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I just want to know if my logic sounds generally strong. My actual correspondence table isn't thought by me to be very accurate, because I did this roughly and with very little regard for detail, such as accurate standard deviations, and other things.
So according to: http://www.assessmentpsychology.com/iq.htm (sorry, it's the only site where I could find this information), the average physician "has" an ACT score of 27. If you look under the first table, you'll see that it comes from some source of the year 1972. The first table indicates that the average M.D. physician has (did have) an iq of 125, which is how they were able to determine that the average ACT of physicians was 27. If we try to look for old MCAT data, we see that only data as far back as 2002 is shown. The average MCAT for matriculants in that year is 29.6, and that average steadily increases each year until 2013, where it hit 31.3. This indicates an increase in average MCAT scores of medical students (and therefore physicians). Therefore, if we move backward in time from 2013, we see steadily decreasing ACT scores. If we extrapolate that trend to try to predict average MCAT scores for matriculants in 1972, we will find that it is very close to 25. But let's be generous, and say that average MCAT scores for students of that time was about 29.0, which is .6 points lower than the MCAT score of the students of 2002 (rather than closer to 5 points less, which is what line extrapolation would predict).
Then we will find that an MCAT score of 29.0 (the score of the average soon-to-be physician in 1972) corresponds to an ACT score of 27 (the ACT score of the average physician in 1972, according to the data on the given website). The standard deviation for the MCAT is 6.4, and the standard deviation for the ACT is 5.2 . We find that 2013 had a 2.1 point increase in average MCAT scores (for matriculants) compared to 1972, where we assumed that the average medical student scored a 29, so therefore we should expect approximately a 2.1*5.2/6.4 = 1.7 ACT point increase compared to that time. So the average modern medical student would then be expected to have an ACT score of 28.7.
The reason that I say that we should estimate that the physicians of 1972 wouldn't have an average MCAT score of 25, as the extrapolation would predict, is because that would predict an average ACT score for modern medical students to be about 33, which we know is simply not true. Also, that would be saying that the average physician would have an average MCAT score, which is also simply not true. So I am simply making the assumption that the MCAT scores of that time would be lower than students of 2002, but not as much lower as a simple extrapolation would expect.
And if the average modern medical student has an ACT score of 28.9, and the average modern medical student has an average MCAT score of 31.1, then then a 28.9 ACT score can roughly correspond to a 31.1 MCAT score. And to determine further ACT score/ MCAT score correspondences, we would simply add however much standard deviations we want to each score. E.g. the ACT STDV = 5.2, and the MCAT STDV is 6.4, therefore if we wanted to see how much one standard deviation below the average MCAT corresponds to as far as ACTs, we would simply subtract 6.4 from the reference MCAT score (31.1) and compare that to the reference ACT score of 28.9, minus its standard deviation (5.2). So then a 24.7 MCAT would correspond to a 23.7 ACT score.
TL;DR
The whole premise behind this very rough, possibly reckless analysis is that if we can find the average ACT of a modern medical student, then we can roughly assume that that average ACT score corresponds to the average MCAT of today's matriculants, and to find other corresponding scores, we would simply add the same number of respective standard deviations to each score. So if an average MCAT is 31.1, which corresponds to an ACT of 28.7, we can simply add multiples of 6.4 (the MCAT's supposed standard deviation) to the MCAT, and add the same multiples of 5.2 (the supposed standard deviation of the ACT) to the ACT score.
So: 31.1+6.4*x MCAT score ~=~ 28.7+5.2*x ACT score (where the x is the same number).
Or alternatively (if we find that I was using incorrect standard deviations, and/or incorrect estimates of current medical matriculant ACT averages):
Average MCAT (m. matriculant) + (STDV of MCAT)*x ~=~ Average ACT (m. matriculant) + (STDV of ACT test)*x
where x is the same value for both sides of the equation, and ~=~ here means "corresponds to"
This is consistent with the conjecture that the following correspondences are roughly accurate:
In short:
ACT MCAT
5.2 6.4 (standard deviations)
24.4 ~ 25.8
25.7 ~ 27.4
27.0 ~ 29.0
28.7 ~ 31.1
30.0 ~ 32.7
31.3 ~ 34.3
32.6 ~ 35.9
33.9 ~ 37.5
35.2 ~ 39.1
36.5 ~ 40.7
If by whatever extravagant methods, we find that the average ACT of modern medical students should be estimated to be 28.2 instead of 28.7, all we would have to do is subtract each of the numbers in the left hand column by .5, while leaving the corresponding MCAT scores the same (assuming standard deviations are correct). If other problems are found, an error in one of the numbers used in the bolded equation seems likely to be the source.
****
Assumptions:
-both score sets follow a bell curve, or are similarly skewed in score distribution.
-standard deviations are consistent across the entire range of possible scores for each test.
-MCAT scores of past medical students are lower than those of today's
-MCAT scores of past medical students are higher than expected from a simple line extrapolation from recent years score data.
-the early-mentioned website gave accurate numbers, (ACT of physicians in 1972 = 27, etc.)
-others that I can't recall
-others that I didn't even consider
-etc.
***********
***********
Alternative method, using same basis of 27 ACT ~ 29 ACT
This uses the data sheet found at http://www.act.org/newsroom/data/2012/pdf/profile/National2012.pdf
The method:
In a nutshell: (# of people scoring ABOVE the given ACT score + 1/2*# of people scoring AT the given ACT score)/(Total # of People whose data was included in sample). This gives the decimal fraction of the people who scored higher than the average person with a given ACT score. I did this for every ACT score. I used the percentile of the basis 27 ACT (85.27) and corresponded that to the MCAT of 29 (percentile: 72.4). Then to find additional MCAT correspondences, I used the ratio of the # of people scoring higher than the average person with a given ACT score divided by the # of people scoring above a point below that score, and multiplied this ratio by the % of MCAT people who would have scored better than the equivalent.
Concrete example:
ACT 27 = MCAT 29
# of people scoring higher than a given person with a 27 ACT? This is equal to the number of people who scored a 28 + 29 + 30 + 31 +32 +33 +34 +35 + 36 + 1/2* the number of people who scored 27. (this is because half of the people who scored a 27 should be assumed to be slightly better than a 27, and the other half slightly worse, hopefully you know what I'm saying). Now divide this sum by the total number of people in the sample. We'll call this percentage "x". Now, the number of people who scored higher than a 28 is the number of people who scored a 29 + 30 +...+36 + 1/2*number of people who scored 28. Divide this sum by the total number of people in the sample, and we'll call this decimal percentage "y". Therefore the ratio of rarities of y to x is y/x. Well, we know that y/x*x gives you y. And we also know that 1-x (which is the ACT percentile) corresponds to some corresponding MCAT percentile we'll call z (which is the MCAT percentile of those who scored 29 on their MCAT in this case). We can say that the percent of people ("decimal percentage") of those scoring above that corresponding MCAT score is 1-z, and it corresponds to the percent of people scoring above it's associated ACT score, which we defined to be "x." Therefore x~1-z therefore just as y/x *x gives the percent of people scoring above a 27 on their ACT, y/x*(1-z) gives the corresponding percent of people taking the MCAT who would score above 28 ACT.
In a word: if one ACT score is 10 times rarer than a previous ACT score, then one's equivalent MCAT score should be 10 times rarer than the previous corresponding MCAT score. If we go from 85th percentile to 98.5th percentile on ACT, we should go from 72nd to 97.2nd on the MCAT.
Too long; didn't read?
Here is a table showing the end results (The second table is same as the one shown above). Notice the consistency between the two methods' results, except a slight discrepancy at the very top scores:
According to data collected from these two threads (I don't know if this is reliable, considering a huge likelihood that there is some sort of bias of those who chose to post their respective scores or not), these tables underpredict your MCAT by almost exactly one point:
http://forums.studentdoctor.net/threads/act-score-and-mcat-score-correlation.526626/
http://forums.studentdoctor.net/threads/act-vs-mcat.289029/
Therefore a table more consistent with that good/bad set of data may look more like:
ACT MCAT
36 42
35 40
34 39
33 38
32 36
31 35
30 34
29 32
28 31
27 30
Which also may suggest that the average incoming medical student scored 28 on their ACT. But again, that is based off of a change in results due to a potentially biased thread (coming from a MCAT study forum).
***********
***********
Want to use the tables, but did not take the ACT, or certain circumstances rendered your SAT score more representative? Convert SAT to ACT here: http://www.act.org/solutions/college-career-readiness/compare-act-sat/.
Comment if you think I made a poor assumption regarding some of this. Including whether a 27 ACT should correspond to 29 MCAT, whether you think perhaps one of the two populations would have a larger standard deviation that should in no way correspond to the standard deviation of the other population, etc.
Edit: Changed the word "would" to the word "may" right before the last table.
So according to: http://www.assessmentpsychology.com/iq.htm (sorry, it's the only site where I could find this information), the average physician "has" an ACT score of 27. If you look under the first table, you'll see that it comes from some source of the year 1972. The first table indicates that the average M.D. physician has (did have) an iq of 125, which is how they were able to determine that the average ACT of physicians was 27. If we try to look for old MCAT data, we see that only data as far back as 2002 is shown. The average MCAT for matriculants in that year is 29.6, and that average steadily increases each year until 2013, where it hit 31.3. This indicates an increase in average MCAT scores of medical students (and therefore physicians). Therefore, if we move backward in time from 2013, we see steadily decreasing ACT scores. If we extrapolate that trend to try to predict average MCAT scores for matriculants in 1972, we will find that it is very close to 25. But let's be generous, and say that average MCAT scores for students of that time was about 29.0, which is .6 points lower than the MCAT score of the students of 2002 (rather than closer to 5 points less, which is what line extrapolation would predict).
Then we will find that an MCAT score of 29.0 (the score of the average soon-to-be physician in 1972) corresponds to an ACT score of 27 (the ACT score of the average physician in 1972, according to the data on the given website). The standard deviation for the MCAT is 6.4, and the standard deviation for the ACT is 5.2 . We find that 2013 had a 2.1 point increase in average MCAT scores (for matriculants) compared to 1972, where we assumed that the average medical student scored a 29, so therefore we should expect approximately a 2.1*5.2/6.4 = 1.7 ACT point increase compared to that time. So the average modern medical student would then be expected to have an ACT score of 28.7.
The reason that I say that we should estimate that the physicians of 1972 wouldn't have an average MCAT score of 25, as the extrapolation would predict, is because that would predict an average ACT score for modern medical students to be about 33, which we know is simply not true. Also, that would be saying that the average physician would have an average MCAT score, which is also simply not true. So I am simply making the assumption that the MCAT scores of that time would be lower than students of 2002, but not as much lower as a simple extrapolation would expect.
And if the average modern medical student has an ACT score of 28.9, and the average modern medical student has an average MCAT score of 31.1, then then a 28.9 ACT score can roughly correspond to a 31.1 MCAT score. And to determine further ACT score/ MCAT score correspondences, we would simply add however much standard deviations we want to each score. E.g. the ACT STDV = 5.2, and the MCAT STDV is 6.4, therefore if we wanted to see how much one standard deviation below the average MCAT corresponds to as far as ACTs, we would simply subtract 6.4 from the reference MCAT score (31.1) and compare that to the reference ACT score of 28.9, minus its standard deviation (5.2). So then a 24.7 MCAT would correspond to a 23.7 ACT score.
TL;DR
The whole premise behind this very rough, possibly reckless analysis is that if we can find the average ACT of a modern medical student, then we can roughly assume that that average ACT score corresponds to the average MCAT of today's matriculants, and to find other corresponding scores, we would simply add the same number of respective standard deviations to each score. So if an average MCAT is 31.1, which corresponds to an ACT of 28.7, we can simply add multiples of 6.4 (the MCAT's supposed standard deviation) to the MCAT, and add the same multiples of 5.2 (the supposed standard deviation of the ACT) to the ACT score.
So: 31.1+6.4*x MCAT score ~=~ 28.7+5.2*x ACT score (where the x is the same number).
Or alternatively (if we find that I was using incorrect standard deviations, and/or incorrect estimates of current medical matriculant ACT averages):
Average MCAT (m. matriculant) + (STDV of MCAT)*x ~=~ Average ACT (m. matriculant) + (STDV of ACT test)*x
where x is the same value for both sides of the equation, and ~=~ here means "corresponds to"
This is consistent with the conjecture that the following correspondences are roughly accurate:
In short:
ACT MCAT
5.2 6.4 (standard deviations)
24.4 ~ 25.8
25.7 ~ 27.4
27.0 ~ 29.0
28.7 ~ 31.1
30.0 ~ 32.7
31.3 ~ 34.3
32.6 ~ 35.9
33.9 ~ 37.5
35.2 ~ 39.1
36.5 ~ 40.7
If by whatever extravagant methods, we find that the average ACT of modern medical students should be estimated to be 28.2 instead of 28.7, all we would have to do is subtract each of the numbers in the left hand column by .5, while leaving the corresponding MCAT scores the same (assuming standard deviations are correct). If other problems are found, an error in one of the numbers used in the bolded equation seems likely to be the source.
****
Assumptions:
-both score sets follow a bell curve, or are similarly skewed in score distribution.
-standard deviations are consistent across the entire range of possible scores for each test.
-MCAT scores of past medical students are lower than those of today's
-MCAT scores of past medical students are higher than expected from a simple line extrapolation from recent years score data.
-the early-mentioned website gave accurate numbers, (ACT of physicians in 1972 = 27, etc.)
-others that I can't recall
-others that I didn't even consider
-etc.
***********
***********
Alternative method, using same basis of 27 ACT ~ 29 ACT
This uses the data sheet found at http://www.act.org/newsroom/data/2012/pdf/profile/National2012.pdf
The method:
In a nutshell: (# of people scoring ABOVE the given ACT score + 1/2*# of people scoring AT the given ACT score)/(Total # of People whose data was included in sample). This gives the decimal fraction of the people who scored higher than the average person with a given ACT score. I did this for every ACT score. I used the percentile of the basis 27 ACT (85.27) and corresponded that to the MCAT of 29 (percentile: 72.4). Then to find additional MCAT correspondences, I used the ratio of the # of people scoring higher than the average person with a given ACT score divided by the # of people scoring above a point below that score, and multiplied this ratio by the % of MCAT people who would have scored better than the equivalent.
Concrete example:
ACT 27 = MCAT 29
# of people scoring higher than a given person with a 27 ACT? This is equal to the number of people who scored a 28 + 29 + 30 + 31 +32 +33 +34 +35 + 36 + 1/2* the number of people who scored 27. (this is because half of the people who scored a 27 should be assumed to be slightly better than a 27, and the other half slightly worse, hopefully you know what I'm saying). Now divide this sum by the total number of people in the sample. We'll call this percentage "x". Now, the number of people who scored higher than a 28 is the number of people who scored a 29 + 30 +...+36 + 1/2*number of people who scored 28. Divide this sum by the total number of people in the sample, and we'll call this decimal percentage "y". Therefore the ratio of rarities of y to x is y/x. Well, we know that y/x*x gives you y. And we also know that 1-x (which is the ACT percentile) corresponds to some corresponding MCAT percentile we'll call z (which is the MCAT percentile of those who scored 29 on their MCAT in this case). We can say that the percent of people ("decimal percentage") of those scoring above that corresponding MCAT score is 1-z, and it corresponds to the percent of people scoring above it's associated ACT score, which we defined to be "x." Therefore x~1-z therefore just as y/x *x gives the percent of people scoring above a 27 on their ACT, y/x*(1-z) gives the corresponding percent of people taking the MCAT who would score above 28 ACT.
In a word: if one ACT score is 10 times rarer than a previous ACT score, then one's equivalent MCAT score should be 10 times rarer than the previous corresponding MCAT score. If we go from 85th percentile to 98.5th percentile on ACT, we should go from 72nd to 97.2nd on the MCAT.
Too long; didn't read?
Here is a table showing the end results (The second table is same as the one shown above). Notice the consistency between the two methods' results, except a slight discrepancy at the very top scores:
According to data collected from these two threads (I don't know if this is reliable, considering a huge likelihood that there is some sort of bias of those who chose to post their respective scores or not), these tables underpredict your MCAT by almost exactly one point:
http://forums.studentdoctor.net/threads/act-score-and-mcat-score-correlation.526626/
http://forums.studentdoctor.net/threads/act-vs-mcat.289029/
Therefore a table more consistent with that good/bad set of data may look more like:
ACT MCAT
36 42
35 40
34 39
33 38
32 36
31 35
30 34
29 32
28 31
27 30
Which also may suggest that the average incoming medical student scored 28 on their ACT. But again, that is based off of a change in results due to a potentially biased thread (coming from a MCAT study forum).
***********
***********
Want to use the tables, but did not take the ACT, or certain circumstances rendered your SAT score more representative? Convert SAT to ACT here: http://www.act.org/solutions/college-career-readiness/compare-act-sat/.
Comment if you think I made a poor assumption regarding some of this. Including whether a 27 ACT should correspond to 29 MCAT, whether you think perhaps one of the two populations would have a larger standard deviation that should in no way correspond to the standard deviation of the other population, etc.
Edit: Changed the word "would" to the word "may" right before the last table.
Last edited:
