The normality assumption was tested by computing a Shapiro-Wilk test for each variable. Some distributions violated the normality assumption (see
Supplementary Table S3). Hence, each distribution was rescaled to approximate a normal distribution. First, we shifted the data distribution to positive values only. Second, we removed outliers based on modified
z-scores, which are computed from the median and median absolute deviation rather than the mean and standard deviation, respectively, according to a 3.5 criterion (
Iglewicz & Hoaglin, 1993). Third, we optimized the λ exponent of a Tukey power transformation (see
Supplementary Table S3) to maximize normality according to the Shapiro-Wilk test. Fourth, including the previously removed outliers, data were transformed using the Tukey transformation with the optimized λ parameter. Fifth, we standardized the data by computing modified
z-scores. Outliers were removed only in the visual variables. Last, we flipped the sign of visual variables when lower values indicated better performance (CrowdSize, CrowdPeri, Contrast, Poggendorff, Zöllner, Orient, RDK hor, RDK rad, ReacTtime, proTravel, proSac, antiTravel, antiSac, VBM, VisSrch4, and VisSrch16). Higher values indicate better performance in all gaming variables.
We imputed outlying and missing values using the “mice” function from the mice R package with method “norm” (Bayesian linear regression with 20 imputation samples) to compute factor analysis and regression models.