Standardizing test scores for a target population: The LMS method illustrated using language measures from the SCALES project

Background: Centile curves and standard scores are common in epidemiological research. However, standardised norms and centile growth curves for language disorder that reflect the entire UK local school population do not exist. Methods: Scores on six language indices assessing receptive and expressive functioning of children were obtained from the SCALES population survey. Monolingual English speaking participants were aged between five and nine years. Children who attended special schools at study intake, or who were learning English as an additional language were excluded. We constructed language norms using the LMS method of standardisation which allows for skewed measurements. We made use of probability weights that were produced from a two-step logistic model. Distributions of estimated standard scores from an intensively assessed sub-population and from the full population were contrasted to demonstrate the role of weights. Results: Non-overlapping centile curves and standardised scores at each age were obtained for the six language indices. The use of weights was essential at retrieving the target distribution of the scores. An online calculator that estimates standardised scores for the measures was constructed and made freely available. Conclusions: The findings highlight the usefulness and flexibility of the LMS method at dealing with the standardisation of linguistic and educational measures that are sufficiently continuous. The paper adds to the existing literature by providing population norms for a number of language tests that were calculated from the same group of individuals.