A note on methodology.

There are two primary goals to our methodology. First, we considered no single category to be more important than any other. Second, the final rankings needed to reflect excellence across the full breadth of our measures, rather than reward an exceptionally high focus on, say, research. All categories were weighted equally when calculating the final score. In order to ensure that each measurement contributed equally to a school's score in any given category, we standardized each data set so that each had a mean of zero and a standard deviation of one. The data were also adjusted to account for statistical outliers. No school's performance in any single area was allowed to exceed three standard deviations from the mean of the data set. Thanks to rounding, the top few schools in each category have a final score that is displayed as 100. We have ranked them according to their pre-rounding results.

Each of our three categories includes several components. We have determined the community service score by measuring each school's performance in three different areas: the size of its Army and Navy Reserve Officer Training Corps programs relative to the size of the school; the percentage of its alumni currently serving in the Peace Corps; and the percentage of its federal work-study grant money spent on community service projects.

A school's research score is also based on three measurements: the total amount of an institution's research spending (according to the National Science Foundation); the number of science and engineering PhDs awarded by the university; and the number of undergraduate alumni who have gone on to receive a PhD in any subject. For national universities, we weighted each of these components equally to determine a school's final score in the category. For liberal arts colleges, which do not grant doctorates, baccalaureate PhDs were given double weight. As some readers pointed out last year, our research score rewards large schools for their size. This is intentional. It is the huge numbers of scientists, engineers, and PhDs that larger universities produce, combined with their enormous amounts of research spending, that will help keep America competitive in an increasingly global economy.

The social mobility score is more complicated. We have data that tells us the percentage of a school's students on Pell Grants, which is a good measure of a school's commitment to educating lower-income kids. But, while we'd also like to know how many of these students graduate, schools aren't required to track those figures. Still, because lower-income students at any school are less likely to graduate than wealthier ones, the percentage of Pell Grant recipients is a meaningful indicator in and of itself. If a campus has a large percentage of Pell Grant students--that is to say, if its student body is disproportionately poor--it will tend to diminish the school's overall graduation rate.

We have a formula that predicts the graduation rate of the average school given its percentage of Pell students and its average SAT score. (Since most schools only provide the 25th percentile and the 75th percentile of scores, we took the mean of the two.) Schools with graduation rates that are higher than the "average" school with similar stats score better than schools that match or, worse, undershoot the mark. Four schools had comparatively low Pell Grant rates and comparatively high SAT scores, and had predicted graduation rates of over 100 percent. We left these results alone to keep the metric consistent. In addition, we used a second metric that predicted the percentage of students on Pell Grants based on SAT scores. This indicated which selective universities (since selectivity is highly correlated with SAT scores) are making the effort to enroll low-income students. The two formulas were weighted equally.--Eds.