Why med school interview success is a random variable

[slightlygifted]

I constantly see people on here saying that there is no component of randomness whatsoever when it comes to med school admissions. To say this means that you are sure, with absolute certainty, that if an applicant applied to 10,000 different schools 10,000 different times then their results would be exactly the same each time. This is clearly not the case, and it has been shown that in a similar problem, an interview situation where applicants are accepted or denied immediately following the interview, the best applicant is only chosen from the applicant pool at most 37% of the time. It is a higher percentage for med schools because they wait until they have about 20 applicants before deciding on them and then moving on to the next pool, but they don't decide on all applicants at once and thus they are subject to this famous problem.

http://en.wikipedia.org/wiki/Secretary_problem

This means that medical school admission acceptance is a random variable, much like a coin flip. This is mainly because medschools often review around 20-40 people at once, and so it is random which group you get placed in and thus medschool admissions does have a "lottery" component to it. This means that it is better to apply to more schools. Edited for conciseness.

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[Leoz M Jiliums]

You can write out equations on SDN??? Why in the world is that a feature?

 

[OCDOCDOCD]

You can write out equations on SDN??? Why in the world is that a feature?

It's an image.

 

[Leoz M Jiliums]

It's an image.

Damn, that's a let down for sure.

 

[gobigorgohome22]

Dude you have too much time on your hands....

Focus on getting in, not on why you are not getting in..

 

[circulus vitios]

I don't really know enough about the topic to dispute it, but I like how you copy and pasted formulas as an appeal to authority / a proof by intimidation.

 

[slightlygifted]

Dude you have too much time on your hands....

Focus on getting in, not on why you are not getting in..

This took me about 20 minutes to write because I have taken statistics and already have knowledge of probability distributions and the secretary problem. Just trying to help people with med schools admissions. I did this partly for myself to see if it is worth applying to a lot of schools. I think it is now.

 

[LuciusVorenus]

After I finished my diff eq class I promised myself I would never see that equation again. I hate you op.

 

[Deadlifts]

I haven't seen a single credible person on these forums advocate for applying to a small number of schools. I'm not sure why you're making a probability argument when the general mantra on SDN is apply early, apply broadly.

 

[Mad Jack]

It's obviously very random. Your application could be viewed by the wrong person, you could interview with the wrong interviewer, you could end up sick on the day of the interview, your app could end up lost, etc etc etc, there are a million variables. The more schools you apply to, the less likely a negative variable will affect your chance of success. More apps is basically always better if you can afford them and take the time to properly fill them out.

 

[slightlygifted]

I haven't seen a single credible person on these forums advocate for applying to a small number of schools. I'm not sure why you're making a probability argument when the general mantra on SDN is apply early, apply broadly.

In every adcom thread I've seen then they say that there is no point in applying to a lot of schools because it is not a random process. It probably doesn't feel very random, sitting down with a committee and deciding on people in a logical fashion. But I am just saying that even if it was the exact same interviewer with no bias for every person, there is still a fundamental randomness due to the whole applicant pool not being voted on at once. The fact that med schools decide on 20 people at a time or so is what makes the process inherently random, and I just decided to post the actual problem that has been solved for 50 years that reflects this. But idk, is the week after spring break for me so I have no tests or anything and can sit down and post random stuff on the forum for a bit lol.

 

[AlbinoHawk DO]

It doesn't matter. If you want in, play the game. If you want things changed, that can only happen if you get in and advocate for change.

 

[thegypsyqueen]

I don't really know enough about the topic to dispute it, but I like how you copy and pasted formulas as an appeal to authority / a proof by intimidation.

You only say this because you don't understand it. If you did, then this is just evidence to OP's argument.

 

[Lucca]

I think there is an upper bound for applications where the extra chance of admission, if there is any to be gained, does not exceed the cost and time of putting together a quality app/secondary. I know a lot of people that didn't send secondaries or withdrew from interviews out of pure burnout. It's just an optimization problem and the optimized number seems to sit at 12-20 schools depending on the person

 

[NickNaylor]

You have "proven" with math what common sense and any halfway intelligent pre-med adviser will tell you: apply to a bunch of schools. This isn't rocket science. That said, there are inherent limitations to applying to a bunch of schools. It just isn't possible to apply to all of them. As Lucca mentions above, it ultimately depends on what your goals are and how hard you want to work to achieve them.

 

[slightlygifted]

You have "proven" with math what common sense and any halfway intelligent pre-med adviser will tell you: apply to a bunch of schools. This isn't rocket science. That said, there are inherent limitations to applying to a bunch of schools. It just isn't possible to apply to all of them. As Lucca mentions above, it ultimately depends on what your goals are and how hard you want to work to achieve them.

Thats why hardcore premeds pre write their secondaries and take all online classes during interview season! jk no one is that crazy but idk. Blame my education, for some reason all the math and science classes I have ever taken feel the need to prove things like balls fall down when dropped, even though it seems obvious to everyone involved.

 

[mcloaf]

Blame my education, for some reason all the math and science classes I have ever taken feel the need to prove things like balls fall down when dropped, even though it seems obvious to everyone involved.

And that right there is why I hated intro physics lab.

 

[Patros]

That was the most roundabout and inefficient way to prove something that is clearly obvious. For your next project, please use the the Heisenberg uncertainty principle to demonstrate that a 44 mcat is better than a 24.

 

[Goro]

Right after the Vietnam War ended, a US colonel got tired of hearing from a Vietnamese general about how the Vietnamese beat the Americans. The colonel got tired of this and yelled out "you never beat us on the battlefield!"

To which the Vietnamese general said "That is true, but is also irrelevent."

Your pedanticism will not help people get into medical school.

I constantly see people on here saying that there is no component of randomness whatsoever when it comes to med school admissions. To say this means that you are sure, with absolute certainty, that if an applicant applied to 10,000 different schools 10,000 different times then their results would be exactly the same each time. This is clearly not the case, and it has been shown that in a similar problem, an interview situation where applicants are accepted or denied immediately following the interview, the best applicant is only chosen from the applicant pool at most 37% of the time. It is a higher probability for med schools because they wait until they have about 20 applicants before deciding on them and then moving on to the next pool, but they don't decide on all applicants at once and thus they are subject to this famous problem.

http://en.wikipedia.org/wiki/Secretary_problem

This means that medical school admission acceptance is a random variable. We can treat a medical school interview as a Bernoulli trial, an event that can only result in a success or a failure. This means that repeated Bernoulli trials will result in a binomial distribution, where if we have

http://en.wikipedia.org/wiki/Binomial_distribution
Then p is the probability of acceptance (taking into account the random nature due to the secretary problem and your stats), n is the number of interviews you have had, and k is the number of times you are accepted. If we plot P vs k, we get a binomial distribution which looks kind of like a Gaussian (a bell curve). Hopefully if you are a qualified applicant then the distribution will cluster around a mean number of acceptances that is not 0. But if you only apply to like 4 schools then there are not enough values to observe the binomially distributed nature and outliers are more likely (such as not getting into any school). The more schools you apply to and interviews you get, the smaller the variance of the distribution becomes and the more likely you get into a mean number of schools that is not 0. Maybe this argument is flawed, but I think it is better to apply to a lot of schools rather than apply to 4 while assuring everybody that your chances of getting in are equal to the person who applied to 30 schools. Many adcoms advocate for the nonrandom view so that they have less applications to look through, but it is simply in the applicants favor to apply to more schools. I would not mind a cap of say 15 or 20 schools so that the playing field is level, but as it is now you put yourself at a disadvantage by applying to less schools.

 

[listener23]

I literally saw the equation first than stopped reading….

 

[Blizzard18]

Can't write an equation for just plain being good at an interview and not a weirdo.

 

[knv2u]

Thats why hardcore premeds pre write their secondaries and take all online classes during interview season! jk no one is that crazy but idk. Blame my education, for some reason all the math and science classes I have ever taken feel the need to prove things like balls fall down when dropped, even though it seems obvious to everyone involved.

 

[_drinkcoffee_]

Can't write an equation for just plain being good at an interview and not a weirdo.

Center the distribution at zero acceptances

 

[slightlygifted]

That was the most roundabout and inefficient way to prove something that is clearly obvious. For your next project, please use the the Heisenberg uncertainty principle to demonstrate that a 44 mcat is better than a 24.

Idk, I don't think it is so obvious that the biggest source of inherent randomness might just be that admissions committees use a rolling admissions model as opposed to reviewing everybody at once. As for inefficient.....The only argument I made for medschool interview success being a random variable was linking to the secretary problem. That one link was my argument essentially. The rest was just using the binomial distribution to show that as with all Bernoulli trials the more you do the more the distribution clusters around a mean. That is something that is taught in any basic statistics course and I was just reiterating it for anyone who might not have taken statistics.

 

[justAstudent]

Can confirm.

Took math about 5 years ago.

 

[Patros]

Idk, I don't think it is so obvious that the biggest source of inherent randomness might just be that admissions committees use a rolling admissions model as opposed to reviewing everybody at once. As for inefficient.....The only argument I made for medschool interview success being a random variable was linking to the secretary problem. That one link was my argument essentially. The rest was just using the binomial distribution to show that as with all Bernoulli trials the more you do the more the distribution clusters around a mean. That is something that is taught in any basic statistics course and I was just reiterating it for anyone who might not have taken statistics.

Exactly! All you had to say was "Medical school admissions has a random element because adcoms are human beings and can't read the future," which is the gist of your first paragraph. Your second paragraph is "Each applicant has a certain probability of being accepted at any one interview, and going to multiple interviews increases your chances of being accepted somewhere." See? Both of these are self-evident, and you were arguing against a strawman (not even a strawman, I've never met anyone who believes the opposite of these two statements).

But I don't mean to come off as a non-imaginative jerk, I know it's loads of fun to analyze things like this. Here, have a hug.

*Hug*

 

[slightlygifted]

Exactly! All you had to say was "Medical school admissions has a random element because adcoms are human beings and can't read the future," which is the gist of your first paragraph. Your second paragraph is "Each applicant has a certain probability of being accepted at any one interview, and going to multiple interviews increases your chances of being accepted somewhere." See? Both of these are self-evident, and you were arguing against a strawman (not even a strawman, I've never met anyone who believes the opposite of these two statements).

But I don't mean to come off as a non-imaginative jerk, I know it's loads of fun to analyze things like this. Here, have a hug.
*Hug*

you are right. Edited the main post to make it more concise. Idk, I swear that I saw in the thread about how to make med school admissions better than there was a huge debate going on as to whether or not med school admissions has a random component to it. More than just interviewer bias, but an inherent randomness much like a coin flip or something. And I think it does now.

 

[figlu]

Actually, OP's argument is invalid. The outcome for a medical school interview can be treated as a Bernoulli RV, but the probability of success is different for each medical school because of "compatibility." This makes medical school interviews different Bernoulli trials. Since the Binomial RV is derived from repeated Bernoulli trials, and not different ones, the Binomial distribution is a poor statistical model for medical school interviews.

Source: I work on a Beet farm

 

[_drinkcoffee_]

you are right. Edited the main post to make it more concise. Idk, I swear that I saw in the thread about how to make med school admissions better than there was a huge debate going on as to whether or not med school admissions has a random component to it. More than just interviewer bias, but an inherent randomness much like a coin flip or something. And I think it does now.

You have to be careful with "inherent randomness." A coin flip is theoretically completely deterministic according to classical physics, it's just much easier to represent statistically. In the same way, your statistical model is an excellent model for this deterministic process.

I won't even pretend to know enough about quantum weirdness.

 

[slightlygifted]

Actually, OP's argument is invalid. The outcome for a medical school interview can be treated as a Bernoulli RV, but the probability of success is different for each medical school because of "compatibility." This makes medical school interviews different Bernoulli trials. Since the Binomial RV is derived from repeated Bernoulli trials, and not different ones, the Binomial distribution is a poor statistical model for medical school interviews.

Source: I work on a Beet farm

I assumed the applicant is mostly applying to schools with largely similar average mcat and gpas, because I figure that is what most applicants do besides a few reach schools. But you can take the binomial distribution as the same person applying to the same school 100 times and seeing how many times they get a certain amount of acceptances in each 100 application set. And then repeat that 100 application set like 10,000 times to get a nice distribution. Then it is a good approximation on a per school basis.

 

[qtpai]

Adcom logic: Ah yes young man I can totally tell how solid your future career will be based upon how comfortable you are in an artificially constrained 30 minute social encounter, where you are constantly aware that your entire future is on the line and talking about yourself like a used car salesman is about as close to your natural state as taking a brick up your ass

Yeah makes perfect sense adcoms that acceptance decisions should be made largely on this basis

Research shows over and over again that interview performance is a poor indicator of job performance but okay, you adcoms can stick with the 20th century hunch-based, research-averse selection process if you like

 

[figlu]

I assumed the applicant is mostly applying to schools with largely similar average mcat and gpas, because I figure that is what most applicants do besides a few reach schools. But you can take the binomial distribution as the same person applying to the same school 100 times and seeing how many times they get a certain amount of acceptances in each 100 application set. And then repeat that 100 application set like 10,000 times to get a nice distribution. Then it is a good approximation on a per school basis.

Sorry if I sound mean; I enjoy this kind of stuff

 

[rain4venus]

Idk, I don't think it is so obvious that the biggest source of inherent randomness might just be that admissions committees use a rolling admissions model as opposed to reviewing everybody at once. As for inefficient.....The only argument I made for medschool interview success being a random variable was linking to the secretary problem. That one link was my argument essentially. The rest was just using the binomial distribution to show that as with all Bernoulli trials the more you do the more the distribution clusters around a mean. That is something that is taught in any basic statistics course and I was just reiterating it for anyone who might not have taken statistics.

I can't help but feel that you're ignoring the fact that the groups themselves are not completely random
a) interviews are first extended to the best pre-interview candidates
b) the earlier you apply (as a strong candidate) the earlier you'll get an interview (also not random)
c) which interview date you attend is also in your control (especially if you get an early II)

That said I did see several people who had cancelled flights due to the horrible weather this winter - including at least one who had a date scheduled before the class was full. However, by the next available interview date, the class was full. That is certainly some randomness.

 

[Aerus]

Not necessarily, since being a reapplicant changes your application. It is impossible to apply with the exact same application more than once, since if you did no new activities in your year, your app will get hurt.

 

[sourdoughllama]

.

 

[knv2u]

Adcom logic: Ah yes young man I can totally tell how solid your future career will be based upon how comfortable you are in an artificially constrained 30 minute social encounter, where you are constantly aware that your entire future is on the line and talking about yourself like a used car salesman is about as close to your natural state as taking a brick up your ass

Yeah makes perfect sense adcoms that acceptance decisions should be made largely on this basis

Research shows over and over again that interview performance is a poor indicator of job performance but okay, you adcoms can stick with the 20th century hunch-based, research-averse selection process if you like

I think preliminary phone interviews would be awesome! Admissions would randomly call you with no warning so you have less time to script answers!

 

[infinitessimal]

Honestly, I don't understand why people think if you have a weak(er) application, applying to tons of schools will increase your chances of getting in. You can research a school pretty much down to their daily class schedule to see if it's somewhere you want to go, and somewhere where your stats/ECs are a good fit with the average student. Regardless of your MCAT and gpa, apply to ~5 schools you like best whose median scores are exactly in your range (maybe 2 that are slightly higher), and ~5 you also really like but whose averages are slightly below your scores. Spend your time/energy on acquiring ECs and life experience instead of figuring out if there's a randomness factor in interviewing (there is). I know there are some unique nontrad applicants for whom this is a gross generalization, but I think this applies to the majority.

So yeah, I'm spending a lot of time researching schools and plan to apply to 10 carefully chosen ones instead of shooting my gunk across the field for another 5K and hoping it sprouts somewhere.

 

[Aerus]

Naw dawg. I didn't get in last year and did squat last year and this cycle has been great. I think it depends on the application

Just because your chances are lower does not mean you won't be able to get in. Keep in mind, that unless you applied with everything being the same, including date submission, personal statements, etc. that there are other confounding factors. I'm a believer that this isn't a completely random process, but there is some degree of randomness, just because it is a human-driven process.