The authority ran NFER tests among P4-P6 pupils in the Whitburn school cluster and found that many results were out of line with 5-14 testing, carried out by individual teachers once they feel confident a pupil has completed a particular level.
At P4 and P6 stages, 7 per cent of the 200 pupils in each cohort were out of line with national test results in reading, 11 per cent for maths and 16 per cent for writing.
Moira Niven, head of education, said the evidence showed that some pupils who were failing to attain a level were capable of much more. Others were identified as underperforming compared to pupils with a similar score who had already gone beyond the level normally associated with their stage.
Teachers appeared to be cautious in putting pupils forward for testing while many more pupils could be pushed further, Ms Niven said.
She added: "The context is that national testing has its weaknesses and we see standardised testing as giving us fairer information which we will be able to target on the needs of individual children. It is very much better quality information for teachers."
Isobel Chalmers, education officer, said: "Where there have been big differences in English and maths standard scores for individuals, schools have checked that pupils have been tested for specific learning difficulties. Some schools have used the results to amend their language programmes to put more emphasis on an area that was showing up as a bit below national levels in the group analysis."
The authority estimates it will cost up to pound;50,000 a year to deploy the tests and hopes to introduce them more widely over the next two to three years.
Further testing of the same batch of pupils will be repeated in May to explore their progress.