## 2 Materials and Methods
### Synthetic Data Evaluation  
Evaluation of GANs is a complex issue with little general agreement on suitable evaluation metrics [49]. Considering how most practitioners in GAN research work with computer vision applications, many papers use manual inspection of images to evaluate synthesized data [61]. Image evaluation, for example, often consists in the visualization of GAN outputs to check whether they are realistic or not, or the use of specified algorithms that are very image-specific [61]. For the synthesis of numeric data, manual inspection is evidently a very subjective means of evaluating information, while calculations such as Inception-score are not applicable to this type of data [49; 61; 62]. Under this premise, the majority of metrics used in GAN literature is of little value to the present study, as they almost exclusively focus on the evaluation of images [60; 62]. Multidimensional numbers are incredibly difficult to visualize, meaning that precise human inspection of this data is impossible. To overcome this, a number of statistical metrics were adopted for GAN evaluation. Firstly homogeneity of GM data was tested. In most traditional cases, the elimination of size and preservation of allometry in GPA is known to normalize data [63]. Nevertheless, this assumption does not always hold true. The first logical step was to therefore evaluate distribution homogeneity and normality via multiple Shapiro tests. Synthetic distributions were then compared with the real data to assess the magnitude of differences and the significance of overlapping. For this, a \"Two One-Sided\" equivalency Test (TOST) was performed. TOST evaluates the magnitude of similarities between samples by using upper (\(\epsilon\)S) and lower (\(\epsilon\)I) equivalence bounds that can be established via [PERSON]'s \(d\). This assesses H\({}_{0}\) and H\({}_{a}\) using an \(\alpha\) threshold of \(p<0.05\), with H\({}_{a}\) implicating significant similarities among samples [35; 64; 65; 66; 67]. For TOST the test statistics used to assess these similarities were dependent on distribution normality. These varied between the traditional parametric method using [PERSON]'s \(t\)-statistic [68], or a trimmed non-parametric approach using [PERSON]'s robust \(t\)-statistic [69; 70]. To differentiate between the two, from this point onwards non-parametric robust TOST will be referred to as rTOST. More traditional univariate descriptive statistics were also employed. For distributions matching Gaussian properties, sample means and standard deviations were calculated. These were accompanied by calculations of sample skewness and kurtosis. For significantly non-Gaussian distributions, robust statistical metrics were used instead. In these cases, measurements of central tendency were established using the sample median (\(m\)), while deviations were calculated using the square root of the Biweight Midvariance (_BWMV_) (Equations (6)-(9)) [29; 71; 72]. \[MAD=m(\left[x_{i}-m_{x}\right]) \tag{6}\]  
\[U=\frac{x_{i}-m}{9 MAD} \tag{7}\]  
\[a_{i}=\left\{ \begin{array}{l}1,if|U_{i}|<1\\ 0,if|U_{i}|\geq 1\end{array} \right. \tag{8}\]  
\[BWMV=\frac{n\sum_{i=1}^{n}a_{i}(x_{i}-m)^{2}\Big{(}1-U_{i}^{2}\Big{)}^{4}}{ \left(\sum_{i=1}^{n}a_{i}\Big{(}1-U_{i}^{2}\Big{)}\Big{(}1-5U_{i}^{2}\Big{)} \right)^{2}} \tag{9}\]  
Robust skewness and kurtosis values were calculated using trimmed distributions. Trims were established using Interquatile Ranges (IR) [71], with confidence intervals of \(p=[0.05\text{:}0.95]\). Both the IR range and the trimmed skewness and kurtosis values were reported. Finally, wherever possible, correlations were calculated to compare the effect of hyperparameters on the quality of synthesized data. For homogeneous data, the parametric Pearson test was used [73], whereas inhomogeneous data was tested using the non-parametric Kendall \(\tau\) rank-based test [74]. Considering neural networks are stochastic in nature, these correlations were performed using data obtained from multiple training runs of each GAN to ensure a more robust calculation.