# Biomechanics of Punching--The Impact of Effective Mass and Force Transfer on Strike Performance
## 2 Materials and Methods
### Statistical Analysis  
Statistical analyses were conducted using Statistica 13 (TIBCO software). Descriptive statistics were computed for all variables, and the Shapiro-Wilk test was used to assess the normality of distributions. Since the result indicated a non-normal distribution, the Kruskal-Wallis test was applied to compare groups. The Kruskal-Wallis test was chosen as it is well-suited for small samples and does not assume a normal distribution, making it appropriate for analyzing biomechanical data with potentially non-homogeneous variance. The consistency of the findings across multiple performance metrics (effective mass, impulse, acceleration) further reinforces the reliability of the results. While alternative statistical approaches for small samples exist, the current methodology was selected to balance robustness and interpretability. Additionally, beta (\(\beta\)) coefficients were calculatedusing a multivariate regression model, with R\({}^{2}\) and adjusted R\({}^{2}\) determined to explore potential relationships between the recorded variables. A significance threshold of \(p<0.05\) was established. Effect sizes were calculated to assess the magnitude of observed differences. For the Kruskal-Wallis test, effect size was determined using eta squared (\(\eta^{2}\)). The interpretation of effect size follows common guidelines: \(\eta^{2}\) = 0.01 indicates a small effect, \(\eta^{2}\) = 0.06 represents a medium effect, and \(\eta^{2}\) = 0.14 or higher signifies a large effect.  
In addition to the Kruskal-Wallis test, the statistical analysis also evaluated differences between punch types using the Mann-Whitney U test and interpreted practical significance via Glass rank-biserial correlation (G scores). For the Lead Jab vs. Rear Cross comparison (jab: n = 118, cross: n = 127), the sample size was sufficient, clearly detecting significant and practically meaningful differences, particularly large for Total_GRF (G = 0.712), moderate for afist (G = 0.369) and AUC/afist (G = \(-\)0.435), and small for AUC (G = \(-\)0.233). The negligible differences found in Me (G = 0.017) and %Me (G = 0.031) were not practically meaningful, and given the large sample size, additional participants would unlikely alter these results.  
In contrast, for the Rear Hook vs. Lead Hook comparison (rear hook: n = 127, lead hook: n = 132), the sample size, despite being similarly robust, proved sufficient to identify only small to negligible differences, such as in Total_GRF (G = \(-\)0.146) and AUC (G = \(-\)0.122). The negligible differences observed in afist (G = \(-\)0.075), Me (G = 0.008), %Me (G = 0.016), and AUC/afist (G = 0.023) suggest these metrics are inherently similar between these punch types. Given the minimal effect sizes observed, achieving statistical significance would require impractically large sample sizes. Thus, the existing samples were more than adequate to conclude minimal practical differences exist between rear and lead hooks across these measures.  
Additionally, we performed the Mann-Whitney U test to verify the effect solely between pairs of jab-rear cross, and lead-rear hook.  
Figure 3: Sample visualization of the algorithm output for force impulse computation, represented as the area under the force distribution curve over time, referred to as impulse.