Lecture 12 - Yale University1 Statistics 101-106 Lecture 12 (1 Dec 98) David Pollard Lecture 12 Each year the U.S. News and World Report provides rankings of US colleges (and universities),

1

Statistics 101-106 Lecture 12 (1 Dec 98) David Pollard

Lecture 12

Each year the U.S. News and World Report provides rankings of US colleges (and universities), based ondata provided by the colleges themselves. The web page at http://www.usnews.com/usnews/edu/college/corank.htm

documents (see Rankings information) the methods that US News uses.

The data for the 1994 rankings (downloaded from the web site for the Journal of Statistics Education:gopher://jse.stat.ncsu.edu:70/11/jse/) are linked to the datasets page at Stat100++ web site. The data consist ofthe following variables:

FICE = FICE (Federal ID number)name = College Name (abbreviated)State = Statetype = Public/private indicator (public=1, private=2)SATm = Average Math SAT scoreSATv = Average Verbal SAT scoreSAT = Average Combined SAT scoreACT = Average ACT scoreSATm25 = First quartile - Math SATSATm75 = Third quartile - Math SATSATv25 = First quartile - Verbal SATSATv75 = Third quartile - Verbal SATACT25 = First quartile - ACTACT75 = Third quartile - ACTnew.applied = Number of applications receivednew.accepted = Number of applicants acceptednew.enrolled = Number of new students enrollednew.top10HS = Pct. new students from top 10% of H.S. classnew.top25HS = Pct. new students from top 25% of H.S. classundergrads = Number of fulltime undergraduatesparttime = Number of part-time undergraduatestuition.in = In-state tuitiontuition = Out-of-state tuitionroom+board = Room and board costsroom = Room costsboard = Board costscost.fees = Additional feescost.books = Estimated book costscost.pers = Estimated personal spendingfac.phd = Pct. of faculty with Ph.D.’sfac.term = Pct. of faculty with terminal degreesf.ratio = Student/faculty ratiodonate = Pct.alumni who donateexp.stud = Instructional expenditure per studentgraduate = Graduation rateCollege = College name (in full)

A star (*) in the original data indicates a missing value. The software that I use writes NA for missingvalues.

I extracted the subset of the data , consisting of the 1133 colleges for which there is AAUP salary dataavailable.

The U.S. News derives ranks by taking weighted combinations of scores derived from such data. Forexample, ‘Student selectivity’ contributes 15% to the ranking score, with average SAT/ACT scorescontributing 40% towards the ‘Student selectivity’.

Missing data complicate comparisons of SAT/ACT scores across colleges. For some colleges we haveonly first and third SAT quartiles; for others we have only average SAT scores; for others we have onlyACT scores or quartiles. How should we combine these pieces of partial information into a single SATmeasure?

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400 500 600 700

020

4060

80

SATm

300 400 500 600

020

4060

8010

0

SATv

600 800 1000 1200 1400

020

4060

80

SAT

20 25 30

020

4060

8012

0

ACT

200 300 400 500 600 700

020

4060

80

SATm25

400 500 600 700 800

020

4060

80

SATm75

200 300 400 500 600

020

4060

8010

0

SATv25

400 500 600 700

020

4060

80

SATv75

10 15 20 25

020

4060

8010

0

ACT25

15 20 25 30 35

020

4060

80

ACT75

SATm SATv SAT ACT SATm25 SATm75 SATv25 SATv75 ACT25 ACT75Min. 320 280 600 16 220 370 200 330 10 151st Qu. 467 426.2 896.5 21 420 540 380 490 18 23Median 507 460 968 22 460 585 420 530 20 25Mean 512.6 465.3 977.7 22.27 467.2 587.3 422.7 533.7 19.96 25.213rd Qu. 550 495.8 1043 24 510 630 450 570 22 27Max. 750 665 1410 31 740 785 630 720 29 35NA’s 471 471 470 506 439 439 439 439 526 526

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For all except 2 colleges with SAT present, both SATm and SATv are also present. For only 1 college withboth SATm and SATv present, is SAT missing. In most cases SAT = SATm +SATv. No college has onlytwo or three of the four SAT quartiles, or only one of the ACT quartiles.

+++ + +++

+

+ ++ ++ ++ +++

+ + ++++ ++ +++ ++ + ++ ++++ + +++ ++ ++++ ++ ++ ++ ++ +++ + +++ +++ ++ ++ ++ ++ ++++ + + ++ +++ +++ ++

+

+ +

+

+++++ ++++ + +++ + + +++ ++ ++++ + ++++ +++ ++ ++ + +++ + ++ ++ ++ ++ +++ +++ + + ++++

+

+ ++ +++ +++ ++ ++ ++ + ++ ++ ++ +++ ++ +

+

++ +

+

+++ ++++ + ++++++

+++ +++ ++ + ++ ++ +++ ++ + ++ +++ + + ++ ++++ +++ ++++ + +++ +++ +++ ++

+ +++++ +

+

+++ + + ++ ++ ++ ++ + + +++ +++ +++ ++++ + +++ ++ + + ++++ + + ++ ++ ++++ ++ + ++ ++ +++ +++ +++

+

+ +++ ++

+

+++ ++ ++ + ++ +++ +++ ++ + ++++

+

+ +++ +++ ++ + + +++ ++ + + +++ +++ + ++ ++ +++++

+

++ + ++++ + + +++ ++ ++ ++ ++ + +++ +

+

+ ++ + + ++ + + ++ ++ ++ +++ ++ + + +++ ++

+

+ + ++ ++ + + +++ ++ ++ ++ ++ +++ + ++ +++

+

+ ++ + +++++ + +++

++ ++

+

++++ + + + ++++++ + +++ ++ ++ +++ +++ + ++ ++ + ++ ++ ++ ++ ++ + ++ + ++ +++ + +++ ++++ + ++ +++ + + ++ ++ +++ +++ + + ++ ++++ + ++ ++ ++++ +++ ++ + ++++ +

+

++ ++ ++ +++ + + +++ ++ +++ ++ +++++ ++ ++ +++ ++ ++ +++ ++ +++ + +++ +

+

+ + ++ +++

1041

1083

1479

1488

18012003

2032

2190

2346

2584

2603

2685

2825

3016

8795

3245

3298

3706

3809

-120

-100

-80

-60

-40

-20

0

20

600 800 1000 1200 1400

SAT

SA

T -

SA

Tm

- S

AT

v

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Presence/absence of SAT/ACT scores

* SATm25* 332 138SAT 107 556

* ACT25* 366 140ACT 160 467

* sat (any form)* 83 283act (any form) 249 518

* ACT

*

ACT25

* SATm25 * 61 0SAT 59 40

* SATm25 * 53 78SAT 0 9

* SATm25 * 135 6SAT 15 311

* SATm25 * 83 54SAT 33 196

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How to predict SAT scores?

Which is better: use to the coarser ACT scores to predict SAT, vice versa?

600 800 1000

1000 1200 1400

1000

1200

1400

600

800

1000SAT

300 400 500

500 600 700

500

600

700

300

400

500SATm25

400 500

600 700

600

700

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500

SATm75

200 300 400

400 500 600

400

500

600

200

300

400SATv25

400 500

600 700

600

700

400

500SATv75

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600 800 1000

1000 1200 1400

1000

1200

1400

600

800

1000SAT

16 18 20 22

24 26 28 30

24

26

28

30

16

18

20

22ACT

10 15

20 25

20

25

10

15

ACT25

15 20 25

25 30 35

25

30

35

15

20

25ACT75

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Predict SAT from ACT

Value Std. Error t value Pr(>|t|)(Intercept) 71.8210 21.1620 3.3939 0.0008 ACT 40.0024 0.9231 43.3366 0.0000

Residual standard error: 50.12 on 423 degrees of freedomMultiple R-Squared: 0.8162

Predict SAT from ACT25 and ACT75

Value Std. Error t value Pr(>|t|)(Intercept) 115.8312 24.9292 4.6464 0.0000 ACT25 23.7215 2.0022 11.8476 0.0000 ACT75 15.5143 1.9658 7.8921 0.0000


Predict SAT from SATm25 , SATm75 , SATv25 , SATv75

Value Std. Error t value Pr(>|t|)(Intercept) 58.6716 10.8146 5.4252 0.0000 SATm25 0.6203 0.0502 12.3530 0.0000 SATm75 0.3112 0.0457 6.8154 0.0000 SATv25 0.3625 0.0658 5.5083 0.0000 SATv75 0.6018 0.0559 10.7662 0.0000


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fitted value

resi

dual

700 800 900 1000 1100 1200 1300

-200

-100

010

020

0SAT~ACT

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fitted value

resi

dual

800 1000 1200

-200

-100

010

020

0SAT~ACT25+ACT75

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fitted value

resi

dual

600 800 1000 1200 1400

-200

-100

010

020

0

SAT~SATm25+SATm75+SATv25+SATv75

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600 800 1000 1200 1400

0.0

0.00

10.

002

0.00

3

SAT

600 800 1000 1200 1400

0.0

0.00

10.

002

0.00

30.

004

estimated sat’s

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top10HS

’sat

sco

re’

0 20 40 60 80 100

600

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original SATestimated sat

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public

private

CT

5000 10000 15000 20000 25000

MA NH

5000 10000 15000 20000 25000

NJ

public

private

NY PA

5000 10000 15000 20000 25000

RI VT

5000 10000 15000 20000 25000

tuition

14


CT

MA

NH

NJ

NY

PA

RI

VT

tuition.gps

800 1000 1200 1400

tuition.gps tuition.gps

800 1000 1200 1400

CT

MA

NH

NJ

NY

PA

RI

VT

tuition.gps tuition.gps

800 1000 1200 1400

tuition.gps

sat

15


800

1000

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1400CT

5000 10000 15000 20000 25000

MA NH

5000 10000 15000 20000 25000

NJ

NY PA

5000 10000 15000 20000 25000

RI

800

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1400VT

5000 10000 15000 20000 25000

tuition

sat

Documents

Lecture 12 - Yale University1 Statistics 101-106 Lecture 12 (1 Dec 98) David Pollard Lecture 12 Each year the U.S. News and World Report provides rankings of US colleges (and universities),