## The new SAT curve: more forgiving, though potentially misleading

This month, the College Board released scoring tables for the redesigned SAT. These tables reveal the College Board’s intended curve for the new test, enabling us to better understand how the change in difficulty levels from the current SAT to the new SAT will affect students’ scores. The four full-length practice tests that the College Board released earlier this summer provided a definitive look at the content that students will encounter when the new SAT is first administered in March 2016. Now, the scoring tables tell us how the College Board will treat students’ performance on that content, converting raw scores (number of correct answers) for each section on the new SAT into the scaled scores (200 to 800) that are reported to students and colleges.^{1}

As anticipated, the curves for each section correlate to the shift in difficulty for that section. The curve for the redesigned math section is more forgiving than the curve on the current SAT math section, helping to compensate for the significantly harder math content on the new test. Similarly, the curves of the redesigned reading and writing tests more closely resemble their equivalents on the current SAT, reflecting the smaller shift in difficulty on those sections.

An unexpected (and perhaps unintended) consequence of the curve on the new SAT is that it is possible for a student to receive a score in the mid-300s on a single section by randomly guessing. This would either indicate a dramatic shift in the curve, which currently allows random guessers to obtain a score in the 200s at best, or, more likely, an error that will be corrected when official scores are released.

**Scoring the Math Section**

The math section is known for having the steepest curve of any SAT section. We observed a particularly harsh math section curve on the October 2014 test, where a single mistake reduced a math score of 800 to 750. Students will be happy to know that the curve for new SAT math appears much more forgiving. On the new test a student can miss 4 items and attain a score of 750, placing much less pressure on any individual item.

To attain a math score of 700 on the current SAT, a student can only miss an average of 4 items. On the redesigned SAT, a student can miss 8 items to attain the same score. Likewise a student can miss 20 items on the new SAT compared to only 13 items on the current SAT to attain a score of 600, 32 items compared to 21 for a 500, and 43 compared to 32 for a 400. At every score level, the new math curve is more forgiving.

Current SAT (54 items) |
Redesigned SAT (58 items) |
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Math Section Scaled Score | Incorrect Answers | Percent Accuracy | Incorrect Answers | Percent Accuracy |

700 | 4 | 93% | 8 | 84% |

600 | 13 | 76% | 20 | 66% |

500 | 21 | 57% | 32 | 45% |

400 | 32 | 41% | 43 | 26% |

Below 400, the curve yields a curious outcome, resulting from two significant changes to the scoring process. First, the redesigned SAT will decrease the number of answer choices from 5 to 4. Second, it will eliminate the ¼ point penalty for incorrect items. With these changes, a student can achieve 25% accuracy on the 48 multiple choice questions by guessing randomly and lose no points for the incorrect guesses. Generally, taking a test by randomly guessing should result in a very low score. On the current SAT, for example, a random guesser could be expected to attain a score of roughly 230, a score typically in the first percentile of the scoring distribution.^{2} But the scoring tables for the new SAT reveal that a random guesser attaining 25% accuracy on the multiple choice items would achieve a math score of 360, a score falling typically in the 9th percentile. The number of students who score between 230 and 360 represents a significant portion of the population (8% of test takers in 2014, representing over 133,000 students).

Will a 360 be the new base of the scoring curve? This is highly unlikely, for the distribution of SAT scores typically approximates the normal curve. More likely, these students will see scaled scores closer to 230 once the curve is populated with official scores from the March 2016 test. Consequently, many students relying upon these seemingly inflated scores may get a rude awakening and a significant score drop come May or June.

**Scoring the Reading Section**

The reading curve on the redesigned SAT is closer to that found on the current test. Whereas the new math curve allows students to miss many more items to attain a comparable score, this is not the case when it comes to reading. A student who misses 8 items on *either* the current SAT or the redesigned SAT will come out with the same reading score: 700 (as noted in the first footnote, we are grossing up the reading section to 800 points for the sake of comparison; the reading score will only account for 50% of the newly combined English and Writing section score). The table below illustrates the relationship between the old and new scoring curves.

Current SAT (67 items) |
Redesigned SAT (52 items) |
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Reading Section Scaled Score | Incorrect Answers | Percent Accuracy | Incorrect Answers | Percent Accuracy |

700 | 8 | 88% | 8 | 84% |

600 | 16 | 76% | 18 | 65% |

500 | 29 | 57% | 27 | 52% |

400 | 41 | 39% | 37 | 29% |

As with the math section, a reading score of 400 requires barely more than the 25% accuracy level of random guessing. Were a student to guess randomly on the reading section of the current SAT, he would typically attain 13 right answers and 54 wrong answers with a corresponding penalty of 54*1/4, yielding a raw score of 0 points, corresponding to a scaled reading score of 230. Contrast this with a random guesser on the redesigned test who would guess correctly on 13 of the 52 items, yielding a scaled reading score of 380. Again, this is a highly significant difference and one that we anticipate the College Board will address.

**Scoring the Writing Section**

Like the reading curve, the writing curve on the redesigned SAT more closely approximates that found on the current test.^{3}

Current SAT (49 items) |
Redesigned SAT (44 items) |
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Writing Section Scaled Score | Incorrect Answers | Percent Accuracy | Incorrect Answers | Percent Accuracy |

700 | 4 | 92% | 5 | 88% |

600 | 9 | 82% | 10 | 75% |

500 | 17 | 65% | 17 | 58% |

400 | 27 | 49% | 24 | 40% |

Random guessing seems to have less efficacy on the Writing section. Were a student to randomly guess on the old SAT, he would typically gain 12 points for correct answers, lose 9 points for incorrect answers and yield a raw score of 3, which converts to a scaled score of 280. In comparison, a student who guesses randomly on the new SAT would typically gain 11 raw points, which scales to a 320. Thus only a 40 point gap separates the writing scores of random guessers on the old and new tests.

**Implications**

So what does this mean for students? In a nutshell, test takers can miss more items on the redesigned SAT without sacrificing their scores. Errors are not as costly. A harder test has been paired with a gentler curve. And this is good news.

Now that we have the scoring tables, students should use them to calibrate progress towards their goals on the 2016 SAT; however, students scoring toward the bottom of the curve should view their scores with caution.

^{1} For our analysis of the scoring of the new SAT we used the scoring table for test 1, which is nearly identical (a variance of 10-20 points when comparing differences between raw and scaled scores) to the scoring tables of tests 2,3, and 4. As the Writing and Reading scores each now account for 50% of the total score of the new SAT’s Evidence-Based Reading and Writing Section, we had to gross up the individual Writing and Critical Reading scores to attain a scaled score of 800, thereby allowing for a comparison with the current SAT. For our analysis of the scoring of the current SAT, we used the average scaled scores for the October 2014, January 2015 and May 2015 tests.

^{2 }If a student guesses randomly on the 44 multiple choice math items, he would typically answer 1/5 of them correctly and be penalized ¼ point for each missed multiple choice item. The student could reasonably pick up 9 points for random correct answers, and lose 9 points for wrong answers, yielding 0 raw points and a scaled score of roughly 230.

^{3} This analysis does not include the essay portion of the current SAT Writing Section.