1. Adapting Designs Professor David Torgerson University of York Professor Carole Torgerson Durham University

2. Trial design Numerous trial designs are available to answer different questions. Sometimes the same question could be answered using different designs. Trade-off between: »Statistical efficiency (including contamination); »Post-randomisation bias; »Generalisability; »Cost.

3. Numerous trial designs Individual randomisation; Cluster randomisation.

4. Individual allocation “Standard” RCT (Summer schools) Waiting list RCT »Within school year waiting list (ECC); »Outside school year waiting list; Factorial; Combined with regression discontinuity (SHINE); Incomplete block design.

5. Cluster randomisation School cluster (Calderdale); Class cluster (Grammar for writing); Year cluster (Third space); Waiting list (Third space outside school); Stepped wedge; Partial split plot (Grammar for writing); Full split plot.

6. ECC & Online Maths In this session we will discuss two RCTs and their designs: »Every Child Counts (ECC) evaluation; »Third space (online maths) evaluation (EEF funded study).

7. Independent evaluation of Every Child Counts intervention ‘Numbers Count’ Effectiveness research question: Is the ECC numeracy intervention ‘Numbers Count’ better at improving mathematics achievement than normal classroom teaching in numeracy? Year 2 pupils at risk in numeracy Intervention: one to one teaching, focus on number, every day for 12 weeks Control: usual classroom teaching in number and other mathematical concepts a Torgerson, C.J., b Wiggins, A., c Torgerson, D.J., c Ainsworth, H., c Hewitt, C., Testing policy effectiveness using a randomized controlled trial, designed, conducted and reported to CONSORT standards, Journal of Research in Mathematics Education, March, 2013 Funded by Dept. for Education, £305K, 2009-11

8. Design of experiment 12 children in each of 44 schools selected as eligible for ‘Numbers Count’ intervention Maths test (Sandwell test) (pre-test) at beginning of autumn term (administered by teachers) Random allocation of 12 children to term of delivery: autumn, spring or summer: ‘waiting list’ design Intervention group: autumn children Control group: spring and summer children Maths test (Progress in Maths test) after 12 weeks (administered by independent testers) (post-test) Simple analysis: compare the mean maths post-test score of intervention children with mean maths score of control children and conclude whether ‘Numbers Count’ is more effective than usual teaching Rigorous design: excludes some alternative explanations for results

9. Design features that increased internal validity and acceptability Randomisation: intervention and control groups are equivalent at start so design controls for history, maturation, regression to the mean, selection bias Large sample size: excludes chance finding Intervention and control conditions are both numeracy interventions and both last for 30 mins. per day for 12 weeks: the comparison is a ‘fair’ one Independent ‘blinded’ testing: eliminates possibility of tester bias ‘Waiting list’ design so all eligible pupils received intervention Small number of ‘wild cards’ allowed

10. Results Intervention Group Control Group Effect Size 95% Confidence Interval PIM 6 (0-30)15.8 (4.9) N = 144 14.0 (4.5) N = 440 0.33 (0.12 to 0.53)

11. Design limitations: Generalisability ECC schools were identified: by policy- makers/funders of programme - education policy ‘roll out’ in England, i.e., schools in disadvantaged areas Ideally, a random sample of all secondary schools in England should have been approached and asked to take part

12. Design limitations: Intervention One to one teaching with intervention children being withdrawn from classroom Problem of attribution: was effect due to NC intervention? one to one teaching? Design could have included additional one to one arm

13. Design limitations: Intervention One to one teaching with intervention children being withdrawn from classroom Problem of attribution: was effect due to NC intervention? one to one teaching? Design could have included additional one to one arm

14. Design limitations: ‘Contamination’/’spill over’ effects Children withdrawn from usual classroom teaching – may have benefited remaining children; teachers using programme may have applied it to some control children. Instead of randomising individual children design could have randomised by school (cluster randomisation, where school is the cluster) to avoid these problems.

15. Design limitations: Long term effects Wait list design prevented long term follow-up; effects may have ‘washed out’ soon after intervention was finished. Could have used cluster randomisation; Could have recruited 3 additional children above threshold and randomised these to intervention or control for long term follow-up; All options (above) rejected by funder.

16. Conclusions Design and conduct warranted conclusion NC (as delivered) more effective than usual classroom teaching BUT because of design limitations couldn’t answer some really important questions These questions could have been answered if a different experimental design had been used: cluster randomisation (randomisation of schools), long-term follow-up (control group that didn’t receive intervention); one to one control group (literacy or other numeracy)

17. Online maths evaluation EEF have funded Third Space to deliver to 600 children 1 school year of face to face online maths tuition delivered from tutors based in India; York Trials Unit with Durham University have designed a trial to evaluate this intervention; Several design options are possible.

18. Individual randomisation 600 children randomised to tuition and 600 allocated to nothing would give 80% power to show 0.11 ES difference (pre-post correlation 0.70); Unequal allocation 600 to tuition 1200 would increase efficiency to show 0.10 difference; Problems: »Resentful demoralisation from control children; »Difficulty in getting schools to take part.

19. Waiting list We could instead randomise 600 children such that all could receive the intervention; 300 in term one and 300 in term two (similar to ECC evaluation); Power: 80% to show 0.16 ES; Problems: »Lack of long term follow-up; don’t know if intervention’s effects will be sustained.

20. Cluster trial We could randomise schools which would avoid resentful demoralisation at the child level; 600 children (assuming 10 per school; ICC 0.19; pre/post 0.70), would give us 80% power to show 0.19 ES difference; Problem: »Schools in the control group may be more likely to drop-out introducing attrition bias.

21. Cluster/wait list design We could randomise schools to offer intervention to children in year 6 and the waitlist schools to get the intervention for their next year’s year 6 pupil; Prevent school level drop-out; Allow long term follow-up; Problem: »Lower efficiency than previous design (0.26 ES detectable), but lower risk of bias.

22. What has actually happened? Aimed to recruit 60 schools with an average of 10 pupils per school; However, over-recruited 72 schools so we are recruiting 8 pupils per school; This improves our efficiency so that we now can detect an effect size of 0.25 rather than 0.26.

23. Activity In small groups discuss your EEF trials where the trial design has been adapted to increase: acceptability or implementation of the intervention; internal validity; or external validity; Select the most interesting/significant example for feedback to whole group.