Statistical analysis
Multilevel linear modeling (MLM) was applied to examine effects of NF training on Fmθ, and to examine training-related changes in Fmθ and behavioral performance measures during the Go-NoGo shooting task (% errors of commission, accuracy, RT). Models were constructed in four steps and participants were used as the level 2 grouping variable. Several models were run for each dependent measure: intercepts only models, inclusion of level 1 predictors, inclusion of the level 2 predictors of session number and interactions with session number, and the full model including the level 2 predictors group and group interactions, see equations 1 and 2. Data were analyzed using R (version 4.1.0) in conjunction with several packages: lme4, jtools, ggplot2, and interactions.EQ1. Equations for full NF modelsLevel 1: ŷLevel 2: π        π        πEQ2. Equations for full SH task modelsLevel 1: ŷLevel 2: π        πBefore conducting the modeling, several assumptions related to performing an MLM analysis were examined and outliers were removed. MLM analyses are better able to handle assumptions of independence compared to traditional general linear models but are still subject to many of the same assumptions including normality, linearity, multicollinearity, homogeneity of variances, issues related to residuals, and outliers [Fixed effects are reported as unstandardized beta weights with standard errors. Additionally, intraclass correlation coefficients (ICC) were obtained from each model, large ICCs and design effects of greater than 2 provide evidence for multilevel structure to the data. The estimation method used was restricted maximum likelihood (REML). REML tends to lead to more accurate results than full maximum likelihood (FML), when the sample size of the level two identifier is small [