Table 1 Glossary of terms

Intracluster correlation coefficient (ICC)

A measure of the amount of clustering within schools

Individual autocorrelation (IAC)

Correlation for the same pupil between two different time points

Cluster autocorrelation (CAC)

Correlation for the same school between two different time points

Cross-sectional design

Different pupils are measured at each time point

Closed cohort design

The same pupils are measured repeatedly over time points; pupils cannot join the study once it has started

Open cohort design

Pupils are repeated are measured repeatedly over time points, but pupils may join or leave the study at any time

Seasonal trend

Seasonal changes in outcome, the same from year to year

Secular trend

Changes in outcome over time

Sequence

A sequence of control and intervention statuses at each time period and whether measurement at this time occurs or not. Schools are randomly allocated to a sequence and sequences may have multiple schools allocated

Step

A planned time point when one or more schools switch from control to intervention status

Measurement period

The period of time covered by one step

Implementation period

A period of time to implement and fully embed the intervention

Stepped wedge configuration

the configuration of sequences, steps, allocations, timings and measurement schedule that form a specific stepped wedge design

Incomplete design

A stepped wedge design where measurements are only taken in some schools at each measurement point, rather than for all schools at all times.

Data generating model

Statistical model used to generate data in the simulation study

Analysis model

Statistical model used to analyse data in the simulation study