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NEW YORK — Some of the country’s top colleges and universities are changing their rules to better calculate how much financial aid students need, The New York Times reported Friday. 

Yale, Cornell, Stanford and 25 other institutions were expected to announce new guidelines Friday for need-based financial aid, the newspaper said. 

The schools adopting the new guidelines have agreed to increase aid for the neediest students, with some getting increases of more than $1,500 a year, university officials said. The schools said that some students may receive less assistance under the guidelines. 

The new principles are being adopted at a time when states and colleges are increasingly directing aid toward merit-based scholarships. 

“In all too many instances, aid is going to the squeakiest wheel, rather than the neediest students,” Charles Vest, president of the Massachusetts Institute of Technology, told the Times. MIT is one of the 28 participating schools. 

The new guidelines include considering the cost of living in more expensive cities; reducing the amount families are expected to contribute to students’ tuition; learning more about the financial status of students from divorced or separated parents; and making allowances for parents not covered under retirement programs. 

The new guidelines could take more than a year to implement. 

The participating colleges all have need-blind admission policies, meaning students are admitted regardless of their ability to afford tuition, and are then given financial aid. 

Two of the country’s wealthiest universities, Harvard and Princeton, said they agree with the guidelines but did not sign up because they would have been forced to reduce the aid they give to students, the Times said.  

They already offer more financial aid than most of their competitors.