the correlation between the psat and sat

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The Correlation Between the PSAT and SAT

M. Wang & A. MilamDivision of Accountability, Assessment, and Research

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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?

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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)

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Correlation Between the PSAT and SAT

Correlation Coefficient SAT Score

Verbal Math Writing Verbal +Math Verbal + Math + Writing

PSAT Score

Verbal 0.817

Math 0.816

Writing 0.761

Verbal + Math 0.858

Verbal + Math + Writing 0.866

• The PSAT and SAT scores are strongly correlated.

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The Mean Scores of the PSAT and SAT (AACPS)

Mean Score

PSAT Verbal Score 45

PSAT Math Score 48

PSAT Writing Skills Score 47

Combined PSAT Score 140

SAT Verbal Score 512

SAT Math Score 527

SAT Writing Score 500

Combined SAT Score 1539

• 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.

Highest Among Verbal, Math, and Writing

Lowest Among Verbal, Math, and Writing

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

The Combined PSAT Verbal, Math, and

Writing Score60-75 76-90 91-105 106-120 121-135 136-150

Number of Students 30 121 561 1105 1421 1400

The Mean of theCombined SAT Verbal,

Math, and Writing Score1126 1063 1148* 1292* 1439* 1581*

The Combined PSATVerbal, Math, and

Writing Score151-165 166-180 181-195 196-210 211-225 226-240

Number of Students 1183 704 342 122 44 3

The Mean of theCombined SAT Verbal,

Math, and Writing Score1711* 1830* 1944* 2074* 2182* 2197*

* 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.

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

SAT Verbal + Math SAT Verbal + Math + Writing

1000 1100 1200 1500 1650 1800

Corresponding PSATVerbal + Math Score 88 100 111

Corresponding PSATVerbal + Math + Writing

Score135 152 169

* 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.

SAT Verbal SAT Math SAT Writing

500 550 600 500 550 600 500 550 600

CorrespondingPSAT

Verbal Score44* 50 56

CorrespondingPSAT

Math Score45* 50 56

CorrespondingPSAT

Writing Score47 53 60

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

PSAT Verbal < 44 PSAT Verbal >= 44

Count Col % Count Col %

SAT Verbal < 500 2522 78.2%* 565 14.8%

SAT Verbal >= 500 702 21.8% 3254 85.2%*



SAT Verbal < 550 4036 85.2% 416 18.0%

SAT Verbal >= 550 699 14.8% 1892 82.0%



SAT Verbal < 600 5356 88.9% 189 18.6%

SAT Verbal >= 600 669 11.1% 829 81.4%

* Students had a 85.2% chance of scoring 500 or above on the SAT Verbal, if they have scoredat least 44 on the PSAT Verbal, and a 78.2% chance of scoring below 500 on the SAT Verbal, ifthey have scored lower than 44 on the PSAT Verbal.

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

PSAT Math < 45 PSAT Math >= 45


SAT Math < 500 2104 77.4%* 576 13.3%

SAT Math >= 500 615 22.6% 3748 86.7%*



SAT Math < 550 3303 83.3% 655 21.3%

SAT Math >= 550 662 16.7% 2423 78.7%



SAT Math < 600 4759 87.6% 399 24.7%

SAT Math >= 600 671 12.4% 1214 75.3%

* Students had an 86.7% chance of scoring 500 or above on the SAT Math, if they have scoredat least 45 on the PSAT Math, and a 77.4% chance of scoring below 500 on the SAT Math, ifthey have scored lower than 45 on the PSAT Math.

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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.

PSAT Writing < 47 PSAT Writing >= 47


SAT Writing < 500 2807 75.2% 537 16.3%

SAT Writing >= 500 927 24.8% 2765 83.7%



SAT Writing < 550 4236 84.1%* 496 24.8%

SAT Writing >= 550 802 15.9% 1502 75.2%*



SAT Writing < 600 5605 89.5% 226 29.2%

SAT Writing >= 600 656 10.5% 549 70.8%

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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.

PSAT Verbal + Math < 88 PSAT Verbal + Math >= 88


SAT Verbal + Math < 1000 2283 81.8% 566 13.3%

SAT Verbal + Math >= 1000 507 18.2% 3687 86.7%



SAT Verbal + Math < 1100 3894 86.5%* 410 16.1%

SAT Verbal + Math >= 1100 608 13.5% 2131 83.9%*



SAT Verbal + Math < 1200 5240 90.5% 276 22.0%

SAT Verbal + Math >= 1200 547 9.5% 980 78.0%

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

Linear Regression

PSAT Verbal + Math + Writing < 135

PSAT Verbal + Math + Writing >= 135


SAT Verbal + Math + Writing < 1500 2578 82.0% 481 12.4%

SAT Verbal + Math + Writing >= 1500 567 18.0% 3410 87.6%











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

PSAT Cut Score V + M = 88 V + M = 100 V + M =111 V + M + W = 135

V + M +W = 152

V + M +W = 169

SAT Cut Score V + M = 1000 V + M = 1100 V + M = 1200 V + M +W = 1500

V + M +W = 1650

V + M +W = 1800

Correct Percentof Prediction 84.7%* 85.6% 88.3% 85.1% 86.1% 89.8%

• 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%).

PSAT Cut Score V 44 V 50 V 56 M 45 M 50 M 56 W 47 W 53 W 60

SAT Cut Score V 500 V 550 V 600 M 500 M 550 M 600 W 500 W 550 W 600

Correct Percentof Prediction 82.0%* 84.2% 87.8% 83.1% 81.3% 84.8% 79.2% 81.5% 87.5%

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Disaggregated Results By NCLB Group

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Percent of Test Takers – By Special Service Group

FARMS Special Education ESOL

Number ofStudents

Percent ofStudents

Number ofStudents

Percent ofStudents

Number ofStudents

Percent ofStudents

No 6898 97.9% 6911 98.1% 7043 100.0%

Yes 145 2.1% 132 1.9% 0 0.0%

Total 7043 100.0% 7043 100.0% 7043 100.0%

• 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.

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Number and Percent of the SAT and PSAT Test Takers – By Ethnicity

Ethnicity Number of Students Percent of StudentsAsian 333 4.7

African American 1119 15.9Hispanic 147 2.1

American Indian 25 .4White 5419 76.9Total 7043 100.0

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The Mean Scores of the PSAT and SAT – By NCLBEthnicity

Asian African American Hispanic American

Indian White FARMS Special Education

PSAT Verbal Score 45 39 42 44 47 37 36

PSAT Math Score 51 40 44 47 49 41 39

PSAT Writing Skills Score 47 41 44 46 48 41 38

Combined PSAT Score 142 120 130 137 144 119 113

SAT Verbal Score 510 440 483 498 528 443 401

SAT Math Score 554 442 487 511 544 457 417

SAT Writing Score 498 430 477 457 515 439 380

Combined SAT Score 1562 1312 1447 1467 1587 1,339 1198

• 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.

Highest Among Verbal, Math, and Writing

Lowest Among Verbal, Math, and Writing

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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

Group60-75 76-90 91-105 106-120 121-135 136-150

N Mean N Mean N Mean N Mean N Mean N Mean

Countywide 30 1126 121 1063 561 1148 1105 1292 1421 1439 1400 1581

Asian 1 970 5 1066 25 1156 50 1258 53 1457 76 1580

AfricanAmerican 18 984 59 983 232 1099 293 1224 263 1399 142 1530

Hispanic 4 1130 17 1069 32 1312 37 1418 28 1571

AmericanIndian 4 1060 3 1337 5 1442 3 1610

White 11 1374 53 1148 283 1194 727 1320 1063 1449 1151 1587

FARMS 3 1003 13 1072 33 1135 40 1266 21 1420 13 1592

Special Education 6 853 14 927 33 1020 38 1202 20 1366 10 1530

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

Group151-165 166-180 181-195 196-210 211-225 226-240

N Mean N Mean N Mean N Mean N Mean N Mean

Countywide 1183 1711 704 1830 342 1944 122 2074 44 2182 3 2197

Asian 53 1729 41 1820 15 1976 11 2110 2 2100

AfricanAmerican 70 1677 25 1811 12 1851 2 1715 2 2140

Hispanic 19 1683 4 1865 4 1930 2 2255

AmericanIndian 7 1599 3 1730

White 1034 1714 631 1832 311 1946 107 2074 40 2188 3 2197

FARMS 13 1715 7 1811 1 2070 1 1530

Special Education 7 1594 3 1633 1 2040

Higher than countywide average Lower than countywide average Countywide average or same as countywide average

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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

GroupCombined SAT Verbal, Math, and Writing

Combined PSAT Verbal, Math, and Writing Score

< (Less than) 135 >= (Greater Than Or Equal To) 135


Asian< 1500 111 84.7% 24 11.9%

>= 1500 20 15.3% 177 88.1%

African American

< 1500 787 92.5% 68 25.5%

>= 1500 64 7.5% 199 74.5%

Hispanic< 1500 72 82.8% 9 15.0%

>= 1500 15 17.2% 51 85.0%

American Indian

< 1500 8 72.7% 3 21.4%

>= 1500 3 27.3% 11 78.6%

White< 1500 1600 77.5% 377 11.3%

>= 1500 465 22.5% 2972 88.7%

FARMS< 1500 100 93.5% 3 7.9%

>= 1500 7 6.5% 35 92.1%

Special Education

< 1500 105 97.2% 9 37.5%

>= 1500 3 2.8% 15 62.5%

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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

GroupCombined SAT Verbal, Math, and Writing




Asian< 1650 180 84.5% 16 13.4%

>= 1650 33 15.5% 103 86.6%

African American

< 1650 980 96.8% 30 28.3%

>= 1650 32 3.2% 76 71.7%

Hispanic< 1650 106 89.8% 8 27.6%

>= 1650 12 10.2% 21 72.4%

American Indian

< 1650 15 93.8% 4 44.4%

>= 1650 1 6.2% 5 55.6%

White< 1650 2838 84.4% 315 15.4%

>= 1650 524 15.6% 1737 84.6%

FARMS< 1650 119 96.7% 7 31.8%

>= 1650 4 3.3% 15 68.2%

Special Education

< 1650 120 99.2% 7 63.6%

>= 1650 1 .8% 4 36.4%

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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

RaceCombined SAT Verbal, Math, and Writing




Asian< 1800 245 88.8% 10 17.9%

>= 1800 31 11.2% 46 82.1%

African American

< 1800 1062 98.2% 14 38.9%

>= 1800 20 1.8% 22 61.1%

Hispanic< 1800 133 96.4% 2 22.2%

>= 1800 5 3.6% 7 77.8%

American Indian

< 1800 21 95.5% 3 100.0%

>= 1800 1 4.5%

White< 1800 4035 90.1% 191 20.4%

>= 1800 441 9.9% 747 79.6%

FARMS< 1800 135 97.1% 3 50.0%

>= 1800 4 2.9% 3 50.0%

Special Education

< 1800 129 99.2%

>= 1800 1 .8% 2 100.0%

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

PSAT CutScore V + M + W = 135 V + M + W = 152 V + M + W = 169

SAT CutScore V + M + W = 1500 V + M + W = 1650 V + M + W = 1800

Group A B H W F S A B H W F S A B H W F S

Correct Percent of Prediction

87 88 84 85 93 91 85 95 86 85 92 94 88 97 95 88 95 99

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

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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.

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SummaryCountywide 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%.

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SummaryDisaggregated 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.

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

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Frequency Table of the Combined PSAT Scores for Students Who Took the PSAT Without Taking the SAT

Before Graduating from High SchoolsCombined

PSAT Score Number ofStudents

Percent ofStudents

60-75 27 1.976-90 184 13.0

91-105 334 23.6106-120 358 25.3121-135 244 17.3136-150 147 10.4151-165 87 6.2166-180 25 1.8*180-195 6 .4*196-210 2 .1*

Total 1414 100.0

Below 136 136 or Above

* Only 2.3% of the Non-SAT takers scored166 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.

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Number of the Non-SAT Takers Who Scored at Least

136 on the PSAT – by Ethnicity and Gender Race Gender Number of Students Percent of Students

Asian

Female 4 1.5

Male 3 1.1

Total 7 2.6

AfricanAmerican

Female 12 4.5

Male 18 6.7

Total 30 11.2

Hispanic

Female 1 0.4

Male 4 1.5

Total 5 1.9

White

Female 103 38.6

Male 122 45.7

Total 225 84.3

All

Female 120 44.9

Male 147 55.1

Total 267 100.0

• Note that none of these students were FARMS orESOL students.

the correlation between the psat and sat

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