Children's development at the start of school in Scotland and the progress made during their first school year: An analysis of PIPS baseline and follow-up assessment data

Appendix F

Does the link between deprivation and progress vary across schools or are some schools better at improving equity?

For this investigation it was important to include as much data as possible to increase the power of the analyses which was carried out using multi-level models. All of the data which was available in 2014/15 was used, providing pupils had scores at the start and end of Primary 1. Information was used from 987 schools and 24,473 pupils.

Pupils were nested in schools and three models were generated for each outcome. The null model simply partitioned the variance of the end scores between schools and pupils. The second introduced three variables: the start of Primary 1 score on the relevant variable, deprivation (decile centred on the grand mean) and sex (dummy variable identifying girls). In the third (Model 2) the devipration variable was allowed to vary across schools. The results with total score as the outcome are shown below.

Figure F-1: Multi-level models for the total score

Standard errors are given in parentheses

The Null model indicates that 13% of the variance in the total score was associated with school membership and 87% resided with pupils. Introducing the total score at the start of the year, deprivation and sex reduced the school level variance by 12% and the pupil level variance by 58% in Model 1. Schools varied and a large proportion of the variance (31%) was located with the schools. This can be interpreted as evidence that the progress made in schools varied considerable. The prior score (start of Primary 1 score) was a strong significant predictor, responsible for the reduction in the school level and pupil level variances. Deprivation was a weak significant predictor in that when it was added to the model after the Primary 1 score the variances at the school and pupil level remained the same. Sex was not significant. One point to note here is that the prior attainment score, in a sense, already has information about deprivation and sex and this may explain why the other two variables add so little.

Model 2 allowed deprivation to vary across school but the variation was not significant (p>.05). Figure F-2 shows the school intercept residuals and school deprivation slope residuals. Both include standard errors. In other words the first figure below shows how the progress in each school differ from the average - as in Figure 24 - and the second figure shows how the link to deprivation differs from the average for each school.

Figure F-2: School residuals for intercepts and slopes

Figure F-2 supports the conclusions drawn from the tables. There were large differences between the mean progress made across schools but there was no evidence of differential impact on equity. This means that although schools made a big difference to academic progress this progress varied from school to school. Further, schools generally had little impact on the educational gap and this was the same across schoolls.

Parallel models were run for maths and reading. Again there was no significant difference in the link between progress and deprivation across schools.