## 2 Materials and Methods
### Participants  
Using the G*Power program (Version 3.0, University of Dusseldorf, Dusseldorf, Germany;), an a priori power analysis was conducted to determine the required sample size, with \(\alpha\) set at 0.05 and power (1-\(\beta\)) set at 0.80. The analysis revealed that a total sample size of 13 participants would be sufficient to detect significant differences, with an actual achieved power of 0.82 in the current study. Twenty professional male boxers voluntarily participated (mean age 22.64 \(\pm\) 3.12 years, training experience 5.11 \(\pm\) 0.88 years, body weight 70.20 \(\pm\) 10.13 kg, body height 184.28 \(\pm\) 5.38 cm), divided into two groups:  
* Group 1--Pivometric Stair Jump (PSJ): 10 subjects; age mean \(\pm\) SD 23 \(\pm\) 3.56 years (range 18-27), training experience mean \(\pm\) SD 6.11 \(\pm\) 0.72 years (range 4.7-7).
* Group 2--Pivometric Reaction Box Jump (PRJ): 10 subjects; age mean \(\pm\) SD 24.4 \(\pm\) 2.63 years (range 19-28), training experience mean \(\pm\) SD 6.13 \(\pm\) 0.60 years (range 5-6.8).  
While the sample size met the power analysis requirements, it remained modest, and the study cohort consisted exclusively of elite male boxers. Therefore, the generalizability of these findings to other populations--such as female athletes, youth boxers, or amateur practitioners--should be approached with caution. Future research should consider larger and more diverse samples to enhance the external validity of the results.  
Initially, a total of 21 national-level professional boxers were recruited for the study. The participants held competitive status, were members of the national team, and had achieved gold and bronze medals in national championships. Prior to the study, all athletes received comprehensive written and verbal explanations regarding the study procedures, and written informed consent was obtained. Furthermore, all participantsunderwent medical examinations at a fully equipped hospital, confirming the absence of medication use, substance influence, or any cardiovascular or metabolic conditions that could impede full participation. Inclusion criteria required that participants (a) had competed as professional boxers in national matches for a minimum of five years, and (b) had engaged in regular boxing training for at least five years, supplemented by at least two years of strength and power training. During the screening process, one participant was excluded due to various reasons such as injury or incompatibility. Consequently, the final sample size included in the analyses was 20. These 20 participants were randomly assigned to two groups using a computer-generated randomization method: the Plyometric Stair Jump group (\(n=10\)) and the Plyometric Reaction Box Jump group (\(n=10\)) (see Figure 1). The randomization process was employed to prevent bias and ensure comparable groups, thereby enhancing the internal validity and reliability of the study results [30].  
The demographic and training characteristics of the groups were as follows: The Stair Jump group had a mean age of 23.00 \(\pm\) 3.56 years (range 18-27) and a training experience of 6.11 \(\pm\) 0.72 years (range 4.7-7). The Reaction Box Jump group had a mean age of 24.40 \(\pm\) 2.63 years (range 19-28) and a training experience of 6.13 \(\pm\) 0.60 years (range 5-6.8). The normal distribution of age and training experience was confirmed through appropriate statistical tests in both groups. This rigorous participant selection, thorough health screening, and systematic randomization process supported the methodological rigor and reproducibility of this study.  
Figure 1: Experimental design flowchart (* the type of 8-week intervention program implemented for each study group).