This post will explain how I score an SHSAT practice test, i.e. how to convert a raw score into a scaled score. The DOE doesn’t share how they convert the raw scores. I will explain the assumptions I make and each step of my conversions.
What is the raw score?
The SHSAT has two scores, a raw score, and a scaled score. Every correct answer is worth 1 raw point and everything else, incorrect or blank, is worth 0 points.
The DOE creates multiple versions of the SHSAT exam each year. Each one is different to prevent cheating and information sharing. To compare everyone’s score, they convert each raw score to a scaled score. They keep their conversion formula a secret.
Sources and Assumptions
In 2016 and the previous years since 2006, calculating a scaled score was easy. 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). Some assumptions are thus necessary. First, I assume the following statement by the DOE is 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.
Second, I assume an outdated article by testprepshsat.com.and a 2008 study they cite are both accurate. The study, by Ph.D. Joshua Feinman, is available at the following link: https://nepc.colorado.edu/publication/high-stakes-but-low-validity.
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 still reliable for the 2016 exam. 87.7 percent of 50 is 43.85, so between a scaled score of 290 or 298.
For tutoring, I assume the lower score since I like students to 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.
The average scenario?
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 tested my method against their chart and I’ve found that I agree with their numbers. I am going to use their chart from now on and I you can too. So what was the point of this post? If you agree with my logic you can now confidently ignore workbook conversion charts. And you know why you can trust the following chart.
How are the results used for admissions?
Starting from the highest score on down, each student, in turn, is placed in that student’s highest listed school in which seats are still available . Therefore, if all the seats in a student’s first-choice school have been offered to students who scored higher, the student is placed in their second-choice school if seats are available . If all the seats in the student’s second-choice school have been offered to students who scored higher, the student is offered a seat in their third-choice school if there are still seats available, and so on . This process continues until there are no seats available in any of these eight Specialized High Schools.
When are the results reported?
The DOE releases results in mid-March. They only release the scaled scores, but not the raw scores.
The next post is going to look at the Scaled Slope column found in the first chart. I am going to create another table that includes that information and follow it with a post that explains how to take advantage of it. Spoiler: showing proficiency in one section is better than doing average in both if the total raw scores are the same. And also a bit more than that.