Kenyon Early Decision Plans

1
Early Decision at Kenyon
Introduction I approached the topic of Early
Decision at Kenyon with many questions. First
off I wanted to prove, using formal statistical
inference, that applying Early Decision increases
ones chance of admission to Kenyon. Using the
data provided to me by the Kenyon Office of
Admissions, I used hypothesis tests to explore
this and other questions about admissions trends
at Kenyon. I also wanted to compare Kenyons
proportion of Early Decision applicants to that
of other similar schools. To start my analysis
I had to take the raw numbers from the Office of
Admissions website and files and organize it
into tables which may require some explanation.
  Explanation of Tables I expanded a minimal
amount of data by displaying it in different ways
and then organized the data into the eight tables
at right. I created tables 1, 2, 5, and 6 to
give data in raw numbers, and created tables 3,
4, 7, and 8 to show percents of these same
numbers. Though we are ultimately interested in
what the percents tables show, it is not
sufficient to only display the data in percents
because this can make the data misleading. For
example, examine table 3. The percent of
applicants who applied Early Decision drops in
2006. Compared to the percents of Early Decision
applicants in 2003, 2004, and 2005, it appears as
if less people applied Early Decision this year.
A look at table 1 however, which gives data in
raw numbers, proves that this is not the case.
In fact, a higher number of people applied Early
Decision in 2006 than in any of the three
preceding years. The reason for this discretion
is that in 2006 a larger number of people applied
to Kenyon overall the proportion in table 3 is
smaller than usual only because the denominator
used to determine it (total number of applicants)
is larger. Thus it is necessary to display the
data both ways in raw numbers and percents.
Key ED 1 Early Decision Option 1 is one of
Kenyons two possible ways to apply early, and is
described in detail in the portion
of the presentation labeled Kenyon Early
Decision Plans ED 2 Early
Decision Option 2 is the other possible way to
apply early to Kenyon, and is
described in detail in the portion of the
presentation labeled Kenyon Early Decision
Plans Though I provide data for both
of these options by themselves, I often combine
the two pools (ED total) when
comparing Early Decision and Regular Decision
data overall. REG Regular
Decision at Kenyon has a much later deadline and
is not binding. The vast majority
of applicants to Kenyon choose this
option. Table 1 divides all the applicants up by
the two categorical variables of application type
(ED 1, ED 2, or REG) and year
applied (2003-2006). Table 2 divides all the
students admitted to Kenyon in the same way table
1 does, only the pool of students is
smaller. Table 3 changes the values from table
1 into percents for easy comparison. To find
these percents I divided each
cell entry by its row total (not its column
total), and this includes the bottom row of
totals itself.
The values in the bottom row of table 3 can be
interpreted as average values for all of the four
years. Table 4 interprets the values from
table 2 as percents in the same way table 3
interprets table 1, and again, the
bottom row gives the averages for all four
years. Table 5 looks just at the applicants who
applied Early Decision (both ED 1 and ED 2
combined) and divides them up by
the two categorical values of year (2003-2006)
and admission status (admitted or denied). Table
6 looks just at the applicants who applied
Regular Decision and divides them up by the two
categorical values of year
(2003-2006) and admission status (admitted or
denied). Table 7 changes the values from table 5
into percents for easy comparison. To find these
percents I divided each cell
entry by its column total (not its row total).
The values in the rightmost column of table 7
can be interpreted as average values
for all of the four years. Table 8 interprets
the values from table 6 as percents in the same
way table 7 interprets table 5, and again, the
rightmost column gives the averages
for all four years.
Discussion This portion of the presentation
explores and answers my questions one by one.
But first I need to illustrate a paradox that I
discovered in the data as I was exploring my own
questions. Simpsons Paradox The highlighted
cell in table 4 shows that of all admitted
students, 92.6 of them applied Regular Decision
and only 7.4 of them applied Early Decision.
Thus it looks as if Kenyon Admissions favors
Regular Decision applicants. However, this is
not a true statement. Look at the highlighted
cells in tables 7 and 8. The college actually
admitted 82.4 of Early Decision applicants and
only 60 of Regular Decision applicants. Now it
looks as if Kenyon Admissions favors Early
Decision applicants. This seeming paradox
results when a confounding variable is
overlooked. In this case, the variable is the
number of applicants who chose each option.
The vast majority of applicants apply Regular
Decision. Between 2003 and 2006, Kenyon admitted
5352 (or 60) of its 8913 Regular Decision
applicants and 430 (or 82.4) of its Early
Decision applicants. Just because more admitted
students had chosen to apply Regular than Early
does not mean Kenyon admitted a higher percentage
of those who applied Regular. This is a classic
example of Simpsons Paradox. Question
1 Does applying Early Decision (either Option 1
or Option 2) increase ones chances of being
admitted to Kenyon? To answer this question I
performed a single-proportion hypothesis test
where my null hypothesis was that the proportion
of admitted Early Decision applicants was the
same as the proportion of admitted Regular
Decision applicants, and my alternate hypothesis
was that the former proportion was greater than
the latter. Minitab calculated a z-value of
10.44, which corresponds to a p-value of zero at
an alpha level of 0.05. This confirmed my guess
that Kenyon does indeed admit a significantly
higher proportion of its Early Decision
applicants than of its Regular Decision
applicants. Does this mean though that applying
Early Decision increases ones chances of being
admitted to Kenyon? Not necessarily. The Kenyon
website claims that Early Decision candidates
are judged by the same standards as all other
applicants they are simply evaluated in the
context of a smaller group. The relationship
between choosing to apply Early Decision and
getting accepted to Kenyon may not be causation
as much as it is common response. An important
factor in the decision process for admissions
officers is an applicants interest in Kenyon.
Students for whom Kenyon is a first choice are
more attractive to admissions officers. Students
for whom Kenyon is a first choice often apply
Early Decision. It does not follow, however,
that students who apply Early Decision are
automatically attractive to admissions officers.
It is their interest in Kenyon that gives them an
edge on many Regular Decision applicants.
Interest in Kenyon is only one of many factors
that contributes to the admissions process, all
of which I was not able to take into account when
performing this test. From the numbers I can
only conclude that the proportion of Early
Decision applicants admitted to Kenyon is
significantly higher than the proportion of
Regular Decision applicants. Question 2 How
does Kenyons proportion of admitted Early
Decision applicants compare to other schools like
Kenyon? Do we admit a significantly higher or
lower proportion of Early Decision applicants
than similar schools? To answer this question I
first had to make a lot of phone calls, from
which I developed the following table. I called
the 10 schools that Kenyon experienced the most
overlap with (i.e. many people applied to these
schools along with Kenyon) in the year 2006. Due
to lack of time (for returned phone calls, etc)
and also lack of consistency between different
college admissions offices, the values below are
estimates, but they at least give an idea of
where Kenyon stands. (Note Denison, Carleton,
Bowdoin, and Vassars statistics were not
obtained in time to be displayed.
) Compared to other similar colleges,
Kenyons acceptance rate, particularly for Early
Decision applicants, seems unusually high. I
constructed the following 95 confidence interval
to determine the range outside of which the other
colleges ED acceptance rates would be
significantly different from Kenyons
(0.738391, 0.867051) Since all of the
other colleges ED acceptance rates are less than
73, we can say that Kenyons rate is
significantly higher than all of these other
colleges rates. Conclusion Using hypothesis
tests and confidence intervals I was able to
confirm that Kenyons proportion of admitted
students who applied Early Decision is
significantly higher than the proportion of those
who applied Regular Decision, and that the rate
at which Kenyon accepts Early Decision applicants
at Kenyon is significantly higher than many of
the colleges with which Kenyon experiences
application overlap. The statistics lead us to
an interesting question Why does Kenyon have to
accept so many applicants to fill a similar
number of spots as colleges like Hamilton or
Middlebury? According to our Office of
Admissions, Kenyon tends to have a smaller
proportion of of admitted students who
matriculate, meaning that we have to accept many
more students than we have room for in order to
ensure all spots will be filled. This trend is
changing however, as recently Kenyon has become
more competitive. In 2006 we received a very
high 2838 applications, and accepted 1433 of
them. Thats a record low of50. Kenyon is
growing increasingly competitive.

Percents of Applicants who applied ED and REG for
each year
Kenyon Early Decision Plans Why should you apply
Early Decision? Candidates who feel strongly that
Kenyon is their first choice for college should
apply under one of the Early Decision plans. The
Early Decision plans allow candidates the comfort
of making a college choice early in their senior
year, thus relieving a great deal of the anxiety
many experience about the college admissions
process. Each year, Kenyon accepts 20 to 25
percent of its first-year class of four hundred
thirty students through its Early Decision
plans. Option 1The deadline for this plan is
December 1, with notification of the decision by
December 15. The 350 enrollment deposit must be
made by January 15. Option 1 is intended for
candidates who have decided by mid-fall that
Kenyon is their first college choice. These
applicants must have taken the appropriate
standardized tests during the spring or at the
first fall date. Option 2The deadline for this
plan is January 15, with notification of the
decision by February 1. The 350 enrollment
deposit must be made by February 15. Option 2 is
intended for candidates who decide in the late
fall or early winter that Kenyon is their first
college choice. Applicants who believe their
fall-semester grades or the results of
standardized tests taken in December will be
important to their candidacy should choose this
option. (This is an excerpt from the Admissions
page of the Kenyon College website.)
Early Decision candidates are judged by the same
standards as all other applicants they are
simply evaluated in the context of a smaller
group.