Parents’ income and census data to measure family size would be among the information used to redistribute funding between school systems under a major shakeup proposed to the federal government by a new review.

The review of socioeconomic status (SES) score methodology has delivered a win to Catholic school systems leading a revolt against the Coalition’s $24.5bn Gonski 2.0 schools funding package, with recommendations that stakeholders believe would trigger a redistribution of up to $100m a year from independent to Catholic schools.

The SES review board recommended developing a more precise measure of parents’ capacity to pay for schools using a “direct measure” of their income through tax and census data, which would then affect the amount of government funding from 2020 onwards.

The education minister, Simon Birmingham, said “the vast majority of projected school funding is unaffected”, although the report states the recommendations would have “material differences at a school level within both the Catholic and independent school sectors”.

The report says the new “direct SES scores for independent schools sit higher than the scores for Catholic schools”, meaning that, overall, independent schools would lose out and Catholic schools would gain from the changes.

However, it does not contain modelling to show the sector-by-sector effect of changes, which will be developed and released in coming weeks.

The government has not yet formally responded, but Birmingham said the report set out a “strong case” to adopt a “more precise” formula.

“An effective measure of a school community’s capacity to contribute is essential to ensure the greatest taxpayer support is allocated towards those school communities with the least capacity to pay school fees,” he said. “This approach puts school choice within reach of as many parents and families as possible.”

The National Catholic Education Commission greeted the report with more enthusiasm than the Independent Schools Council of Australia, although both emphasised more work needed to be done to create and test the new SES formula.

The commission’s acting executive director, Ray Collins, said the report endorsed the Catholic sector’s position that the SES score methodology was “fundamentally flawed and negatively impacts a significant number of Catholic schools, as well as some independent schools”.

“We are very pleased that the [review board] has recognised the inherent inequities with the current methodology and look forward eventually to a new approach to ensure fair and equitable funding for non-government schools,” he said.

The executive director of the Independent Schools Council, Colette Colman, warned the recommendations represented a “significant change from the present methodology” and the proposed methodology “will require significant work to determine whether it would produce accurate and valid information at the individual school level”.

“The independent sector must be assured that any direct measure will be significantly more accurate and will be consistently applied to all non-government schools.”

The report found new direct measures of families’ means were “reasonably well-aligned” to the old SES measures, which were based on average income of parents in the school area.

The report says a “direct measure of parental income” was now possible by using “de-identified data that protects privacy”. Similarly, census data would be “confidentialised” to create a more targeted measure and preserve privacy.

The report found that the total private income of schools – including their fees – should not be included in the formula because this would in effect “double count” parents’ income.

Prof Greg Craven, the vice-chancellor of the Australian Catholic University, dissented from that finding, warning that the SES measure would be “seriously flawed” if it did not contain a measure of school income.

He argued that measuring schools’ fee income would improve transparency and public confidence in the measure, and it would not pass the “pub test” to say fees did not reflect capacity to pay.

Craven suggested that the fact some parents could afford fees of between $20,000 and $30,000 was a fair measure of their capacity to pay, in the same way as a “significant number of Australians” would draw conclusions about the financial capacity of people who could afford to buy a C-class Mercedes Benz Cabriolet at a cost of $95,000.

The report said household wealth could not currently be considered, but could be added to the formula if “suitable and reliable direct data become available”.