Others, such as the French International School, say quite clearly from the outset that they are looking for ''the brightest children''.

The English Schools Foundation and most international schools say they are testing only the children's ability to follow English language instruction. Whether they admit it or not however, there is more to it than that since some children with English as their mother tongue fail to get places.

Even parents of children who have successfully won places at the most selective schools are sceptical about the admissions interview. Few believe they are really fair or even an accurate measure of anything but the child's mood at that time of day.

Some complain the schools make no attempt to make the tests fair.

Some schools even schedule interviews in the afternoons at times when many four-year-olds have a nap or a rest, or keep children and parents waiting for a long time before the interview so that children are bored and merely want to go home.

Most schools conduct informal interviews and have children carry out a series of tasks - asking them to draw, to construct something from bricks or cut and stick while talking about what they are doing, for instance. Such activities may be carried out with the parents present, with the children on their own or with a group of children together.

Few, if any, carry out formal pencil and paper exercises like the old IQ tests, which required children to complete a sequence or tick the right answer.

Whatever the method of testing, and despite improvements in them, there are pitfalls. Language tests are the most culturally biased, even though schools that use them claim to be ''international'' schools testing a child's ability to learn and take instruction in English.

''Assessment techniques which are most culturally fair are those which rely least on language,'' said Sam Winter, educational psychologist at Hong Kong University's department of education.

Asking children to draw pictures - a common one is to ask children to draw mum and dad and their home - merely tested ''the child's experience with pen and paper'', Mr Winter said, adding that some assumptions could be made about general mental maturity depending on the detail in the drawing, whether mum and dad were wearing clothes, had fingers, hair, and, if so, a hairstyle, the expression on the face and so on.

Great store is set by educationalists and child psychologists in the significance of drawings to reflect a child's developmental stage at a given moment.

But, Mr Winter cautioned, it was ''not difficult to train children to do drawings''.

Why else do so many children in Hong Kong still represent a house as a box with a triangular roof with two windows and a door when the overwhelming image in Hong Kong is of tall rectangles with many windows? Interviews are often a test of personality in which the most outgoing and articulate perform best. Tests are also a measure of the child's stress, anxiety, distractibility, concentration, and previous experience.

''Any test is a snapshot of the child's achievement at that particular point in time,'' Mr Winter said. ''At no point can you make a judgment about the child's ability to achieve in the future.

''The only way to find out how a child responds to instruction is to teach him.'' But schools agree the greatest barrier to objective testing is the anxiety that is generated by the feeling that the test is a major event. An anxious child is most likely to clam up in front of strangers.

The Canadian International School tests children without their parents, in informal groups of three to four - a teacher in a play situation.

''That way the child doesn't feel that he or she is in the spotlight,'' said principal Neil Johnston.

The teacher, sometimes helped by a ''passive'' observer - who watches the children and takes notes - will try to find something that catches the child's imagination and then attempt to engage the child in conversation about it. If that does not work the child may be invited back another time. And in very special cases Mr Johnston has visited the child's pre-school to conduct the test in a familiar environment.

Familiarity is a catchphrase at Kennedy School, an ESF primary which is at the forefront of making such tests more parent and child-friendly.

David Meredith, deputy head at Kennedy, this year visited all the pre-school groups which regularly feed into the school and watched the children at play. Meetings were arranged with the parents in the pre-school, often less daunting than a large school, and also a more relaxed atmosphere.

''The parents' anxiety level at the meeting drops,'' he said. ''When they brought their children to our school for interview, the children's anxiety level was noticeably lower. There was no crying or clinging. They recognised me, I recognised them.

''Tension was taken out of the whole process by not making the whole thing a big event,'' said Mr Meredith, adding that he had ''noticed a lot less rote priming by parents this year''.

At the actual admissions interview at Kennedy, the children are allowed to play in a room full of toys in groups of eight. Friends from pre-school are kept together wherever possible.

''While they are playing, we involve ourselves in their play, look at what they are drawing and encourage them to talk to us,'' Mr Meredith said.

This reduces, but does not eliminate, the problem of the very shy child. The Canadian International School and ESF schools do their best to give shy children a fair chance to show their ability, making the interview as informal as possible, often asking the family to come again if the child will not respond. But realistically, shy children were at a definite disadvantage, Mr Johnston said.

The system pioneered at Kennedy School is likely to be adopted by other ESF schools. But other international schools may not be so innovative.

''Our admissions policy is geared towards screening children in,'' Mr Meredith said. ''The admissions policy of many schools is about keeping the vast majority of children out. They may see no reason to change their procedure.''