Appendix 1—figure 1. No clear indication of inflated statistical artefact in GLM1a.

GLM1a includes regressors HV-LV, D-HV and (HV-LV)(D–HV) to predict choice accuracy. (a) In Simulation 1, choice accuracy data was simulated using the effect size of HV-LV estimated by GLM1a from actual participants and assuming that the D-HV and (HV-LV)(D–HV) effects are absent. Then GLM1a was applied again to analyse the simulated choice accuracy data. In 1000 iterations, the chance of obtaining a significant effect (p<0.05; at the dashed line) from the HV-LV term is 100% (i.e. 0% Type II error; orange). For the D-HV and (HV-LV)(D–HV) terms, for which no effect is assumed, the chances of obtaining Type I errors are 5.6% and 5.1% respectively (yellow and purple respectively). (b) Simulation 2 is similar to Simulation 1, except that the effect size of HV-LV was estimated from the empirical data using a GLM that only includes the HV-LV term. (c) Simulation 3 assumes that HV-LV, D-HV and (HV-LV)(D–HV) effects are all present in the simulated choice accuracy data. The chances of obtaining a significant effect are 0%, 0.1% and 4.7% respectively. Note that in (a) and (b) the blue and orange lines overlap with each other; in (c) the blue, orange and yellow lines overlap with each other.