Permutation testing was used to assess the significance of differences in model fits between stimulated and non-stimulated trials. The regression model was fit separately to stimulated and non-stimulated trials to give two sets of population level parameters θs={μs,Σs} and θn={μn,Σn}, where θs are the parameters for the stimulated trials and θn are the parameters for the non-stimulated trials. The difference between the population level means for the stimulated and non-stimulated conditions were calculated as:27Δμtrue=μs−μnAn ensemble of N=5000 permuted datasets was then created by shuffling the labels on trials such that trials were randomly assigned to the ‘stimulated’ and ‘non-stimulated’ conditions. The model was fit separately to the stimulated and non-stimulated trials for each permuted dataset and the difference between population level means in the stimulated and non-stimulated conditions was calculated for each permuted dataset i as:28Δμpermi=μsi−μniThe distribution of Δμperm over the population of permuted datasets approximates the distribution under the null hypothesis that stimulation does not affect the model parameters. The P values for the observed distances Δμtrue are then given by:29P=2min(MN,1−MN)Where M is the number of permutations for which Δμpermi>Δμtrue.
