Statistical analyses and computational routines

All statistical analyses were performed with IBM SPSS for Windows, version 21.0, and MATLAB Version 7.13.0.564 (R2011b) (MathWorks), both with built-in functions as well as with functions commonly available on the MathWorks online repository or custom written code.

For MVPA results, mean decoding accuracies were averaged across the participants. Statistical analyses were performed with two-tailed t-tests against a chance accuracy of 50%. For multiple comparisons, we used the Holm–Bonferroni procedure (see below), and we report corrected P values.

The effects of DecNef on behavioural data were statistically assessed using repeated measures ANOVA tests as well as two-tailed, or single-tailed were warranted, t-tests were utilized for comparisons.

For multiple comparisons, we used the Holm–Bonferroni correction, where the P values of interest are ranked from the smallest to the largest, and the significance level α is sequentially adjusted based on the formula for the i-th smallest P values. In the text, for enhanced clarity, we present the results as corrected P values.

We used Matlab optimization routines to solve our systems of nonlinear equations with a nonlinear programming solver, under least squares minimization. The Matlab solver was fmincon, utilizing the following optimization options. A sequential quadratic problem (SQP) method was used, specifically, the ‘SQP' algorithm. This algorithm is a medium scale method, which internally creates full matrices and uses dense linear algebra, thus allowing additional constraint types and better performance for the nonlinear problems outlined in the previous section. As compared with the default fmincon ‘interior point' algorithm, the ‘SQP' algorithm also has the advantage of taking every iterative step in the region constrained by bounds, which are not strict (a step can exist exactly on a boundary). Furthermore, the ‘SQP' algorithm can attempt to take steps that fail, in which case it will take a smaller step in the next iteration, allowing greater flexibility. We set bounded constraints to allow only certain values in the parameter space to be taken by the estimates. As such, boundaries were set as: Δ ∈ [0 Inf], ɛ ∈ [−1 0], γ ∈ [0 1], and α ∈ [0 1]. The function tolerance was set at 10⁻²⁰, the maximum number of iterations at 10⁶ and the maximum number of function evaluations at 10⁵.