It is the time of year when high-school seniors zip uncountable college applications across the country. Many yearn to be accepted in top private colleges and universities such as Harvard or Williams and fear that they might get stuck at a lowly "state school."

This bias is age-old, and was perhaps most succinctly described by Friedrich Nietzsche, who said that "in large states public education will always be mediocre, for the same reason that in large kitchens the cooking is usually bad."

But are public universities in the U.S. really that bad? A new study by the website Payscale.com analyzed a massive data set representing millions of observations and estimated the rate of return on investment in higher education for people who attended a wide array of U.S. colleges and universities.

Payscale has a large database of wage and salary data, allowing it to compare the pay of workers who attended, say, the University of Florida with that of a control group of high-school graduates and then estimate what the typical student gets out of her investment in college. The calculations are done for a very large sample of U.S. institutions of higher learning, so one can compare the annualized return on investment (ROI) for public and private universities.

The results, which are summarized in the nearby chart, are startling. The public institutions trounce the private ones in terms of the percentage return on investment. With the exception of Brigham Young University, which is somewhat unrepresentative because it receives much support from the Mormon Church, the top 16 rates of return were all posted by public institutions.

To see how much this turns conventional wisdom on its head, consider that the 15th-place institution is the University of Delaware, the 16th is the University of California at San Diego, and the 17th and 18th places are held by Caltech and MIT.

All told, the average annual ROI for the top ten public institutions is 13.4 percent. The average annual ROI for the top ten private institutions is 12.3 percent. The chart also provides a clue about why the public institutions are such good buys. The average total cost for a bachelor's degree from a public institution is $83,695; for a private institution it is $171,026. The higher tuition at top schools brings diminishing returns.

While annual ROI is a useful measure of bang for the buck, one caveat is in order. Even though the rates of return are lower for private schools, they are compounding off of an investment that is larger, so the actual cash haul associated with a private college education can be higher. For example, a person with an MIT degree can expect to earn about $1.7 million more than a high-school graduate over the next 30 years, while a graduate of the Georgia Institute of Technology will see a return of $1.1 million more over the same period.

Neither number is chump change, and the relatively high returns for the public universities mark them as first-rate investments. The University of Virginia and Williams College, for example, provide almost exactly the same 30-year income.

So if you are anxious this application season, relax. In most cases, the impact of ending up at a state school rather than a "first choice" will be small indeed.