Lawper Report: A Percentile-based Model for MCAT Scale Conversion

This report will address a new method of converting from the 2015 MCAT scale (or really any MCAT scale) into the old, 45-point scale. Superficially, it seems similar to my previous report on LizzyM scores, but I felt the model was of immediate importance (since people don't have to repeatedly consult AAMC Conversion Tables).

Note the model produces the old MCAT in the range of 7 to 43, not 0 to 45, since it involved percentile matching and histogram analyses of AAMC percentile data. I will likely update it when more AAMC percentile data for the new MCAT are out, but for most important values, the model works well

old MCAT = (45/70) * (new MCAT - 461.5) (MCAT Conversion Model)

And here is the calculator

Percentile Curve

@efle previously provided useful AAMC conversion/comparison tables based on side-by-side percentile comparisons. When percentiles are plotted against the 2015 MCAT scores, we observe the following percentile curve.

Lawper's Two-Sigma Method

The key assumption involved is that the distribution of the MCAT scores resembles a normal distribution. This means we are dealing with the mean (i.e. average) and standard deviations (also called "sigmas"). The average score is represented by the 50th percentile. Each score above a standard deviation from the mean is determined by the "68-95-99.7" rule, so the 68th, 95th, and 99.7th percentiles are respectively 1, 2, and 3 sigmas from the average.

From the above percentile curve, the most linear part is marked within two standard deviations from the mean. So, the percentiles used for modeling are the 5th and 95th. The corresponding MCAT scores are 481 (5th percentile), 500 (50th percentile) and 516 (95th percentile).

The MCAT spread is defined as 2 * (95th percentile - 5th percentile), and thus equal to 2 * (516 - 481) or 70.

Consequently, mapping the new MCAT scale to the old, 45-point MCAT scale can be determined by the following formula:

old MCAT = (45 / MCAT spread) * (new MCAT - lowest new MCAT + correction factor)

Or more simply:

old MCAT = (45/70) * (new MCAT - 472 + correction factor)

I added the correction factor because further analysis (credit to @efle for finding this) of the histograms comparing the old and new MCAT indicates that the 528 on the new MCAT does not correspond to a 45 on the old MCAT. Because 43-45 is virtually indistinguishable on the old MCAT as opposed to significantly more people scoring 526-527 on the new MCAT, the 528 on the new MCAT will actually correspond to a 43 on the old MCAT.

Setting the old MCAT = 43 and new MCAT = 528, the correction factor is equal to -98/9 or -10.889. After few slight adjustments, the following model for comparing the 2015 MCAT to the old MCAT is the following:

old MCAT = (45/70) * (new MCAT - 461.5) (MCAT Conversion Model)

Data Analysis
Of course, another way to determine a formula for MCAT conversions is by plotting two MCAT scales based on AAMC Percentile Conversion Tables and carrying out a simple regression on Excel. But that's not fun and the derivation is way more complicated. Additionally, the two-sigma method only requires new MCAT scores for three percentiles, so plotting out all the data is unnecessary. Nonetheless, I decided to include both just for comparison and accuracy testing.

The percentile-matching model is actually linear, but because I was rounding off the decimals to the nearest integer, it looks like a staircase. The R^2 for the model is about 0.9939, so it fits very well to the plotted data, although it is slightly weaker than the regression model. Equally important is that the rounded off data is one point more than the actual reported MCAT equivalent in some cases where MCAT > 509, and is one point lower in some cases where MCAT < 504. But that is the consequence of trying to plot a linear model into a nonlinear data that looks linear.

LizzyM Scores

Since medical schools evaluate both the old and new MCAT based on percentile comparisons, the percentile-matching model is effective and even stronger than the previously reported score-conserving model. However, since strict matching was involved in analyzing AAMC data, the equivalent ranges from the model for the old MCAT are from 7 to 43 instead of 0 to 45 (the reported AAMC ranges are from 5 to 43). This means the LizzyM scores are contracted from 0 to 85 to 5 to 83.

Right now, I will keep the score-conserving model as it is until I get more AAMC MCAT percentile data sometime around the end of this year. But hopefully, this model is useful to you! And I provided a calculator just in case

Let me know if you have any questions/concerns/complaints, as well as any problems you find.

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Lawper Report: A Percentile-based Model for MCAT Scale Conversion