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### The Correlation Between the PSAT and SAT

M. Wang & A. Milam

Division of Accountability, Assessment, and Research

Questions

- Are PSAT and SAT strongly correlated?
- A study done in Montgomery County Public Schools concluded that students will have honor/AP potential, if they score at least 44 on PSAT Verbal or 45 on PSAT Math. Are 44 on PSAT Verbal and 45 on PSAT Math an indication of good SAT scores for Anne Arundel County Public Schools’ students?
- What PSAT scores correspond to good SAT scores for AACPS’ students?
- Is PSAT a good predictor of student performance on the SAT?

Background

- A total of 7,043 high school students who took the PSAT in October 2005 and the SAT after October 2005 were included in the study.
- The score of each subject (Verbal, Math, and Writing) on the PSAT ranges from 20 to 80.
- The score of each subject on the SAT ranges from 200 to 800.
- The 2008 national college-bound seniors' average SAT scores are:

- Verbal: 502

- Mathematics: 515

- Writing: 494

- The 2008 average PSAT scores for a national sample of 1,002,119 11th graders and 1,009,739 10th graders are:

- Verbal: 47 for the 11th graders and 42 for the 10th graders

- Mathematics: 49 for the 11th graders and 44 for the 10th graders

- Writing: 46 for the 11th graders and 41 for the 10th graders

(Reference: http://professionals.collegeboard.com/profdownload/understanding-psat-nmsqt-scores.pdf)

Correlation Between the PSAT and SAT

- The PSAT and SAT scores are strongly correlated.

The Mean Scores of the PSAT and SAT (AACPS)

Highest Among Verbal, Math, and Writing

Lowest Among Verbal, Math, and Writing

- Students had the highest mean score on the Math portion and the lowest mean score on the Verbal portion of the PSAT.
- Students had the highest mean score on the Math portion and the lowest mean score on the Writing portion of the SAT.

The Mean of the Combined SAT Score - By Combined PSAT Score Range

* For students who scored higher than 90 on the combined PSAT, the higher the combined PSAT score range, the higher the mean of the combined SAT score.

Deriving the Corresponding PSAT Scores to the SAT Scores Using Regression Analysis

- * Montgomery County Public Schools’ PSAT cut scores (44 on Verbal and 45 on Math)
- for AP potential correspond to 500 points on the SAT Verbal and Math for AACPS students.
- The corresponding PSAT cut scores to 600 on each subject of the SAT are 56 for Verbal, 56 for Math, and 60 for Writing.
- The corresponding PSAT cut scores to 550 on each subject of the SAT are 50 for Verbal, 50 for Math, and 53 for Writing.
- The corresponding combined PSAT cut score to 1800 on the combined SAT is 169.

Predicting Student Performance on the SAT Verbal Using Regression Derived PSAT Verbal Scores

* Students had a 85.2% chance of scoring 500 or above on the SAT Verbal, if they have scored

at least 44 on the PSAT Verbal, and a 78.2% chance of scoring below 500 on the SAT Verbal, if

they have scored lower than 44 on the PSAT Verbal.

Predicting Student Performance on the SAT Math Using Regression Derived PSAT Math Scores

* Students had an 86.7% chance of scoring 500 or above on the SAT Math, if they have scored

at least 45 on the PSAT Math, and a 77.4% chance of scoring below 500 on the SAT Math, if

they have scored lower than 45 on the PSAT Math.

Predicting Student Performance on the SAT Writing Using Regression Derived PSAT Writing Scores

* For example, students had a 75.2% chance of scoring 550 or above on the SAT Writing, if they

have scored at least 53 on the PSAT Writing, and a 84.1% chance of scoring below 550 on the SAT

Writing, if they have scored lower than 53 on the PSAT Writing.

Predicting Student Performance on the Combined SAT Verbal and Math Using Combined PSAT Verbal and Math Scores Derived by Linear Regression

* For example, students had an 83.9% chance of scoring 1100 or above on the combined SAT Verbal and Math, if they have scored at least 100 on the combined PSAT Verbal and Math, and a 86.5% chance of scoring below 1000 on the combined SAT Verbal and Math, if they have scored lower than 100 on the combined PSAT Verbal and Math.

Predicting Student Performance on the Combined SAT Verbal, Math, and Writing Using Combined PSAT Verbal, Math, and Writing Scores Derived by Linear Regression

Correct Percent of Prediction of Using the Linear Regression Derived PSAT Scores to Predict Student Performance on the SAT

- Note that “V” standards for Verbal, “M” stands for Math, and “W” for Writing.
- * For example, the correct percent of prediction using the scenario that students scoring at least 44 on the PSAT Verbal would score at least 500 on the SAT Verbal, and students scoring lower than 44 on the PSAT Verbal would score lower than 500 on the SAT Verbal is 82.0%.
- Note that 46.2% of the students scored 500 or above on the SAT Verbal and scored 44 or above on the PSAT Verbal, and that 35.8% of the students scored below 500 on the SAT Verbal and scored lower than 44 on the PSAT Verbal. So the correct percent of prediction is 82.0% (46.2% + 35.8%).

Percent of Test Takers – By Special Service Group

- Very small percent of the PSAT and SAT test takers belonged to the special services groups.
- None of the 7,043 PSAT and SAT test takers were ESOL students.

The Mean Scores of the PSAT and SAT – By NCLB

Highest Among Verbal, Math, and Writing

Lowest Among Verbal, Math, and Writing

- Most NCLB groups had the highest mean scores on the Math portion and each NCLB group had the lowest mean score on the Verbal portion of the PSAT.
- For each NCLB group, students had the highest mean score on the Math portion and the lowest mean score on the Writing portion of the SAT.

The Mean of the Combined SAT Score - By Combined PSAT Score Range and NCLB Group

Higher than countywide average Lower than countywide average

Countywide average or same as countywide average

The Mean of the Combined SAT Score - By Combined PSAT Score Range and NCLB Group

Higher than countywide average Lower than countywide average

Countywide average or same as countywide average

Predicting Whether or Not Students Scoring At Least or Lower than 1500 on the Combined SAT Using 135 As the Cut Score on the Combined PSAT – By NCLB Group

Predicting Whether or Not Students Scoring At Least or Lower than 1650 on the Combined SAT Using 152 As the Cut Score on the Combined PSAT - By NCLB Group

Predicting Whether or Not Students Scoring At Least or Lower than 1800 on the Combined SAT Using 169 As the Cut Score on the Combined PSAT - By NCLB Group

Correct Percent of Prediction of Using the Combined PSAT Scores to Predict Student Performance on the Combined SAT

- A = Asian, B = African American, H = Hispanic, W = White, F = FARMS, S = Special Education
- The correct percent of prediction range from 84% to 99%.

Summary

- The PSAT and SAT Scores are strongly correlated.
- For students who scored higher than 90 on the combined PSAT, the higher the combined PSAT score range, the higher the mean of the combined SAT score.

Regression Analysis

- The corresponding PSAT cut scores to 500 on each subject of the SAT are 44 for Verbal, 45 for Math, and 47 for Writing.
- Montgomery County Public Schools’ PSAT cut scores (44 on Verbal and 45 on Math) for AP potential correspond to 500 points on the SAT Verbal and Math for AACPS’ students.
- The corresponding PSAT cut scores to 550 on each subject of the SAT are 50 for Verbal, 50 for Math, and 53 for Writing.
- The corresponding PSAT cut scores to 600 on each subject of the SAT are 56 for Verbal, 56 for Math, and 60 for Writing.
- The corresponding combined PSAT cut score to 1800 on the combined SAT is 169.
- The corresponding combined PSAT cut scores to 1500, 1650, and 1800 points on the combined SAT are 135, 152, and 169, respectively.

Summary

Countywide Prediction Results

- Students had an 85.2% chance of scoring 500 or above on the SAT Verbal, if they have scored at least 44 on the PSAT Verbal, and a 78.2% chance of scoring below 500 on the SAT Verbal, if they have scored lower than 44 on the PSAT Verbal.
- Students had an 86.7% chance of scoring 500 or above on the SAT Math, if they have scored at least 45 on the PSAT Math, and a 77.4% chance of scoring below 500 on the SAT Math, if they have scored lower than 45 on the PSAT Math.
- Students had an 83.7% chance of scoring 500 or above on the SAT Writing, if they have scored at least 47 on the PSAT Writing and a 75.2% chance of scoring below 500 on the SAT Writing, if they have scored lower than 47 on the PSAT Writing.
- Students had an 87.6% (83.9%, 78.9%) chance of scoring 1500 (1650, 1800) or above on the combined SAT, if they have scored at least 135 (152, 169) on the combined PSAT, and an 82.0% (87.2%, 91.7%) chance of scoring below 1500 (1650, 1800) on the combined SAT, if they have scored lower than 135 (152, 169) on the combined PSAT.
- The correct percent of predictions of using regression derived PSAT scores to predict student scoring at least or lower than 500, 550, or 600 on an SAT subject and at least or lower than 1500, 1650, or 1800 on the combined SAT range from 79.2% to 89.8%.

Summary

Disaggregated Results

- Of the students who took both SAT and PSAT, 2.1% were FARMS students, 1.9% were Special Education students, and none were ESOL students.
- White students’ average combined SAT score in each 15-points-increment range of the combined PSAT was higher than the county average in the range, while African Americans’ average combined SAT score in each range of the combined PSAT score is lower than the county average in the range.
- The regression derived countywide PSAT cut scores are good predictors of student performance on the SAT for each subgroup.

Appendix: Demographics of the Students Scoring Average or High on the PSAT Without Taking the SAT Before They Graduated from High Schools

Frequency Table of the Combined PSAT Scores for Students Who Took the PSAT Without Taking the SAT Before Graduating from High Schools

Below 136 136 or Above

- * Only 2.3% of the Non-SAT takers scored
- 166 or higher (very high) on the PSAT.
- 267 (18.9%) of the Non-SAT takers scored average to high on the PSAT.
- Note that there were 1879 students scoring at least 136 on the 2005 combined PSAT and 267 (14.2%) of them did not take the SAT before they graduated from high schools.

Number of the Non-SAT Takers Who Scored at Least 136 on the PSAT – by Ethnicity and Gender

- Note that none of these
- students were FARMS or
- ESOL students.

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