average matriculant score is usually lower than the average accepted score. This thinking works for median scores, as well. Just my one quid and six six-pence.

I haven't heard of that, but that is very interesting...

 

[LizzyM]

LizzyM, so are you saying that the 33 is the median when you just sum them up? Or are you adding up 11, 11, 11 to get 33?

I summed each student's 3 sub-scores (call this the total score) and then found the mean and median total scores for the group of 110 students.

 

[mmmcdowe]

I summed each student's 3 sub-scores (call this the total score) and then found the mean and median total scores for the group of 110 students.

In that case perhaps I am wrong in assuming that there is a significant difference, but at the same time when I see a school with an average of 32 and a summed median of 35, I can't help but believe there must be some difference in the median.

 

[LizzyM]

In that case perhaps I am wrong in assuming that there is a significant difference, but at the same time when I see a school with an average of 32 and a summed median of 35, I can't help but believe there must be some difference in the median.

which school and what is the source of your data?

 

[mmmcdowe]

which school and what is the source of your data?

I will find it, hold on. I have to dig through an admissions page.

 

[mmmcdowe]

http://admissions.med.nyu.edu/student-composition

32Q average.

 

[DrYoda]

Problem 1: You are comparing median and average.

Problem 2: You are comparing accepted to matriculated.

 

[mmmcdowe]

Problem 1: You are comparing median and average.

Problem 2: You are comparing accepted to matriculated.

What I'm talking about now is different, LizzyM wanted to know where I saw a 32 ave and a 35 median. And where am I comparing accepted to matriculated? Do you know something about the MSAR data? I assumed all of it was matriculated data.

 

[DrYoda]

What I'm talking about now is different, LizzyM wanted to know where I saw a 32 ave and a 35 median. And where am I comparing accepted to matriculated? Do you know something about the MSAR data? I assumed all of it was matriculated data.

MSAR data is from all accepted., so the difference between the two groups is probably responsible for the wide difference.

 

[mmmcdowe]

That is very interesting, I didn't know that. In that case there is even MORE reason not to trust the total median of the MSAR! lol

 

[RoadRunner17]

Whatever it may be, in the MSAR it gives a median score for each section of the MCAT. So, let's say XYZ Medical School has a median score of 12, 12, 12 for PS, VR, and BS, respectively. The argument the OP is making is that you can't just automatically add up these 3 numbers to get a 36 and call that the total median score. You might get away with it sometimes, but it would most likely be wrong to assume a 36 is the median total score in this case. And, note that nowhere in the MSAR does it actually display a median total score. People have just been adding up the median scores for each section.. not necessarily the correct number!

 

[LizzyM]

In choosing a group of people to interview, schools are likely to be looking for people similar to those that they accepted last year. So, if you wonder if you have what it takes to get an interview, go with the figures provided for accepted applicants. If you want to know how you measure up to the rest of the class (if you are deciding where to matriculate), the figures on matriculants are a more accurate picture of the incoming class.

 

[mmmcdowe]

You're my new best friend roadrunner 😉

 

[LizzyM]

Whatever it may be, in the MSAR it gives a median score for each section of the MCAT. So, let's say XYZ Medical School has a median score of 12, 12, 12 for PS, VR, and BS, respectively. The argument the OP is making is that you can't just automatically add up these 3 numbers to get a 36 and call that the total median score. You might get away with it sometimes, but it would most likely be wrong to assume a 36 is the median total score in this case. And, note that nowhere in the MSAR does it actually display a median total score. People have just been adding up the median scores for each section.. not necessarily the correct number!

You have your own scores in each subsection so just compare each of your scores to the school's mean/median in each subsection and be done with it.

 

[mmmcdowe]

You have your own scores in each subsection so just compare each of your scores to the school's mean/median in each subsection and be done with it.

LizzyM, may I ask. If all things on an application were equal, would you rather have an applicant who was exactly your median in every section, or would you give equal weight to a student who had two points above in one section and 2 points below in another? I think it would be lovely if true medians were available on the MSAR.

 

[Greonis]

The medians compiled in the MSAR taken into account all MCAT scores of accepted applicants (whether or not they ultimately matriculated). A single applicant with multiple acceptances will have his or her numbers be computed for every school that he or she was accepted at.

Therefore, making the assumption that those with higher scores receive more acceptances on average, you can see why the accepted applicants' medians are skewed slightly above those of the matriculating applicants' medians (which naturally only factor in each person to no more than one school). Across the board, higher scores will be factored into the median calculations more often than lower scores, thus a slight rise is to be expected. This is far from a perfect model, of course (it does not cleanly integrate EDP/EAP applicants, those who chose to only apply to a single school, it assumes that certain numbers of "high-scoring" and "low-scoring" applicants get accepted, etc...), but it should nonetheless give you a sense of why the medians are slightly askew.

 

[LizzyM]

LizzyM, may I ask. If all things on an application were equal, would you rather have an applicant who was exactly your median in every section, or would you give equal weight to a student who had two points above in one section and 2 points below in another? I think it would be lovely if true medians were available on the MSAR.

This is a difficult question. The difference between an 11 and a 13 is negligible from a percentile perspective whereas the difference beween a 9 and and an 11 is more substantial. So an uneven score might be less desirable than an "even" score. On the other hand, scores are often summed and a 33 that is a 11 9 13 might be seen as equal to 11 11 11 or it might be considered substandard because of the 9, or the 13 might impress someone who doesn't realize that it represents a slight difference (a couple of questions) from an 11.

 

[RoadRunner17]

You have your own scores in each subsection so just compare each of your scores to the school's mean/median in each subsection and be done with it.

Of course. Its just a pet peeve of mine when other pre-meds add the numbers up and gawk at the "total median scores" schools like WashU, Stanford and Michigan. Nothing major, mind you, because it still gives you an idea of how competitive it is, but by definition you arrive at a faulty conclusion.

 

[student1799]

Whatever it may be, in the MSAR it gives a median score for each section of the MCAT. So, let's say XYZ Medical School has a median score of 12, 12, 12 for PS, VR, and BS, respectively. The argument the OP is making is that you can't just automatically add up these 3 numbers to get a 36 and call that the total median score. You might get away with it sometimes, but it would most likely be wrong to assume a 36 is the median total score in this case. And, note that nowhere in the MSAR does it actually display a median total score. People have just been adding up the median scores for each section.. not necessarily the correct number!

Actually, this IS the right way to do it, because both the total MCAT score and the section scores are from normally distributed populations. (We know that MCAT scores are normally distributed because the scores are really percentile ranks, which by definition come from a normal distribution.) So if the total score is normal and the subscores are normal, so are the medians of these scores, which means that the medians of the subscores should add up to the median of the total score. (You'll notice that this was always true in the examples LizzyM cited.)

If they don't, there are only two possible explanations: rounding error (which could be up to 1.5 points for a given total score, since each the subscore is rounded to the nearest whole number), or the difference between accepted and matriculated scores.

 

[RoadRunner17]

Actually, this IS the right way to do it, because both the total MCAT score and the section scores are from normally distributed populations. (We know that MCAT scores are normally distributed because the scores are really percentile ranks, which by definition come from a normal distribution.) So if the total score is normal and the subscores are normal, so are the medians of these scores, which means that the medians of the subscores should add up to the median of the total score. (You'll notice that this was always true in the examples LizzyM cited.)

If they don't, there are only two possible explanations: rounding error (which could be up to 1.5 points for a given total score, since each the subscore is rounded to the nearest whole number), or the difference between accepted and matriculated scores.

Hm, did not think of that.. you could be right (last time I took stats was 4 years ago!!). However, I believe that it does not always match up. For example, I just made up a bunch of random numbers and called them MCAT scores. The first 3 numbers are subsection scores and the fourth is the sum of these subsection scores.

12 11 12  35
14  9  11  34 
13 13 13  39
10  8  14  32
15  10  9  34

So, the median for the first set is 13, second is 10, and third is 12. Add that up, you get 35. However, if you took the median of the total scores, it is 34. I think what you are saying is that if someone scores in similar percentiles on all 3 subsections, then the total score will reflect that. But in this case, this didn't happen as there were variances in the subscores for individuals. Not everyone who scores above 90th percentile on PS will score above 90th percentile on VR and BS, for example. But there are different ways to achieve 90th percentile in the total score. Maybe that's your rounding error there, maybe it's something else - I just think it's not the exact same thing to add up the median subscores to get a median total score. But it should usually be close, and probably negligible if you have a large sample size.

If you look at the graphs on the AAMC website (http://www.aamc.org/students/mcat/examineedata/pubs.htm) for either '07 or '08 as examples, you'll see that the curves are not perfectly normal distributions. They're close, but not perfectly normal. I suppose I would attribute the slight variance to this, as well as to what I suggested above. Not every MCAT subsection is created equally for each person, after all.

Let me know if I'm completely off my rocker, which is certainly possible. But that's how I see it.

 

[mmmcdowe]

I don't think I follow either, For example, 3% of people get 14 in a given section, but 3% of people don't get 14's in all three sections....

 

[Raryn]

Actually, this IS the right way to do it, because both the total MCAT score and the section scores are from normally distributed populations. (We know that MCAT scores are normally distributed because the scores are really percentile ranks, which by definition come from a normal distribution.) So if the total score is normal and the subscores are normal, so are the medians of these scores, which means that the medians of the subscores should add up to the median of the total score. (You'll notice that this was always true in the examples LizzyM cited.)

If they don't, there are only two possible explanations: rounding error (which could be up to 1.5 points for a given total score, since each the subscore is rounded to the nearest whole number), or the difference between accepted and matriculated scores.

One problem: The total scores are normalized, the individual section scores are not. There are definite skews in the sections. Take a look at the combined 2007 and combined 2008 pdfs...

http://www.aamc.org/students/mcat/examineedata/pubs.htm

 

[radi0headfan]

Seems like people are missing the point. You can't just add up the 3 median scores for the subsections and automatically get the median total score. Sometimes you can get away with it, sometimes you can't; the point is that the scores come in bundles of 3, not individually, to generate the total score.

yea this makes perfect sense...i think the schools prefer to break each section down for their own admissions criteria, but it's incorrect to say: sum of medians in each section = overall median

after looking at the distributions, it appears to me that the individual sections are not being normalized..for each section, there's an inbuilt curve which is based on the # of questions that have to be answered right in order to result a 1-15 score...after the total # of people receiving each score is calculated, im not sure if there's slight tampering that goes on afterward in order to mirror data from previous administrations ...according to the data from 2007, 20%+ of the population that received an M on the writing section...on verbal reasoning, 12% received a score of a 6 while 11% received a score of a 7..so that leads me to believe that the data for the individual sections is raw since it isnt fitting any pretty normal curves...however, there may be some tampering when the final curve is made, because the percentiles from the final distribution look too perfect to have everyone's combination of scores just add up that way..for example, what if there's a large percentage of people that just happen to make 24's after all individual section scores are added up? ..to correct this and essentially normalize the curve, maybe some people are bumped down to a 23 and up to a 25 based on how their individual section scores relate to the rest of the population's #'s?...btw, im making the assumption that before anyone sits down to take the test, the number of questions answered correctly on each section correlates to a certain score from 1-15 (rather than being determined afterward-- like i was saying earlier, it looks like the individual sections have pre-determined curves rather than being messed with after the administration of the test)..maybe my initial assumption is wrong though.. anyone have more insight into this?

 

[itsallthesame]

the answer to the original statement is simple:

if the varience is low between scores for individuals OR the the admissions committee accepts based on total MCAT making all sections weighted equally, then the difference between median total and the sum of the median sections is likely to be slim.

if, however, the school weights each sections differently, uses a non-linear value with regard to the scaled scores to weigh mcats (eg using the % score instead of the #), will forgive a single bad section if the total is above the median or will accept one great score if the total is below the median, or if there is a high degree of variability between the scores of individuals, etc etc etc, then the sum of the median sections could be different from the median overall score (and could be higher or lower depending on the selection criteria used).

these scenarios could also play out if the admissions commitee stochastically accepts individuals who fall into the described categories unintentionally based on GPA, ECs, etc.

also, sampling scores from a single school is worthless because these scenarios all depend upon admissions criteria. some serious bootstrapping would need to be done in order to determine the chance that the medians matched through chance or if there is a true correlation.

come on guys, you're gonna be doctors... take a stats course.

 

[Raryn]

I still say that the median you get by adding up the individual 3 medians is pretty much identical to the true median. You *might* be off by one, but I doubt more than that.

The main difference people see between the median and the mean is usually because our source of medians (MSAR) gives the #s for accepted students, while our source of means (US News) gives the # for matriculated students. That, and I doubt that the population of accepted/matriculated students has anywhere close to a normal distribution.

 

[student1799]

No, the score distributions for the subsections are not perfectly normal, but they're close. I have the curves for the 2007 exam, and while none of them have a perfect bell curve shape, I don't think any of them would violate a statistical test for being normal. In particular, the mean and median scores for each section are the same, which is one of the hallmarks of a normal distribution. And all seem to roughly pass another important test, which is that 2/3 of the scores should be found within 1 standard deviation of the mean. This is true for all; in fact, the verbal and physical science sections have significantly MORE than 2/3 of the scores in this range (VR: 85%, PS: 78%). This means that the mean (and therefore the median) is a MORE reliable measure of the distribution, because fewer extremely high and low scores are found.

Therefore, if you added up the medians for each section, you would expect to get to the median MCAT score, and you do--within rounding error. Medians (ignoring outliers) are: PS ~8.5, VR 8, BS ~8.5, which adds up to 25; the median score (disregarding outliers) looks to be between 25 and 26. If we do this using the means (which are equal to the medians), we get PS 8.4, VR 8, BS 8.8, which adds to 25.2, while the mean MCAT score is 25.1--a very close match.

However, if I round the section medians, that throws off the total: I would get 24 or 26 (depending on which way you round), while the rounded median total score is 25. I think that rounding error would account for most of the discrepancy you are seeing.

btw, im making the assumption that before anyone sits down to take the test, the number of questions answered correctly on each section correlates to a certain score from 1-15 (rather than being determined afterward-- like i was saying earlier, it looks like the individual sections have pre-determined curves rather than being messed with after the administration of the test)..maybe my initial assumption is wrong though

I think you are incorrect here. If you look at the score distributions for the 2007 exam, you'll see that each score corresponds to a percentile range, and that range is identical for the 2008 MCATs as well. (It was printed on my score reports for the 2 MCATs I took in '08.) So an 8 or a 10 on any MCAT section ALWAYS means the same percentile range, even though it might have required a different number of correct answers to achieve that score on 2 different tests. This is not predetermined, but depends on how test takers performed on the test.

Clearly, they designed the scoring system so that 8 would be the median for each section, which would give a 24 median for the total MCAT. This is still true in the verbal section, but scores in the other 2 have been slowly drifting upward over the years: the mean for PS is now 8.4, and the mean for BS is 8.8. If these curves continue to skew to the right, they may have to reset the percentile ranges that go with different numerical scores, but the principle that the section medians add up to the median total score should remain valid.

 

[RoadRunner17]

the answer to the original statement is simple:

if the varience is low between scores for individuals OR the the admissions committee accepts based on total MCAT making all sections weighted equally, then the difference between median total and the sum of the median sections is likely to be slim.

if, however, the school weights each sections differently, uses a non-linear value with regard to the scaled scores to weigh mcats (eg using the % score instead of the #), will forgive a single bad section if the total is above the median or will accept one great score if the total is below the median, or if there is a high degree of variability between the scores of individuals, etc etc etc, then the sum of the median sections could be different from the median overall score (and could be higher or lower depending on the selection criteria used).

these scenarios could also play out if the admissions commitee stochastically accepts individuals who fall into the described categories unintentionally based on GPA, ECs, etc.

also, sampling scores from a single school is worthless because these scenarios all depend upon admissions criteria. some serious bootstrapping would need to be done in order to determine the chance that the medians matched through chance or if there is a true correlation.

come on guys, you're gonna be doctors... take a stats course.

Agreed. This is what I've been trying (somewhat unsuccessfully, apparently) to say. Not every MCAT subscore is created equally in the eyes of the admissions committees, who are the ones that determine the numbers that you see in the MSAR. If the admissions committee puts more weight on the PS than the VR and BS, or the VR over the PS and BS, etc... then it would be invalid to just add the medians up to get the total median. It hearkens back to my argument that there is more than one way to score a 35, aka more than one way to skin a cat.

Student1799's argument does make sense but we are not talking about actual MCAT scores for each person. We're talking about each subscore as a criteria for admissions, not each subscore as part of the total scores for the MCAT test-taking population.

 

[student1799]

the answer to the original statement is simple:

if the varience is low between scores for individuals OR the the admissions committee accepts based on total MCAT making all sections weighted equally, then the difference between median total and the sum of the median sections is likely to be slim.

Yes, I believe this is the case. It is even more likely to be true if you consider the fact that total MCAT is strongly correlated with each section score: a person who scores very well on one section is likely to score well on the others. (Total MCAT is also correlated with the section scores by virtue of the simple fact that the total score is the sum of the section scores.)

It's fairly unusual to see "unbalanced" MCAT scores, which is why admissions committees dislike them. Therefore, no matter what sections a school weights most highly in its admissions policy, the RESULTS of that policy are likely to be indistinguishable from an admissions policy based on total MCAT scores.

if, however, the school weights each sections differently, uses a non-linear value with regard to the scaled scores to weigh mcats (eg using the % score instead of the #)

This makes no sense. The scaled score IS a percentile score, so there is no way to "use a % instead of the #."

will forgive a single bad section if the total is above the median

This is equivalent to admitting based on total scores.

or will accept one great score if the total is below the median,

If this ever happens, it must be extremely rare.

or if there is a high degree of variability between the scores of individuals

There isn't, because each school receives many thousands of applications. Most state med schools in the MSAR (except in states with very small populations) seem to get at least 3,000 apps, and most private schools get at least 7,000; that represents roughly 5-10% of all MCAT takers applying to each school. If the underlying population of MCAT scores is normal, which we've agreed it is, and has no underlying skew with respect to section scores (which it doesn't), it would be extremely unlikely for any one school's applicant pool, which represents 5-10% of the total MCAT pool, to be skewed. And if the applicant pool isn't skewed, it would be even more surprising if the pool of admitted students is skewed. As I said above, schools LIKE "balanced" MCAT scores, so it would be strange if the pool of admitted students was skewed toward any one section.

also, sampling scores from a single school is worthless because these scenarios all depend upon admissions criteria. some serious bootstrapping would need to be done in order to determine the chance that the medians matched through chance or if there is a true correlation.

As I said in after the first quote, the RESULTS of any admissions policy based on section scores are going to come out looking the same as a policy based on total MCAT scores, because you're applying the policy to a population of applicants whose section scores are highly correlated with their total MCAT scores.

 

[RoadRunner17]

Not everyone has balanced scores. Verbal has been a significant stumbling block for people who otherwise do well on the sciences sections, for example. Or, there are humanities majors who do well on Verbal, but not as well on the sciences. These people ARE in the applicant pool. It's asking too much for everyone to be 10/10/10 or 12/12/12. Just from anecdotes, I have a friend who was accepted with 13/8/12, and others with similar scores, for example.

But, point taken; I agree that in a large applicant pool, those differences tend to be minimized. But it is not the same thing to add the medians up to get the total score, and taking the medians of the total scores pool.. which is the point I am getting at. Maybe you can get away with it, but by and far it is not the same thing.

 

[Raryn]

Yes, I believe this is the case. It is even more likely to be true if you consider the fact that total MCAT is strongly correlated with each section score: a person who scores very well on one section is likely to score well on the others. (Total MCAT is also correlated with the section scores by virtue of the simple fact that the total score is the sum of the section scores.)

It's fairly unusual to see "unbalanced" MCAT scores, which is why admissions committees dislike them. Therefore, no matter what sections a school weights most highly in its admissions policy, the RESULTS of that policy are likely to be indistinguishable from an admissions policy based on total MCAT scores.

This makes no sense. The scaled score IS a percentile score, so there is no way to "use a % instead of the #."

This is equivalent to admitting based on total scores.

If this ever happens, it must be extremely rare.

There isn't, because each school receives many thousands of applications. Most state med schools in the MSAR (except in states with very small populations) seem to get at least 3,000 apps, and most private schools get at least 7,000; that represents roughly 5-10% of all MCAT takers applying to each school. If the underlying population of MCAT scores is normal, which we've agreed it is, and has no underlying skew with respect to section scores (which it doesn't), it would be extremely unlikely for any one school's applicant pool, which represents 5-10% of the total MCAT pool, to be skewed. And if the applicant pool isn't skewed, it would be even more surprising if the pool of admitted students is skewed. As I said above, schools LIKE "balanced" MCAT scores, so it would be strange if the pool of admitted students was skewed toward any one section.

As I said in after the first quote, the RESULTS of any admissions policy based on section scores are going to come out looking the same as a policy based on total MCAT scores, because you're applying the policy to a population of applicants whose section scores are highly correlated with their total MCAT scores.

The population of people who actually apply is definitely skewed, because the people with scores of 12 don't apply. In fact, its probably sharply skewed to the left, because I'd be willing to bet that just about everyone who scores above 30 applies, but almost no one (relatively speaking) under 24...

 

[LizzyM]

Do keep in mind that medians are quite robust because they are uninfluenced by outliers. It doesn't matter if the top scoring student has a Verbal of 14 or 12 - in either case half of the students may have a score of 10 or less and half have a score of 11 or more for a median of 10.5

 

[student1799]

The population of people who actually apply is definitely skewed, because the people with scores of 12 don't apply. In fact, its probably sharply skewed to the left, because I'd be willing to bet that just about everyone who scores above 30 applies, but almost no one (relatively speaking) under 24...

That's not the kind of skew I was referring to. I was referring to the fact that the overall pool of MCAT scores was not skewed in favor of ANY ONE SECTION. In other words, the average MCAT taker has a total score composed of ROUGHLY equal PS, VR and BS scores.

The kind of skew you're talking about is in the total MCAT score. I totally agree with you that the pool of med school applicants is self-selecting for students with high total scores, but that doesn't say anything about the distribution of their section scores.

 

[itsallthesame]

i would like to retort that the size of the applicant pool has very, very little to do with the statistics of the accepted pool. i might buy your challenges if MCAT was the only factor considered for admissions. when i say that a school might be more likely to overlook a single section, you have to consider that it's possible that if the biggest thing school X wants is research, and maybe research heavy people are doing worse on the verbal section...

also, i said that it's possible that one school over looks a single bad section if your scores are above the median. this means that school's median is 30; however, they will consider people with verbal 8's if their total mcat is over 30. now, if you do that for a large % of your population, you're pushing your overall mcat up and the verbal median down.

also, the fact that overall, a person's sum of section scores correlates with the overall score is nice, but that only matters if that holds true for the ACCEPTED pool (which is the stipulation that i mentioned). this is likely to hold for people who end up with middle of the road scores, since the % range to get say an 8 is much larger than to get a 14. however, those that get into the upper range (and are likely to hold the most acceptances) are also the ones most likely to have variability. have you ever met anyone with a 14 14 14? as you get into the range of people who make up aceptances, i would bet that the interpersonal variability increases dramatically.