"The classroom effect is nearly three times as large as the school effect and it is the teachers that deliver the results," Professor Fitz-Gibbon said.
The school as a unit of analysis was too complex an organisation to be given a label such as good or bad. "There are no 'similar' schools because the profile is too complex," she said.
Research statistics drawn from maths tests south of the border showed that the school accounted for 15 per cent of variation in performance, the class 43 per cent and 42 per cent was down to individual pupils.
In English, the figures were 12 per cent, 34 per cent and 54 per cent, underlining the importance of the individual teacher.
Professor Fitz-Gibbon told the Headteachers' Association of Scotland's spring conference that too much effort had gone into variables which could not be altered, such as gender, ethnic differences and socio-economic indicators like free school meals.
"What is alterable is what we must look at," she advised.
Professor Fitz-Gibbon criticised the Labour administration south of the border for the failure of its tough approach to driving up standards. Twice as many teachers were leaving the profession since Tony Blair came to power. "Pressure does not necessarily work, it upsets people," she said.
Any alleged rise in standards was the result of "grade inflation" in Government-controlled tests. University engineering departments, for example, observed sharp falls in entry standards. The only genuine rise was in primary school numeracy.
Professor Fitz-Gibbon, who is semi-retired, said it was vital to carry out randomised controlled trials, comparing one group against others, to justify initiatives and find out what works.
Evidence showed that cross-age tutoring was the most effective strategy for many lower ability students. When older students worked with younger pupils for 20 minutes a day over three weeks once a term, the results were impressive for both groups.
"The one thing you should not do with difficult youngsters is put them all together. They feed off each other, become great friends and utterly committed to a lifestyle," she said.