A survey of five decile 10 and five decile 1 primary schools by the NZ Educational Institute, quoted by Dr Wylie in a book on inequality to be published next week, found the schools' total budgets averaged $8,653 a student in decile 10 areas but only $7,518 a student in the decile 1 schools.
"Yet, one US study estimated that students from poor homes needed 40 per cent to 100 per cent more funding per student to provide equitable learning opportunities," she wrote.
The Government gives decile 1 schools up to an extra $758 per student a year, reducing in steps to just $24 a student for decile 9 schools and zero for decile 10.
At first glance this appears to more than make up for differences in parental donations.
Mr Hodge, who was the principal at Tamaki before moving to Rangitoto seven years ago, said the actual collection rate for donations was typically about 70 per cent at high-decile schools compared with 15 per cent at Tamaki.
He said Rangitoto raised $500,000 a year from parental donations of $250 a student plus $2 million from 230 international students and other funding from corporate sponsors and activity fees.
He said all of that only matched the higher Government funding for low-decile schools, giving Rangitoto about the same income per student in total as a low-decile school.
The last official data for all state and integrated schools, for the 2010 year, shows that schools' total declared income per student actually declined with higher decile from $9,687 per student in decile 1 to $7,974 in decile 10.
Schools' "local funds" in that year, including donations, activity fees and international student fees, totalled $594 million compared with total Government grants of $5.6 billion.
Dr Wylie said her secondary schools survey, which included 1,477 parents, found that 40 per cent of parents sent their children to a secondary school that was not their closest school - usually to a higher-decile school. That left low-decile schools stuck with even bigger proportions of students from low-income and minority ethnic groups than in their surrounding communities. For example, the Tamaki Redevelopment Company said this week that 45 per cent of Tamaki people were of Pacific ethnicities, 23 per cent Maori and 32 per cent European and other. But at Tamaki College, 73 per cent of students are Pasifika, 21 per cent Maori, and only 6 per cent European and other.
Nationally, Dr Wylie said students in decile 1 to 3 schools declined by 12 per cent from 2000 to 2011, while the numbers in decile 8 to 10 schools grew by 23 per cent. "This last challenge reflects New Zealand's policy emphasis on parental choice, coupled with stand-alone, self-managing schools that compete for students," she wrote.
"Such an emphasis has left many low-decile schools smaller than they were and less able to attract their community's higher-performing students."
Who pays
State and integrated schools, 2010, in millions of dollars:
• Government grants $5,596
• Local funds $594
• Investments $39
• Hostels $21
• Other $100
• Total revenue: $6,350
Source: educationcounts.govt.nz