1. 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 1 The 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 2 The 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.) 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 one’s 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 Kenyon’s 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 Kenyon’s 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. Early Decision candidates are judged by the same standards as all other applicants; they are simply evaluated in the context of a smaller group. 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. Simpson’s 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 Simpson’s Paradox. Question #1: Does applying Early Decision (either Option 1 or Option 2) increase one’s 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 one’s 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 applicant’s 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 Kenyon’s 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 Vassar’s statistics were not obtained in time to be displayed. ) Compared to other similar colleges, Kenyon’s 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 Kenyon’s: (0.738391, 0.867051) Since all of the other college’s ED acceptance rates are less than 73%, we can say that Kenyon’s rate is significantly higher than all of these other colleges’ rates. Conclusion Using hypothesis tests and confidence intervals I was able to confirm that Kenyon’s 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. That’s a record low of50%. Kenyon is growing increasingly competitive. Percents of Applicants who applied ED and REG for each year: