The SHSAT has two types of scores- raw scores and scaled scores. The DOE keeps the conversion a secret, but thanks to a 2008 study by Ph.D. Joshua Feinman, we can make some assumptions and grade our own practice tests.
You can skip to the end of this post for a chart that lets you easily convert a raw score to a scaled score. It doesn’t account for some of the more nuanced assumptions that I’ll cover below, but it is still handy.
What is a raw score?
The SHSAT has two main sections- the reading and the math. They each have 57 questions for a total of 114 questions. Of the 57 questions in each section, 10 of them are field questions that aren’t scored. They don’t specify which questions are field questions, however.
Of the 47 questions that are counted in each section, every correct answer is worth 1 raw point and everything else, incorrect or blank, is worth 0 points.
What is a scaled score?
The scaled score is converted from the raw score. It can range from around 10-350 points for each section. Based on a 2008 case study by Ph.D. Joshua Feinman and the DOE’s SHSAT handbook, the conversion rewards raw scores as they get closer to a perfect score.
Calculating a scaled score used to be easy
In 2016, and the previous years since 2008, calculating a scaled score was easy.
The exam used to offer a total of 100 raw points split between the two sections. The exam also hadn’t gone through any changes in more than a decade and there was plenty of data available to figure out how they were being scored. The 2008 study I mentioned above was able to suggest how people should convert raw scores into scaled scores.
The exam changed in 2017 and then again in 2018. There are now 10 field questions in each section which they don’t count at all, and also 19 more questions (95 to 114).
Nevertheless, I still find the 2008 study to be the most comprehensive of its kind and still highly relevant. I believe that after some adjustments, we can continue to use the study to convert raw scores into scaled scores for practice tests. The rest of this post will go through the assumptions I make and the sources I use.
The 2008 study by Ph.D. Joshua Feinman is available at the following link: https://nepc.colorado.edu/publication/high-stakes-but-low-validity.
First, I assume the following statements by the DOE are true:
the raw scores and scaled scores are not proportional… For example, in the middle of the range of scores, an increase of one raw score point may correspond to an increase of three or four scaled score points. At the top or bottom of the range of scores, an increase of one raw score point may correspond to 10–20 scaled score points. The closer you are to getting every question in a section right (or every question wrong), the more your scaled score goes up (or down) for that section…
The conversion from raw score to scaled score is done separately for each section (ELA and mathematics). The composite score is the sum of the ELA and mathematics scaled scores. The composite score is used to determine admission to a Specialized High School…
SHSAT scores cannot be directly compared between years and there is no set minimum or maximum score. The maximum composite score is usually around 700; however, the actual maximum and minimum scores change from year to year.
How I convert a raw score to a scaled score:
I start with the raw score. Let’s say 50 out of 57 questions in one section. That’s 87.7%. I then convert that to a score out of 50 and use the following table which was reliable for the 2016 exam. 87.7 percent of 50 is 43.85, so between a scaled score of 290 or 298.
I like my students to use the lower score so that they can prepare for the worst. A 50/57 raw score in each section results in a scaled score of 580 or 596. That’s enough for all the specialized schools. So far the estimations have proved to be accurate the past two years since the changes. This calculation assumes that the field questions are spread throughout the correct and incorrect questions. I also calculate a “worst case scenario” score along with the basic calculation.
How I convert for the worst case scenario:
The field questions are the biggest issue. What if 10 of your correct answers are field questions and don’t count for anything? Well, subtract 10 from the number of correct answers and 10 from the total number of questions. With our example, we would assume 40 correct questions out of 47 counted questions. That is is 85.1% or 42.55 out of 50. According to the chart, that is between a scaled score of 283 and 290. The same score in both sections would result in a total scaled score between 566 and 580. The 566 assumption cuts it close for some of the specialized schools.
Best case scenario?
The best-case scenario assumes that the field questions were amongst the incorrect questions. Our original example was 50 out of 57 or 7 questions incorrect. We now assume all 7 incorrect questions are field questions along with 3 of the correct answers. This results in 47 correct questions out of 47 total questions. A perfect score of 720! Great for sleep, bad for prep.
10/57 = ≈ 17.5%. Assume 17.5% of the correct answers are field questions. With our example of 50/57, we assume 8.7 of the correct answers are field questions. The total number of questions minus the field questions would be 47. 50 correct answers minus 8.7 equals 41.3. That number divided by the number of non-field questions (47) would be 87.9% or 43.9 out of 50. According to the chart that equals 290 or 298. The logic and math are like my first method of conversion that I explained above, but a bit more precise.
Whenever I grade a student’s exam I use this method or the very first calculation that I explained. I then give them the worst case scenario calculation. Very rarely do I go over the best case scenario.
While writing this post I found the following chart by thinkprepny.com. I can’t seem to find the exact URL anymore, and I have no idea how they came to these numbers. However, I have tested my method against their chart and I agree with the numbers.
So what was the point of this post? If you agree with my logic you can now confidently ignore the various conversion charts found in workbooks. And you know why you can trust the following chart.