Participants in the ZDHHC9 and control group were matched on age (\(\pm\)2 years). Therefore, statistical comparisons were based on paired sample tests. Due to the rarity of single-gene disorders, the size of the sample was limited. Some controversy exists regarding optimal statistical procedures in small samples. Paired t-test comparisons are both robust to some violation of the normality assumption and to small sample sizes \cite{Fritz_2012, Campbell_1995, Bridge_1999}. In all cases we also tested for any deviation from the normality assumption, using the Shapiro-Wilk test, which provides the best sensitivity \cite{Razali_2011}. Bonferroni correction was also applied to correct for multiple comparisons. For topographical analysis, false discovery rate (FDR) correction using the Benjamini-Hochberg method was applied. This maximizes power in the presence of a very large number of comparisons.

Differences in node-level graph metrics were compared between groups. Deviations from the normality assumption were very rare, being present for only 3 to 5% of regions (Node degree: 3.53, Node strength: 5.88, Clustering coefficient: 3.53, Efficiency: 3.52). For this reason, we retained the paired-sample t-tests as our primary means of comparison – the statistical sensitivity of this method is superior to the non-parametric alternatives – but we disregarded those few instances where the normality assumptions were violated.

The linear association between gene expression and group-average graph metrics was investigated with linear regression models. Separate simple regression models were fitted with the graph metric as the outcome and gene expression and an intercept term as the predictor (model: \(Y_{GraphMetric}=\beta_{GeneExpression}x_{GeneExpression}+\beta_{Intercept}\)). Bonferroni correction was used to correct for multiple comparisons arising from the number of groups (ZDHHC9, control), the number of genes, and the number of graph metrics entered into the analysis.