## 2 Materials and Methods
### Meta-Analyses  
Meta-analyses of this review were conducted via the Review Manager computer program (RevMan 5.4.1) [55]. A non-training control of the placebo group was considered the comparator for this systematic review. RevMan automatically calculates [PERSON] (adjusted) \(g\) effects size (standardised mean difference (_SMD_)) using the mean difference (MD) from baseline and the standard deviation (\(SD\)) of these mean differences for exercise and control groups [56]. The difference between the [PERSON] \(g\) and [PERSON]'s \(d\) is the adjustments of [PERSON] \(g\) effect size calculations for a small sample having fewer than 20 participants [57]. Effect size interpretation was considered the commonly used interpretation for both [PERSON]'s \(g\)[58] and [PERSON]'s \(d\)[59] that small (0.2), medium (0.5) or large (0.8) [60].  
The standard deviations of the mean changes from baseline is defined as a common missing outcome data [61] and difficulties for running a meta-analysis without missing \(SD\)s explained by previous systematic reviews [62; 63]. For calculating missing \(SD\)s, a formula was defined as [64; 65]:  
\[SDchange=\sqrt{SD^{2}baseline+SD^{2}final-(2\times r\times SDbaseline\times SDfinal)}\]  
\(SDchange\) means the \(SD\) of the mean changes from baseline, \(SDbaseline\) represents the \(SD\) of the pre-test, \(SDfinal\) corresponds to the \(SD\) of the post-test, and the \(r\) symbolise the correlations between the baseline and final measurements; this correlation value is not generally presented in the studies. For instance, among the studies eligible for this systematic review, none demonstrate this \(r\)-value. Based on this, this systematic review employed the following process for obtaining the missing outcome data: Firstly, given additional data, e.g., confidence intervals, \(p\)-values, t-values, F-values, and standard errors were controlled and missing \(SDchanges\) from baseline were estimated using RevMan [55]. However, the first step could not be applied due to the lack of information in the included studies. As a second step, corresponding authors of the included studies were contacted to request their data -sets or the mean and \(SDchanges\) from baseline values, as previously recommended [61; 62; 63]. Thirdly, if the corresponding authors did not share their data with this systematic review, and the \(SDbaseline\) and \(SDfinal\) values were known, the \(SDchange\) value was calculated by assigning a value of 0.7 to the \(r\) in the formula [64; 65], to provide a conservative estimate [66] as undertaken by previous systematic reviews [67; 68; 69; 70]. Finally, if there were still missing outcome data, the study was not included in the meta-analysis and is mentioned separately in the -text.  
The heterogeneity of a meta-analysis was measured by the chi-squared (\(\chi^{2}\) or Chi\({}^{2}\)) statistic and the level of heterogeneity was estimated by the \(\hat{\text{I}}^{2}\) statistic, which indicates the percentage ratio of the variability in effect estimates caused by heterogeneity rather than chance [71]. \(\hat{\text{I}}^{2}\) results were interpreted as low (25%), moderate (50%) and high (75%) [72]. When statistical heterogeneity was absent (\(p>0.05\) in the Chi\({}^{2}\) statistics), a meta-analysis was performed for a continuous data, inverse variance, fixed-effect model [73] and a 95% confidence interval (95% CI). However, when statistical heterogeneity was observed, a meta-analysis was performed using a more conservative random effect model for continuous data, inverse variance and a 95% CI [73].