A sizeable number of last summer's tests for 11-year-olds had to be re-marked, some several times. In one case the original marker was sacked by the exam board, according to the National Primary Headteachers' Association.
In another school an 11-year old who used "capillary action" and "photosynthesise" got no marks at all - because he failed to use the word "absorb" which was on the mark scheme.
The association, which has 7,000 members in England and Wales, has conducted a survey of 50 schools. It found that two-thirds of heads were dissatisfied with the marking of English tests for 11-year-olds and nearly 50 per cent were unhappy with science marking. More than one in 10 believed that all their papers had been badly marked.
By 2002, four out of five 11-year-olds must reach the required level in English and three-quarters in maths, according to Government targets. But headteachers in the survey reported little or no confidence in the key stage 2 tests, taken by all 11-year-olds in maths, English and science.
The heads have called for all examiners to be properly trained. They point out that the original marks were frequently changed after "moderation" by groups of senior examiners.
But a spokeswoman for the Qualifications and Curriculum Authority said a tiny proportion of schools had appealed over their test scores. She said:
"Only 3,549 children's scripts, out of 600,000, were subject to appeal last year and just 1,805 led to a level change. Our own questionnaires have revealed some concerns but most schools were happy with the marking of the tests. "
The heads suggest that markers should be more carefully selected and have their judgments checked more often by senior markers.
Chris Davis, an NPHA member and head of a Leicestershire primary, said:
"Our survey produced damning evidence to show that the test results are totally unreliable. The Government must move swiftly and resolutely to ensure the accuracy and credibility of the marking of the tests.
"The survey, across 14 local authorities, showed that this is not a problem particular to one area or exam board; it is nationwide.
"At my own school we believed that more than half the English scripts had been under-marked but because of the Pounds 5 fee to appeal we did not submit them all. Three-quarters of those re-marked went up a level, which gives us absolutely no confidence in the rest of our marks."
David Hart, general secretary of the National Association of Head Teachers, said: "The Government underestimates the degree of anger felt by heads over the delays and errors surrounding these tests. Exam boards seem to expect schools to do their work for them by re-marking scripts. If a head made the kind of errors the boards have, they would face serious criticism. No wonder they feel angry that contracted markers are not doing their job properly."
In English, some examiners were found to have disregarded the mark scheme and consistently marked children down, while in science the mark scheme was rigidly applied.