## 2 Results  
### Modelling Approach  
In order to determine effect sizes and significances of the independent variables (_Adjacency_, _Shear_, _LayoutNo_, _PerfNo_), these variables were regressed on the dependent variable _Inaccuracy_. The method used to calculate _Inaccuracy_ (detailed in Section 4.4) takes account of both pitch errors and timing errors in participants' performances. Due to fundamental differences in the training tasks compared with the test tasks (retention and transfer), the method for calculating their respective _Inaccuracy_ values differs (see Section 4.4). In both cases, however, _Inaccuracy_ takes only positive values, because a value of 0 implies a perfect performance. Initially, linear mixed effects models were fitted to the _Inaccuracy_ data. (_Mixed effects models_ are regressions where participants' coefficients are treated as samples from a single, and best-fitting, multivariate normal distribution. Given this distribution, the means of the coefficients are termed _fixed effects_, their (co)variances are termed _random effects_. For within subject designs, mixed effects models are widely recommended to avoid Type I errors [32]). However, the residuals were skewed and heteroscedastic. For this reason, a generalized linear mixed effects model with a gamma distribution and a log link was used--this combination of distribution and link function providing the best fit to the data. (_Generalized linear models_ are designed to cope with data that do not meet the assumptions required by linear regression models; notably, that the residuals are homoscedastic and symmetric. These violations typically occur when the data can take only a subset of real values, such as _Inaccuracy_, which can take only positive values. For positive-valued data, the gamma distribution with a log link is commonly used. The link function transforms the mean of the chosen distribution so that it is linearly related to the independent variables [33].) The log link means that the exponential of each predictor's fixed effect value represents the multiplicative factor by which _Inaccuracy_ changes for each unit increase of that predictor (all else being equal). For example, a fixed effect of 0.5 means that a unit increase in that predictor multiplies _Inaccuracy_ by \(\exp(0.5)=1.649\); put differently, _Inaccuracy_ increases by 64.9%. In the subsequent tables, this exponential value is shown in the \"Factor\" column. In each model, the intercept was included as a random effect grouped by participant to allow it to take account of participants' differing abilities. Generally, maximal random effects structures [32] (with all fixed effects and their interactions included as random effects) were attempted, but such models failed to converge, even after removing interactions. The resulting models, therefore, assume that the independent variables are invariant across participants in the population, but that particpants' overall ability does vary. The experimental design was unbalanced because nonadjacent layouts occurred only during the second layout (i.e., _Adjacency_\(=0\iff\ LayoutNo=1\)). For this reason, the predictor _Adjacency_ was not included in any interactions. Including _Adjacency_ in interactions results in rank-deficient design matrices or in conditional effects for lower-order terms that are hard to interpret; for example, if the interactions _Shear:Adjacency_ and _Shear:LayoutNo_ are included, then the conditional effect for _Shear_ refers to the effect of Shear when \(LayoutNo=0\) and \(Adjacency=0\), which never actually occurs in the experiment. All other possible interactions were included in the initial model. To simplify interpretation of lower-order terms, any nonsignificant 3-way interactions were removed from the model, and the model was refitted. For the same reason, any nonsignificant 2-way interactions not part of a 3-way interaction were then removed, and the model refitted.