# 1 The Correlation Between the PSAT and SAT M. Wang & A. Milam Division of Accountability, Assessment, and Research.

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1 The Correlation Between the PSAT and SAT M. Wang & A. Milam Division of Accountability, Assessment, and Research

2 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?

3 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 11 th graders and 1,009,739 10 th graders are: - Verbal: 47 for the 11 th graders and 42 for the 10 th graders - Mathematics: 49 for the 11 th graders and 44 for the 10 th graders - Writing: 46 for the 11 th graders and 41 for the 10 th graders (Reference: http://professionals.collegeboard.com/profdownload/understanding- psat-nmsqt-scores.pdf )

4 Correlation Between the PSAT and SAT Correlation Coefficient SAT Score VerbalMathWritingVerbal +MathVerbal + Math + Writing PSAT Score Verbal0.817 Math0.816 Writing0.761 Verbal + Math0.858 Verbal + Math + Writing0.866 The PSAT and SAT scores are strongly correlated.

5 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

6 The Mean of the Combined SAT Score - By Combined PSAT Score Range The Combined PSAT Verbal, Math, and Writing Score 60-7576-9091-105106-120121-135136-150 Number of Students 30121561110514211400 The Mean of the Combined SAT Verbal, Math, and Writing Score 112610631148*1292*1439*1581* The Combined PSAT Verbal, Math, and Writing Score 151-165166-180181-195196-210211-225226-240 Number of Students 1183704342122443 The Mean of the Combined SAT Verbal, Math, and Writing Score 1711*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.

7 Deriving the Corresponding PSAT Scores to the SAT Scores Using Regression Analysis SAT Verbal + MathSAT Verbal + Math + Writing 100011001200150016501800 Corresponding PSAT Verbal + Math Score 88100111 Corresponding PSAT Verbal + Math + Writing Score 135152169 * 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 500550600500550600500550600 Corresponding PSAT Verbal Score 44*5056 Corresponding PSAT Math Score 45*5056 Corresponding PSAT Writing Score 475360

8 Predicting Student Performance on the SAT Verbal Using Regression Derived PSAT Verbal Scores PSAT Verbal < 44PSAT Verbal >= 44 CountCol %CountCol % SAT Verbal < 500252278.2%*56514.8% SAT Verbal >= 50070221.8%325485.2%* PSAT Verbal < 50PSAT Verbal >= 50 CountCol %CountCol % SAT Verbal < 550403685.2%41618.0% SAT Verbal >= 55069914.8%189282.0% PSAT Verbal < 56PSAT Verbal >= 56 CountCol %CountCol % SAT Verbal < 600535688.9%18918.6% SAT Verbal >= 60066911.1%82981.4% * 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.

9 Predicting Student Performance on the SAT Math Using Regression Derived PSAT Math Scores PSAT Math < 45PSAT Math >= 45 CountCol %CountCol % SAT Math < 500210477.4%*57613.3% SAT Math >= 50061522.6%374886.7%* PSAT Math < 50PSAT Math >= 50 CountCol %CountCol % SAT Math < 550330383.3%65521.3% SAT Math >= 55066216.7%242378.7% PSAT Math < 56PSAT Math >= 56 CountCol %CountCol % SAT Math < 600475987.6%39924.7% SAT Math >= 60067112.4%121475.3% * 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.

10 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 < 47PSAT Writing >= 47 CountCol %CountCol % SAT Writing < 500280775.2%53716.3% SAT Writing >= 50092724.8%276583.7% PSAT Writing < 53PSAT Writing >= 53 CountCol %CountCol % SAT Writing < 550423684.1%*49624.8% SAT Writing >= 55080215.9%150275.2%* PSAT Writing < 60PSAT Writing >= 60 CountCol %CountCol % SAT Writing < 600560589.5%22629.2% SAT Writing >= 60065610.5%54970.8%

11 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 < 88PSAT Verbal + Math >= 88 CountCol %CountCol % SAT Verbal + Math < 1000228381.8%56613.3% SAT Verbal + Math >= 100050718.2%368786.7% PSAT Verbal + Math < 100PSAT Verbal + Math >= 100 CountCol %CountCol % SAT Verbal + Math < 1100389486.5%*41016.1% SAT Verbal + Math >= 110060813.5%213183.9%* PSAT Verbal + Math < 111PSAT Verbal + Math >= 111 CountCol %CountCol % SAT Verbal + Math < 1200524090.5%27622.0% SAT Verbal + Math >= 12005479.5%98078.0%

12 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 CountCol %CountCol % SAT Verbal + Math + Writing < 1500257882.0%48112.4% SAT Verbal + Math + Writing >= 150056718.0%341087.6% PSAT Verbal + Math + Writing < 152 PSAT Verbal + Math + Writing >= 152 CountCol %CountCol % SAT Verbal + Math + Writing < 1650411987.2%37316.1% SAT Verbal + Math + Writing >= 165060212.8%194283.9% PSAT Verbal + Math + Writing < 169 PSAT Verbal + Math + Writing >= 169 CountCol %CountCol % SAT Verbal + Math + Writing < 1800549691.7%22021.1% SAT Verbal + Math + Writing >= 18004988.3%82278.9%

13 Correct Percent of Prediction of Using the Linear Regression Derived PSAT Scores to Predict Student Performance on the SAT PSAT Cut ScoreV + M = 88V + M = 100V + M =111 V + M + W = 135 V + M + W = 152 V + M + W = 169 SAT Cut ScoreV + M = 1000V + M = 1100V + M = 1200 V + M + W = 1500 V + M + W = 1650 V + M + W = 1800 Correct Percent of 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 ScoreV 44V 50V 56M 45M 50M 56W 47W 53W 60 SAT Cut ScoreV 500V 550V 600M 500M 550M 600W 500W 550W 600 Correct Percent of Prediction 82.0%*84.2%87.8%83.1%81.3%84.8%79.2%81.5%87.5%

14 Disaggregated Results By NCLB Group

15 Percent of Test Takers – By Special Service Group FARMSSpecial EducationESOL Number of Students Percent of Students Number of Students Percent of Students Number of Students Percent of Students No689897.9%691198.1%7043100.0% Yes1452.1%1321.9%00.0% Total7043100.0%7043100.0%7043100.0% 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.

16 Number and Percent of the SAT and PSAT Test Takers – By Ethnicity EthnicityNumber of StudentsPercent of Students Asian 3334.7 African American 111915.9 Hispanic 1472.1 American Indian 25.4 White 541976.9 Total 7043100.0

17 The Mean Scores of the PSAT and SAT – By NCLB Ethnicity Asian African American Hispanic American Indian WhiteFARMS Special Education PSAT Verbal Score45394244473736 PSAT Math Score51404447494139 PSAT Writing Skills Score47414446484138 Combined PSAT Score142120130137144119113 SAT Verbal Score510440483498528443401 SAT Math Score554442487511544457417 SAT Writing Score498430477457515439380 Combined SAT Score156213121447146715871,3391198 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

18 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 Group 60-7576-9091-105106-120121-135136-150 NMeanN N N N N Countywide 30112612110635611148110512921421143914001581 Asian197051066251156501258531457761580 African American 18984599832321099293122426313991421530 Hispanic 41130171069321312371418281571 American Indian 41060313375144231610 White111374531148283119472713201063144911511587 FARMS31003131072331135401266211420131592 Special Education 685314927331020381202201366101530

19 The Mean of the Combined SAT Score - By Combined PSAT Score Range and NCLB Group Group 151-165166-180181-195196-210211-225226-240 NMeanN N N N N Countywide1183171170418303421944122207444218232197 Asian53172941182015197611211022100 African American 7016772518111218512171522140 Hispanic191683418654193022255 American Indian 7159931730 White1034171463118323111946107207440218832197 FARMS131715718111207011530 Special Education 715943163312040 Higher than countywide average Lower than countywide average Countywide average or same as countywide average

20 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 Group Combined SAT Verbal, Math, and Writing Combined PSAT Verbal, Math, and Writing Score < (Less than) 135>= (Greater Than Or Equal To) 135 CountCol %CountCol % Asian < 150011184.7%2411.9% >= 15002015.3%17788.1% African American < 150078792.5%6825.5% >= 1500647.5%19974.5% Hispanic < 15007282.8%915.0% >= 15001517.2%5185.0% American Indian < 1500872.7%321.4% >= 1500327.3%1178.6% White < 1500160077.5%37711.3% >= 150046522.5%297288.7% FARMS < 150010093.5%37.9% >= 150076.5%3592.1% Special Education < 150010597.2%937.5% >= 150032.8%1562.5%

21 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 Group Combined SAT Verbal, Math, and Writing Combined PSAT Verbal, Math, and Writing Score < (Less than) 152>= (Greater Than Or Equal To) 152 CountCol %CountCol % Asian < 165018084.5%1613.4% >= 16503315.5%10386.6% African American < 165098096.8%3028.3% >= 1650323.2%7671.7% Hispanic < 165010689.8%827.6% >= 16501210.2%2172.4% American Indian < 16501593.8%444.4% >= 165016.2%555.6% White < 1650283884.4%31515.4% >= 165052415.6%173784.6% FARMS < 165011996.7%731.8% >= 165043.3%1568.2% Special Education < 165012099.2%763.6% >= 16501.8%436.4%

22 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 Race Combined SAT Verbal, Math, and Writing Combined PSAT Verbal, Math, and Writing Score < (Less than) 169>= (Greater Than Or Equal To) 169 CountCol %CountCol % Asian < 180024588.8%1017.9% >= 18003111.2%4682.1% African American < 1800106298.2%1438.9% >= 1800201.8%2261.1% Hispanic < 180013396.4%222.2% >= 180053.6%777.8% American Indian < 18002195.5%3100.0% >= 180014.5% White < 1800403590.1%19120.4% >= 18004419.9%74779.6% FARMS < 180013597.1%350.0% >= 180042.9%350.0% Special Education < 180012999.2% >= 18001.8%2100.0%

23 Correct Percent of Prediction of Using the Combined PSAT Scores to Predict Student Performance on the Combined SAT PSAT Cut Score V + M + W = 135V + M + W = 152V + M + W = 169 SAT Cut Score V + M + W = 1500V + M + W = 1650V + M + W = 1800 GroupABHWFSABHWFSABHWFS Correct Percent of Prediction 878884859391859586859294889795889599 A = Asian, B = African American, H = Hispanic, W = White, F = FARMS, S = Special Education The correct percent of prediction range from 84% to 99%.

24 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.

25 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%.

26 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.

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

28 Frequency Table of the Combined PSAT Scores for Students Who Took the PSAT Without Taking the SAT Before Graduating from High Schools Combined PSAT Score Number of Students Percent of Students 60-75 271.9 76-90 18413.0 91-105 33423.6 106-120 35825.3 121-135 24417.3 136-150 14710.4 151-165 876.2 166-180 251.8* 180-195 6.4* 196-210 2.1* Total 1414100.0 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.

29 Number of the Non-SAT Takers Who Scored at Least 136 on the PSAT – by Ethnicity and Gender RaceGenderNumber of StudentsPercent of Students Asian Female4 1.5 Male3 1.1 Total7 2.6 African American Female12 4.5 Male18 6.7 Total30 11.2 Hispanic Female1 0.4 Male4 1.5 Total5 1.9 White Female103 38.6 Male122 45.7 Total225 84.3 All Female120 44.9 Male147 55.1 Total267 100.0 Note that none of these students were FARMS or ESOL students.

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