It's so complex that few principals, and even fewer parents, can understand it.

Call it the "principal effect": University of Melbourne economist Mick Coelli has created an equation that takes into account the quality of students, the demographics of a school and the amount of time a principal spends at the helm to calculate the impact he or she has in the top job.

For all its complexity, the equation's meaning is relatively straightforward.

Principals significantly boost their students' grades if they set goals, promote professional development and encourage interaction between staff.

New research by Dr Coelli and Mike Helal has found that students with high-quality principals were up to two months ahead of their peers in other schools.

"It's important that new principals are told that if you want to have these effects, particularly on literacy and numeracy, these are the kind of things you need to do," Dr Coelli said. "Leadership is extremely important."

The research will be used by the Education Department to train future and current principals. It could also inform policies on "turnaround schools", where new principals breathe life into under-performing schools.

The research, released on Thursday by the Melbourne Institute of Applied Economic and Social Research, also found that a school's morale improved with effective principals.

It feeds into a growing body of work which says pumping more money into schools will not necessarily lead to better student results. A recent Australian Council for Educational Research report on the country's education system found that "a decline in outcomes has often occurred in parallel with increased spending".

The top 10 per cent of Australian 15-year-olds now perform at about the same level in maths as the top 40 to 50 per cent of teenagers in Singapore, South Korea and Taiwan.

The importance of good principals and teachers is highlighted in new ABC documentary series Revolution School, which aired on Tuesday and captures the success and challenges at Kambrya College, a state school in Melbourne's outer south-east.

Principal Michael Muscat is determined to turn the school's results around – it was in the bottom 10 per cent of the state in 2008.

"When you are rock bottom, there's only one way to go," he says during the first few minutes of the episode. Mill Park Secondary College principal Trish Horner does all the things highlighted in the research, and the results are paying off.

When she took over the top job eight years ago, just 30 per cent of students went to university when they finished school.

Around 50 per cent of students now embark on university degrees.

The school has set three goals which Ms Horner said were "simple enough to be tattooed inside the eyelids of every staff member".

They are to improve academic outcomes, students' ambitions and the school's connection with families and the community.

"I'd like to keep pushing and pushing. The real success stories are the students who are the first in their family to go to university, and the students who you didn't expect to finish year 12, and then they do."

The school employs 21 Teach For Australia teachers, high-achieving professionals who are fast-tracked into schools.

Every term, the school runs workshops for an entire week where staff can choose from multiple sessions every day. Staff run the after-school workshops, sharing their knowledge about targeted teaching, using student feedback in the classroom and catering for students with special needs. It doesn't cost any money to run the workshops.

The research, which is the first of its kind in Australia, was based on Education Department data including literacy and numeracy results and detailed parent and staff surveys.