Data analysis plan

In accordance with the Consolidated Standards of Reporting Trials (CONSORT) 2010 statement for cluster-randomised controlled trials guidelines [85], the cluster and participant flow will be reported. Descriptive statistics of recruitment and drop-out will be provided on both the cluster and subject levels. Further, completeness of, and adherence to, the intervention will be reported on a cluster-level only. Baseline characteristics of the randomised groups will be summarised across schools and/or pupils, and will be presented on a pupil level where appropriate.

The primary intention-to-treat analysis comparing maths test performance between intervention and control schools will be conducted by NatCen and is described elsewhere [37]. To account for differences between pupils at baseline, baseline maths performance (Key Stage 2 test score) will be collected from the National Pupil Database (NPD). Analysis of secondary outcome measures will be conducted on an intention-to-treat basis. Per-protocol analyses of secondary measures will also be reported.

Multilevel modelling will be used, as these analyses take the hierarchical structure of the data into account (i.e. pupils within schools) [86]. The models will be used to assess the effect of the intervention, as well as to explore associations between secondary outcome measures, and will adjust for various confounding factors (e.g. sex, socio-economic status, school gender status). Structural equation models (SEMs) may be used for mediation analyses.

MRI data collected as part of the brain imaging sub-study will be analysed and processed using tools from MrTrix3, MATLAB, the FMRIB Software Library (FSL), statistical parametric mapping (SPM) and FreeSurfer, employing parametric and non-parametric statistical analysis methods where appropriate. Details of data (pre) processing and analysis are provided in Additional file 2.