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## Technical appendix

This will be a technical appendix on the potential outcomes framework; for more information, see Morgan and Winship (2014) and Imbens and Rubin (2015). The appendix will express the following ideas in terms of the potential outcomes:

• validity (Section 4.4.1)
• heterogeneity of treatment effects (Section 4.4.2)
• mechanisms (Section 4.4.3)

The appendix will also include a comparison of between-subjects, within-subjects, and mixed designs. The appendix may also include information about using pre-treatment information for design or analysis.