Wednesday, March 15, 2017

Student Debt and The Rise of Private For-Profit Schools


Student Debt and The Rise of Private For-Profit Schools

Question One:  The table below contains information on share of students in three types of institutions – public universities, private non-profit universities, and private for-profit universities for both 2004 and 2012. 

The table also contains information on the percent of students taking out federal loans in 2012 and the average loan balance per student in 2012.


Note that the share of students in both public universities and private non-for profit schools fell and the share of students in private for-profit schools rose.  The increased share of students in for-profit schools is of concern because around 70 percent of students in this sector take out federal student loans.

Based on this information:

What is the best estimate of total loans in dollars for each institution type for 10,000 students representative of all three sectors?

What is the best estimate in total loans in dollars for 10,000 students at each institution type if the share of students across institution types were at their 2004 levels and lending patterns were at 2012 levels?

How did the increase in the share of students attending private for-profit schools impact the issuance of total federal student loans?


Institution Type and Federal Student Loans
Institution Share 2004
Institution Share 2012
% of Students taking out federal   loan in 2012
Average   federal Loan in $ 2012
  Public
76.96%
73.42%
30.96%
$6,012
  Private not-for-profit
14.99%
13.05%
60.00%
$7,095
  Private for-profit
8.05%
13.53%
71.14%
$7,030
The data was obtained from the 2004 and 2012 NPSAS databases accessed from https://nces.ed.gov/datalab/powerstats/default.aspx


Analysis:


10,000 students multiplied by share of institution at each institution is the number of students out of 10,000 students going to each type of institution.  Multiply number of students at each institution type by percent of students taking out loans to get number of borrowers (from 10,000 students) at each institution type.  Multiply total number of borrowers at each institution type by average federal loan per borrower to get total amount borrowed at each institution type for 10,000 students.

Total borrowed for 10,000 students is calculated using 2012 and 2004 institution shares below.



Impact of Change in Institution Share on Loans In $
Total Loans In Dollars 2012 for 10000 Students
Total Loans In Dollars in 2012 for 10,000 Students at 2004 Institution Shares
Change in Dollars (2012 - 2012 at 2004 Institution Share)
Public
$13,668,740
$14,327,789
-$659,048
Private not-for-profit
$5,555,560
$6,381,444
-$825,884
Private for-profit
$6,766,687
$4,026,004
$2,740,683
Total
$25,990,987
$24,735,236
$1,255,751

Observations:

The increase in federal student debt incurred from 10,000 students due to the increased share of students in private for-profit schools is around 2.7 million, which is 10.5% of total debt for 10,000 students.   After netting out the decrease in public school and private non-profit student I get 4.8 percent of the total.

A more apt comparison involves the change in debt due to increase share of students attending for-profit schools to total change in debt.  Again the analysis is based on 10,000 students.  I found that 10,000 students in 2004 would have accumulated around 14.5 million in debt, around $10 million less than debt incurred by 10,000 students in 2012.  After accounting for decreased share of public and private not-for profit schools it appears as though the shift toward private for profit schools is responsible for around 12 percent of the increase in total student debt.


Concluding Thoughts:  The for-profit sector represents around 13 percent of students in 2012 up from 8 percent in 2004.   The shift towards this sector increased federal student debt by around 12 percent between 2004 and 2012.

People interested in a broader overview of changes in three forms of student debt between 2004 and 2012 should read the following post.

Student Debt Overview:








Monday, March 13, 2017

Three Small Sample Hypothesis Testing Problems on Means

Three Small Sample Hypothesis Testing Problems on Means

This post presents three problems concerning hypothesis tests on means for small samples.   The topics covered here include – (1) comparing SAT scores for the original and expanded Big Ten conference, (2) comparing Zillow rent estimates to rent requests, and (3) comparing number of touchdowns for the first QB chosen and the second QB chosen in the NFL draft.

This post contains questions and links to answers published in other posts.

Question One:  Once upon a time the Big Ten consisted of 10 schools.   Four new schools Rutgers, University of Maryland, Pennsylvania State, and University of Nebraska entered the conference in recent years. 

What did the entry of these four schools do to the mean of the 25th percentile of the Verbal SAT score in the Big Ten?

Conduct a hypothesis test for a difference in the mean for Verbal SAT at the 25th percentile between the two groups.


How does the existence of Northwestern the outlier impact the results presented here?



Big Ten Verbal and Math SAT Averages
Original Big Ten Schools

School
Verbal SAT 25th Percentile
1
Ohio State
540
2
University of Michigan
620
3
Michigan State
420
4
University of Minnesota
550
5
University of Iowa
540
6
Purdue
520
7
Indiana University
520
8
Northwestern
690
9
University of Illinois
560
10
University of Wisconsin
530
New Big Ten Schools
1
Rutgers
520
2
University of Maryland
580
3
Penn State
530
4
University of Nebraska
490

Answer to Big Ten Problem:





Question Two:   The table below has data on requested and estimated rents on home in Venice California.


Requested and Estimated Rents for 3+ bed room houses in Venice California

Requested Rent
Zillow
Rent
estimate
Difference Rent - Estimate
% Difference
1
3798
4000
-202
-5.3%
2
4550
5100
-550
-12.1%
3
4600
4700
-100
-2.2%
4
4895
4600
295
6.0%
5
5395
5300
95
1.8%
6
5900
4600
1300
22.0%
7
6500
5100
1400
21.5%
8
6800
5000
1800
26.5%
9
6500
6500
0
0.0%
10
6500
7100
-600
-9.2%
11
6995
7900
-905
-12.9%
12
7750
6000
1750
22.6%
13
7950
6900
1050
13.2%
14
7950
4600
3350
42.1%
15
8000
4800
3200
40.0%
16
8000
5200
2800
35.0%
17
8500
6400
2100
24.7%
18
8500
8500
0
0.0%
19
11500
6900
4600
40.0%
20
12500
12000
500
4.0%
21
12500
6600
5900
47.2%
22
15000
7600
7400
49.3%


Source of data is


Compare the requested rents to the Zillow estimates?

Conduct a classical hypothesis test that the difference between requested and Zillow estimate rent was zero?

Conduct the nonparametric Wilcoxon rent for differences between requested  and Zillow estimate rents


Answers to rent problems:

The descriptive statistics and the result of the classical hypothesis test is presented here:


The results of the Wilcoxon Test is presented here:


Question Three:  The table below contains information on the number of career touchdown passes made by the first QB selected and the second QB selected in every NFL draft spanning the 1970-2002 period.   (I did not include QBs chosen after 2002 because a large number of such QBs have not yet completed their careers and I wanted to focus on QBs that had completed or had almost completed their career.)

What is the average, median, minimum, 25th percentile, 75th percentile, maximum and the standard deviation of career touchdown passes for the first QB choice and the second QB choice?

Conduct appropriate hypothesis tests.

What does your statistical analysis suggest about the relative value of the first QB chosen compared to the second QB chosen in the NFL draft?

What are the potential implications regarding the risk of trading up in order to get the first QB in the draft?


  Data


Touchdowns for First QB Picked and Second QB Picked
Year
First QB Chosen
# of Touchdowns
Second QB Chosen
# of Touchdowns
2002
David Carr
65
Joey Harrington
79
2001
Michael Vick
128
Drew Brees
363
2000
Chad Pennington
102
Giovanni Carmazzi
0
1999
Tim Couch
64
Donavan McNabb
234
1998
Peyton Manning
491
Ryan Leaf
14
1997
Jim Druckenmiller
1
Jake Plummer
161
1996
Tony Banks
77
Bobby Hoying
11
1995
Steve McNair
174
Kerry C ollins
208
1994
Heath Shuler
15
Trent Dilfer
113
1993
Drew Bledsoe
251
Rick Mirer
50
1992
David Klinger
16
Tommy Maddox
48
1991
Dan McGwire
2
Todd Marinovich
8
1990
Jeff George
154
Andrew Ware
5
1989
Troy Aikman
165
Mike Elkins
0
1988
Chris Chandler
170
Don Mcpherson
0
1987
Vinny Testaverde
275
Kelly Stoufer
7
1986
Jim Everett
203
Chuck Long
19
1985
Randall Cunningham
207
Frank Reich
40
1984
Boomer Essiason
247
Jeff Hostetler
94
1983
John Elway
300
Todd Blackedge
29
1982
Art Schlichter
3
Jim McMahon
100
1981
Rich  Campbell
3
Neil Lomax
136
1980
Marc Wilson
86
Mark Malone
60
1979
Jack Thompson
33
Phil Simms
199
1978
Doug Williams
100
Matt Cavanaugh
28
1977
Steve Pisarklewicz
3
Tommy Kramer
159
1976
Richard Todd
124
Mike Kruczek
0
1875
Steve Bartkowski
156
Steve Grogan
182
1974
Danny White
155
David Jaynes
0
1973
Bert Jones
124
Gary Huff
16
1972
Jerry Tagge
3
John Reaves
17
1971
Jim Plunkett
164
Archie Manning
125
1970
Terry Bradshaw
212
Mike Phipps
55



I have written too many posts on NFL draft issues.

Here are some links to my analysis on this topic.

This post has descriptive statistics related to the table above:

This post uses the football data to illustrate three tests – the classical test on differences between means, the paired t-test, and the Wilcoxon rank sum test.