Estimation Methodology

We’ve generated two important numbers about the state-by-state cutoff system: what an equitable national PSAT score cutoff would be (213-216, depending on the year) and what percentage of Semifinalists are direct beneficiaries of the system (around 16%, or 2,400).  The same number of students were also victims of the system.  This page details how we came up with those numbers.

Please note: due to the change in PSAT scoring scale, we are not currently certifying students who took the PSAT in 2015. We hope to have our certification system updated as soon as possible.

The National Cutoff

The national cutoffs used in the home-page widget were generated from data on state-by-state scores provided by the College Board for Junior PSAT takers and data on the NMSC’s state-specific cutoffs.  We’ll take 2012 as our example year (the cutoffs for other years were generated with the same methodology).

We took the score data—which is broken up into reading, writing, and math—and added those averages together to get an overall average score for each state.  These average scores range from 133 in Washington D.C. and New Mexico to 155 in Missouri and Illinois.  The maximum score is 240.

The College Board’s data also includes the standard deviation of each section for each state, but it does not include the standard deviation of the aggregate score (which, unfortunately, we cannot calculate for technical reasons—we do not know how these score covary).  The College Board does report the national standard deviation of PSAT scores (31.0 in 2012), and we importantly make the assumption that each state’s standard deviation is the same as the national standard deviation.

Using the average score of each state, the national standard deviation, and the state’s Semifinalist cutoff, we calculate what percentage of students from each state become Semifinalists (between roughly .5% and 4%, depending on the state).  Then, using a score that seems like it could be close to a fair national average—say, 212—in place of the state cutoffs we calculate the same percentages—what percentage of students would be Semifinalists if that national cutoff were used.

In some states, the numbers are the same (those whose cutoff is 212).  In other states the two numbers are drastically different.

We then have two numbers: the percentage of students who would be a Semifinalist under the state-specific cutoff system, and the percentage of students who would become Semifinalists under a nationwide system.  From these two numbers and the number of test takers in each state we can do a simple calculation: subtract the percentage of test takers who would be Semifinalists under a national system from the percentage under the state-specific system and multiply that by the number of test takers in each state.

This gives you the number of beneficiaries of the state-specific cutoffs (if that number is positive) or victims (if that number is negative).

Then we find the cutoff that equalizes the number of beneficiaries and victims.  Our guess at the cutoff—212—gave us far more victims than beneficiaries.  But a new cutoff—close to 216—produces an equal number of beneficiaries and victims.  This cutoff takes awards away, so to speak, from about 2,400 beneficiaries and gives those awards to 2,400 victims.  This means that around 15% of the 16,000 National Merit Semifinalists in 2012 had lower scores than test-takers in other states.

We did this same analysis for every year 2008-2014, and the average percentage of students who had lower scores than test-takers in other states for the seven years was 15.9%.  The equitable cutoffs range from 213 to 216.  You can download an Excel file with our estimates here.

 

The States that are Most Helped and Hurt

It turns out that many of the same states are hurt and helped by the state-by-state cutoffs every year.  Here are the top five winner and loser states, by number of students (7-year average):

7-year average (2008-2014) of number of students who were helped or hurt by the state-by-state cutoffs

Top 5 States that Benefit Top 5 States that are Hurt
Wisconsin 232 California -717
Michigan 224 New Jersey -356
Florida 167 Massachusetts -353
Arkansas 137 Texas -226
Missouri 121 New York -202

In Wisconsin, an average of 232 students were awarded Semifinalist status with lower scores than students in other states who were not awarded.  An average of 717 students not awarded Semifinalist status in California had higher scores than students in other states who were.

 

Acadium Scholar is not affiliated in any way with the National Merit Scholarship Corporation or the PSAT/NMSQT.

 

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