We have rolled out our interactive flash scatterplots (also known as scattergrams), available on every college page under the ‘My Analysis’ tab.

These graphs display the accepted and rejected applicants scattered across a 2D canvas according to the variables that you choose. For example, you might look at Unweighted GPA & SAT, or Instate & Average AP Score. To get started with this new tool, see Cornell’s scatterplots.

For any given SAT score, valedictorians appear more likely to get into Cornell than non-valedictorians.

Because there are many, many overlaps, you can set a level of jitter, so each point floats near its true value. For example, if you look at Unweighted GPA and Valedictorian Status, everyone will clump on top of one another. (You either are a valedictorian, or you aren’t, so there are only 2 slots that you might possibly fit into – hence lots of clumping.) If you set a 20% jitter to Valedictorian Status, things will spread out nicely, so you can see what is really going on.

With your feedback and criticism (please post it here or in the forums), we’ll work on improving the tool. Enjoy!

In my previous post, I introduced the new college rankings system that we have implemented. In short, the system ranks colleges based on where their admitted students decide to attend. In this post, I will discuss some of the approaches that might be considered in creating a preference-based ranking. In the next post, I will discuss the preference ranking system that we have implemented.

2009 MyChances.net College Rankings

Yield isn’t enough

The goal of a preference-based ranking system is to capture people’s true preferences and represent them faithfully. To discover people’s preferences, a reasonable place to start might be a college’s yield. Yield is calculated as follows:

yield = (# of students attending) / (# of students accepted)

So how can we use yield to compare two schools? Suppose we match the University of Georgia (#70 on our list) against Pomona (#50 on our list). In this matchup, Georgia’s 55% yield actually beats out Pomona’s 39% yield. More of Georgia’s admitted students end up attending—so Georgia appears to be preferable to Pomona. But there is a problem here: we have no direct evidence that students, given the opportunity to attend either school, would choose Georgia. We simply don’t know what the students who were admitted to both schools would do.

In the abstract, there is another problem with this approach. Imagine that 100 students apply to both Georgia and Pomona. Suppose Pomona accepts 50 of them but Georgia accepts all 100. Now, suppose the 50 rejected from Pomona all decide to go to Georgia, giving it a 50% yield. Suppose, also, that 40 of Pomona’s accepted students also get into Harvard, Yale, or Princeton, and they all go off to those schools. This leaves Pomona with a 20% yield. Going by yield, it appears that Georgia is the preferred college by far—but in reality, all of the students admitted to both Pomona and Georgia who attended one of the two decide to go to Pomona. Yield, in this situation, gives us exactly the wrong answer about which school is preferred over the other!

Each student matters

What can we learn from the failure of yield as a measure of preference? Summary statistics simply don’t tell us enough. We need to drill down to the level of individual students. Only then can we build up a picture of their collective preferences. How can we do this? One approach might simply be to ask them what their preferences are. For example, we could survey a bunch of students applying to college, and ask them to order all of the schools they are considering, from most favorite to least favorite.

This is better; if those 100 people in our previous example honestly represented their preferences, we would probably see that the Pomona was preferred over Georgia. This is the intuitively correct result given our (fake) example. But even this approach isn’t perfect.

Talk is cheap; opinions, cheaper

One problem is that there is no cost associated with ranking a school #1 on your own personal list. Until you actually have to decide which college you are going to attend—and pay tuition to—for the next 4 years, your opinions have no teeth. Let’s say you rank UNC as your #1 school and Duke as your #8 (out of 8), because your Tar Heel family hates those Blue Devils. You apply, and get into both schools. Did I mention that you got a merit scholarship to Duke? All of a sudden, you find yourself attending your supposedly bottom-ranked school. You didn’t lie when you gave us your rankings, but you probably exaggerated how much you preferred UNC over Duke. Furthermore, you didn’t have all of the information that you used to make your decision—such as your merit scholarship—when you reported that Duke was your #8 school.

In general, asking people for their preferences leads to these additional problems:

• They may give feedback about colleges where their feedback is of questionable value. If someone with a 1.5 GPA says that they rank State U over Harvard, should that hurt Harvard—even though this person almost certainly wouldn’t be given the opportunity to attend there, anyways?
• They almost certainly give feedback that is based on imperfect information. At the moment where people are making their decision to attend one school out of several that they were admitted to, they have acquired as much information as they think they need to make this huge decision. Beforehand—and, in particular, before they have applied to and been admitted to colleges—their stated preferences may be much more labile.

Understanding these flaws helps flesh out a framework for a powerful-yet-simple preference-based college rankings system: one where students simply report where they were admitted and where they decided to attend. In my next post, I’ll get into some of the details of how to take this information and construct a ranked preference list. I’ll even demonstrate how this approach addresses a common criticism of the currently popular college rankings: that there is no way to truly distinguish between schools closely ranked (e.g., #3 vis-a-vis #5).

Presenting: our new college rankings.

The college admissions landscape is littered with college rankings. In 1983, US News first ranked American universities. Since then, rankings have been a fixture of the college world: they are produced by various businesses (US News, Princeton Review, Forbes, Atlantic Monthly), and heeded by students and colleges alike. To gain advantage, some universities have been alleged to manipulate their own rankings. And, while some of the factors used in the rankings are justifiable (alumni giving rate), some seem to be arbitrary (peer assessment surveys asking other colleges about your college’s ‘faculty dedication to teaching’). Each year, the methodology changes slightly, producing a slightly different list. In the end, the factors that are used to come up with the rankings seem arbitrary; the occasional change in the weighting of each factor, capricious. There is a need for a new approach.

Criteria for a ‘good’ college ranking system

1. The system should be difficult to game; any ‘gaming’ of the system should actually benefit students. In contrast, consider the allegations that some schools tried to manipulate the US News rankings by encouraging more students to apply in order to decrease their acceptance rate.
2. The factors measured should be relevant to students. In contrast, what Cornell’s dean thinks about the faculty dedication at the University of Texas may be irrelevant.
3. The overall procedure for generating rankings should be stable from year to year. In other words, any change in the rankings between 2008 and 2009 should be explained by a substantive change in the underlying factors, not by an arbitrary change in how those factors are weighted.

The MyChances College Rankings

We have implemented the MyChances College Rankings based on revealed student preference. In this system, the college admissions process is treated like a chess tournament. The colleges play matches (which occur when 2 colleges admit the same student). In each match, there is a winner (the college that the student ends up attending) and a loser. The winner gains points; the loser forfeits them. When a high-ranked school beats a low ranked school, the high-ranked school gains few points, and the low-ranked school loses few points. If a low-ranked school beats a high-ranked opponent, it gains more points than if it beat an equally-matched opponent. After playing many games, the colleges that students prefer rise naturally to the top of the rankings.

Does the method of revealed student preference meet the 3 criteria outlined above? I believe it does.

Consider point #1 (gaming the system). Imagine that MIT wanted to beat out Harvard by trying hard to avoid admitting any students that they thought would be admitted to Harvard. They would end up succeeding in a model based on acceptance rate and yield (since their yield would likely increase), but their actual student body would be less qualified. In the revealed preference model, however, they would be less successful. They would not compete head-to-head with Harvard, so would ‘win’ more. But they would be winning against weaker ‘opponents’, earning fewer points for each victory.

For point #2 (relevance), the idea of revealed preference is that it aggregates the sum total of what matters to students – whatever those factors might be. It is likely that students behave rationally (by attending the school that they find most desirable). So long as other students share similar values, then revealed preference rankings will work well in explaining, and even guiding, their decisions.

For point #3 (stability), the tournament style system is simple and straightforward. It is responsive to changes in student preference over time. It does not rely on aggregations of various statistical factors, or college faculty survey results; nor does it depend upon arbitrary weighting of those factors.

The details of the procedure that we use to generate the rankings, and our use of chess-style Elo points, will be explained in a later post. For an academic treatment of a similar college ranking system, I recommend the working paper, “A Revealed Preference Ranking of U.S. Colleges and Universities,” 2005, by Christopher Avery, Mark Glickman, Caroline Hoxby, and Andrew Metrick (free link).

Today we’re letting everyone in on a sneak-preview of our latest tool: the college cross-admit preference tool. We think it’s a simple but powerful way to see which colleges are most favored by admitted college students.

To use it is simple: type in the names of two colleges that you want to compare (perhaps Florida and Florida State?). You’ll then see which fraction of site members prefers which school. Preference is determined by the relative fraction of members admitted to both schools who end up attending one or the other. For example, if 25% of students admitted to both College A and College B ultimately go to College B, we say they prefer College B over College A. When the results are statistically significant at the 95% level, you’ll see the results lit up in bright colors.

For the hardcore college admissions followers out there, this will remind you of this graphic from a 2006 NY Times article. One difference is that our list isn’t limited to 17 schools; as the data continues to become available, we’ll display this information for all 1700 schools that we track.

Requests? Feedback? Suggestions? Let us know.

On each college page you’ll find a “Personalized Analysis” tab. This now shows you about a dozen graphs, breaking the numbers down by accepted/rejected/applying. Your own score range is highlighted. (Note: you have to be logged in to see the graphs.)

I’ve attached an example for those of you who aren’t logged in.

Now when you visit a school’s page, you’ll be able to click through to “Personalized Analysis”, which shows where you fall vs all admitted students (ever) and current applicants (for the next admissions cycle). Currently it is limited to GPA and SAT scores, but we plan to expand this to automatically show all of the categories that apply to you; i.e., if you listed an AP English Language score, we’ll graph that out for you.

Two changes today:

1) Each college page now has a “discussion” tab. Discussion from news sources, blogs, and our own applicants has been moved there. Soon, but not yet, you’ll be able to make comments directly on the school’s page.

2) The “discussion” tab allowed us to free up a lot of space in the “Applicants & Predictions” page for each college. In its place, we now show you the students’ class rank and home state. More to come on this.

As of today, when you visit a university’s page on this site, you’ll find a link to its map in the deep blue menu bar running along the top of the page. Fun things are in the works now that we’ve got the Google Maps working. For now, any suggestions? (If your university doesn’t have a map, it’s because we don’t have its address – send it our way and we’ll update the database.)

Today, I finally put the finishing touches on a form I’ve been working on for a couple of weeks now. It’s the page where you create your college profile. This is an important page, because the computer largely bases its predictions on the information you give it here. Starting today, you’ll be asked to indicate which high school you’re attending (out of a list of about 35,000). If it’s not there, you can easily add it without leaving the page. And for privacy’s sake, you’re invited to hide your high school information before you’re even asked for it.

The benefit in disclosing where you go to high school is that it will allow for better predictions.  Unless you think that it’s an accident that Stuyvesant and Andover flood the Ivies with their graduates every year, you’ll probably agree with me that high school “strength” is a fair indicator of future college acceptance. Well, even if you don’t agree with me, we’ll be testing this hypothesis together over the next few weeks.

Are there any patterns that you think will jump out? How do you think your your high school will compare?

Today we’ve added a new option for you to browse by: Selectivity Ranking. As you might know by now, we’ve developed a formula to give each school a selectivity score based on how difficult it is to get into that school.

Now, we’ve ranked the colleges and given them Selectivity Rankings. You can ‘Browse Colleges’ by these rankings, showing you the most difficult to the least difficult schools to get into.