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阈值测度与优选预测：青少年羽毛球运动员体能敏感指标研究
Threshold measurement and preferential prediction: a study of physical fitness sensitivity indicators in junior badminton players

李彦丽 1 1 ^(1){ }^{1}，夏娇阳 2 ∗ 2 ∗ ^(2**){ }^{2 *}，尤洋 2 2 ^(2){ }^{2}
Li Yanli 1 1 ^(1){ }^{1} , Xia Jiao Yang 2 ∗ 2 ∗ ^(2**){ }^{2 *} , You Yang 2 2 ^(2){ }^{2} .（1．中国石油大学（华东）研究生院，山东 青岛 266580；
(1. Graduate School, China University of Petroleum (East China), Qingdao 266580, Shandong, China;2．中国石油大学（华东）体育教学部，山东 青岛 266580）
2. Department of Physical Education, China University of Petroleum (East China), Qingdao, Shandong 266580)

抽象  abstraction

摘 要：体能作为羽毛球项目获得主动及赢取胜利的重要保障，借助 ROC 曲线（Receiver Operating Characteristic curve）法建立青少年羽毛球运动员体能敏感指标阈值，设定正确的体能目标值，对于评估训练效果和运动员进步的基准具有重要意义。通过分析2022—2024年全国U系列羽毛球比赛 U12—U14 运动员的体能测试数据和羽毛球国少队优选结果，结果表明：1）筛选后的体能敏感指标阈值能够区分国少队优选结果（ P < 0.05 P < 0.05 P < 0.05P<0.05），男运动员符合体能敏感指标阈值要求的优选成功率是未达到体能敏感指标阈值要求的 2．4－4．8 倍（ OR = 2.456 ∼ 4.885 OR = 2.456 ∼ 4.885 OR=2.456∼4.885\mathrm{OR}=2.456 \sim 4.885），女运动员 2.6 − 8.6 2.6 − 8.6 2.6-8.62.6-8.6倍（ OR = 2.674 ∼ 8.690 OR = 2.674 ∼ 8.690 OR=2.674∼8.690\mathrm{OR}=2.674 \sim 8.690）；2）体能敏感指标阈值可以区分不同指标对不同年龄运动员的影响程度，且体能敏感指标阈值随年龄增长呈现逐步提升的趋势。不仅揭示了青少年羽毛球运动员体能素质发展的敏感指标，也为制定个性化的训练计划和优化训练效率提供了有力的数据支持，对羽毛球项目的体能训练具有重要的实践指导意义。
Abstract: Physical fitness is an important guarantee for badminton program to get the initiative and win the victory, with the help of ROC curve (Receiver Operating Characteristic curve) method to establish the threshold of physical fitness sensitive indexes of young badminton players and set the correct target value of physical fitness, which is of great significance for assessing the training effect and the benchmark of athletes' progress. By analyzing the fitness test data of U12-U14 athletes in the national U-series badminton tournaments from 2022-2024 and the results of the badminton national junior team preference, the results show that: 1) the screened fitness-sensitive indicator thresholds are able to differentiate between the results of the national junior team preference ( P < 0.05 P < 0.05 P < 0.05P<0.05 ), and the male athletes who meet the requirements of fitness-sensitive The results showed that: 1) the screening physical sensitivity index thresholds could distinguish the results of the national junior team ( P < 0.05 P < 0.05 P < 0.05P<0.05 ), and the success rate of male athletes meeting the physical sensitivity index thresholds was 2.4-4.8 times higher than that of male athletes failing to meet the physical sensitivity index thresholds ( OR = 2.456 ∼ 4.885 OR = 2.456 ∼ 4.885 OR=2.456∼4.885\mathrm{OR}=2.456 \sim 4.885 ), and the success rate of female athletes was 2.6 − 8.6 2.6 − 8.6 2.6-8.62.6-8.6 times higher than that of male athletes ( OR = 2.674 ∼ 8.690 OR = 2.674 ∼ 8.690 OR=2.674∼8.690\mathrm{OR}=2.674 \sim 8.690 ). The thresholds of physical sensitivity indicators can distinguish the degree of influence of different indicators on different age athletes, and the thresholds of physical sensitivity indicators show a trend of gradual increase with age. It not only reveals the sensitive indicators of physical fitness development of young badminton players, but also provides powerful data support for the development of personalized training plan and optimization of training efficiency, which is of great practical significance for the physical fitness training of badminton program.
Abstract: Physical fitness is an important guarantee for badminton program to get the initiative and win, with the help of ROC curve (Receiver Operating Characteristic curve) method to establish the threshold of physical fitness sensitive indexes for young badminton players, and set the correct target value of physical fitness, which is of great significance for evaluating the training effect and the benchmarks of athletes' progress. By analyzing the fitness test data of U12-U14 athletes in the national U-series badminton tournaments from 2022-2024 and the results of the badminton national junior team preference, the results show that: 1) the screened fitness-sensitive indicator thresholds are able to differentiate between the results of the national junior team preference ( P < 0.05 P < 0.05 P < 0.05P<0.05 ), and the male athletes who meet the requirements of fitness-sensitive The results showed that: 1) the screening physical sensitivity index thresholds could distinguish the results of the national junior team ( P < 0.05 P < 0.05 P < 0.05P<0.05 ), and the success rate of male athletes meeting the physical sensitivity index thresholds was 2.4-4.8 times higher than that of male athletes failing to meet the physical sensitivity index thresholds ( OR = 2.456 ∼ 4.885 OR = 2.456 ∼ 4.885 OR=2.456∼4.885\mathrm{OR}=2.456 \sim 4.885 ), and the success rate of female athletes was 2.6 − 8.6 2.6 − 8.6 2.6-8.62.6-8.6 times higher than that of male athletes ( OR = 2.674 ∼ 8.690 OR = 2.674 ∼ 8.690 OR=2.674∼8.690\mathrm{OR}=2.674 \sim 8.690 ). and the thresholds of physical sensitivity indicators showed a trend of gradual increase with age. It not only reveals the sensitive indicators of physical fitness development of young badminton players, but also provides a powerful data support for the development of personalized training plan and optimization of training efficiency, which is of great practical significance for the physical fitness training of badminton program.

关键词：阈值;青少年羽毛球运动员;体能敏感指标;ROC 曲线 中图分类号：G847
Keywords: threshold; junior badminton players; fitness sensitivity index; ROC curve CCTI: G847
阈值测量与最优预测：青少年羽毛球运动员体能敏感指标研究
Threshold Measurement and Optimal Prediction: a Study on Physical Fitness Sensitive Indicators of Adolescent Badminton Athletes 李艳丽
Threshold measurement and optimal prediction: a study of physical fitness sensitivity indicators in junior badminton players Yanli Li 1 1 ^(1){ }^{1}，夏娇阳 2 ∗ 2 ∗ ^(2**){ }^{2 *}，尤阳 2 2 ^(2){ }^{2}
Threshold Measurement and Optimal Prediction: A Study on Sensitive Indicators of Physical Fitness in Young Badminton Players Yanli Li 1 1 ^(1){ }^{1} , Jiao Yang Xia 2 ∗ 2 ∗ ^(2**){ }^{2 *} , Yang You 2 2 ^(2){ }^{2} .
（1.毕业于中国石油大学（华东）学院，山东 青岛 266580;
(1. Graduate of School, China university of Petroleum (East China), Qingdao 266580, Shandong, China;2.中国石油大学体育系，山东 青岛 266580）
(1. Graduated from the College of China University of Petroleum (East China), Qingdao, Shandong 266580; 2. Department of Physical Education, China University of Petroleum, Qingdao, Shandong 266580)

抽象  abstraction

体能是获得主动权和确保羽毛球胜利的重要基础。使用 ROC 曲线（Receiver Operating Characteristics curve）方法建立青少年羽毛球运动员敏感体能指标的阈值，并设定准确的体能目标值，对于评估训练效果和对标运动员具有重要意义 progress.By 分析 U12-U14 运动员的体能测试数据2022-2024 年全国 U 系列羽毛球比赛和国家青少年羽毛球队选拔结果显示，结果表明：1）筛选敏感体能指标的阈值可以区分国家青少年羽毛球队的选拔结果（ P < 0.05 P < 0.05 P < 0.05P<0.05）.男运动员达到敏感阈值要求的成功率
Physical fitness is an important foundation for gaining the initiative and ensuring victory in badminton. Using the ROC curve (Receiver Operating Characteristics curve) method to establish the thresholds of sensitive physical fitness indicators for junior badminton players and set accurate physical fitness target values is important for evaluating the training effect and benchmarking the athletes progress.By analyzing the physical fitness of U12-U14 athletes Test data 2022-2024 national U series badminton tournaments and national junior badminton team selection results show that the results show that: 1) Screening the threshold of sensitive physical fitness indicators can distinguish the results of the selection of the national junior badminton team ( P < 0.05 P < 0.05 P < 0.05P<0.05 ) . The success rate of male athletes in meeting the requirements of sensitive thresholds

投稿日期：2024－11－11  Submission Date: 2024-11-11
基金项目：国家社会科学基金＂十四五＂规划2022年度教育学一般课题＂幼小儿童身体能力发育模型构建与共育路径研究＂（项目编号：BLA220239）。
Supported by the National Social Science Foundation of China under the "Fourteenth Five-Year Plan" of the year 2022, "Research on the Construction of Physical Ability Development Model and Co-education Path for Young Children" (Project No. BLA220239).
作者简介：李彦丽（2001—），女，山东淄博人，在读硕士研究生，研究方向专项教学理论与方法。
Author's introduction: Li Yanli (2001-), female, Zibo, Shandong, a master's degree student, research direction special teaching theory and method. 作者单位：1.中国石油大学（华东）研究生院，山东 青岛 266580;2.中国石油大学（华东）体育教学部，山东 青岛 266580
Author Introduction: Li Yanli (2001-), female, Zibo, Shandong, a master's degree student, research direction special teaching theory and method. Author Affiliations: 1. Graduate School of China University of Petroleum (East China), Qingdao 266580, Shandong; 2. Physical Education Department of China University of Petroleum (East China), Qingdao 266580, Shandong.
体能指标比做的人高2.4-4.8倍   Physical fitness indicators are 2.4-4.8 times higher than those who do not ( OR = 2.4564 .885 ) not ( OR = 2.4564 .885 ) not(OR=2.4564.885)\operatorname{not}(\mathrm{OR}=2.4564 .885)，而对于女运动员来说，它高出 2.6-8.6 倍 （ OR = 2.6748 .690 OR = 2.6748 .690 OR=2.6748.690\mathrm{OR}=2.6748 .690);2）敏感体能指标的阈值可以区分不同指标对不同年龄运动员的影响程度，并且这些阈值随年龄的增长而逐渐增加。研究结果不仅揭示了青少年羽毛球运动员体能发展的敏感指标，而且为制定个性化训练计划、优化训练效率提供了有力的数据支持，对羽毛球体能训练具有重要的现实意义。
The physical fitness index is 2.4-4.8 times higher than those who do not ( OR = 2.4564 .885 ) not ( OR = 2.4564 .885 ) not(OR=2.4564.885)\operatorname{not}(\mathrm{OR}=2.4564 .885) , and for female athletes, it is 2.6-8.6 times higher ( OR = 2.6748 .690 OR = 2.6748 .690 OR=2.6748.690\mathrm{OR}=2.6748 .690 ); 2) The thresholds of sensitive physical fitness indexes can differentiate the degree of influence of different indexes on athletes of different ages and these thresholds are gradually increasing with the growth of age. The results of the study not only revealed the sensitive indicators of physical fitness development of young badminton players, but also provided powerful data support for the development of personalized training plan and optimization of training efficiency, which is of great practical significance for badminton physical training.
关键词：阈值;青少年羽毛球运动员;体能敏感指标;ROC 曲线
Keywords: threshold; junior badminton players; fitness sensitivity index; ROC curve
2020 年 2 月国家体育总局印发《体育总局办公厅关于进一步强化基础体能训练恶补体能短板的通知》（以下称《通知》）和《国家队体能达标测试评分标准》（以下称《标准》） ) [ 1 ] ) [ 1 ] )^([1]))^{[1]}。有研究表明，《标准》对所有参与测试的运动员进行全面评估，但未能充分考量不同运动项目间的差异性以及运动员性别的特异性，部分测试项目不符合运动项目的自身特点，测试项目的评价标准也存在过高或过低的现象 [ 2 ] [ 2 ] ^([2]){ }^{[2]}。
In February 2020, the General Administration of Sport issued the Notice of the General Office of the General Administration of Sport on Further Strengthening the Basic Physical Training and Mending the Short Board of Physical Fitness (hereinafter referred to as the Notice) and the Scoring Standards for Physical Fitness Achievement Tests for National Teams (hereinafter referred to as the Standards) ) [ 1 ] ) [ 1 ] )^([1]))^{[1]} . Some studies have shown that the Standards provide a comprehensive assessment of all athletes participating in the test, but fail to fully take into account the differences between different sports and the gender specificity of athletes, and that some of the test items are not in line with the characteristics of the sports themselves, and that the evaluation standards of the test items are either too high or too low [ 2 ] [ 2 ] ^([2]){ }^{[2]} .
羽毛球项目属于技能主导类隔网对抗项群，其主要运动形式是运用各种技术动作和战术变化突破对手的防守而得分，体能是获得主动及赢取胜利的重要保障 [ 3 ] [ 3 ] ^([3]){ }^{[3]}。体能与技能是相辅相成的，它们相互统一在＂能量＂二字上：练体能是储备能量，练技能是节省能量，运动水平的高低取决于上述两方面综合能量的高低 [ 4 ] [ 4 ] ^([4]){ }^{[4]}。不同体能素质可能会产生干扰效应，力量和有氧耐力同时训练对肌肉力量的发展有干扰效应 [ 5 ] [ 5 ] ^([5]){ }^{[5]}，运动员难以在所有体能素质上都达到很高的水平，因此确立一个适宜的体能发展目标，协助运动员在多维度体能素质间达成均衡进步，从而优化训练效率，促进整体运动表现的提升。羽毛球运动的快速发展，使羽毛球竞技比赛对运动员的体能提出了更高的要求 [ 5 − 9 ] [ 5 − 9 ] ^([5-9]){ }^{[5-9]}。国家少年羽毛球队（以下称国少队）是中国羽毛球协会与地方政府或相关机构合作共建的，旨在培养国家青少年羽毛球后备人才的重要团体。国少队作为球员走向国家队的第一层阶梯，是开启其国家队生涯系统化培养与高水平竞技平台接触的初步尝试，其选拔标准是全国 U 系列羽毛球比赛 U12—U14 单打比赛前 16 名的运动员以及双打前 4名的运动员。从体能视角下，深入探索入选国少队运动员与未入选运动员之间体能部分的差异，为后续的职业生涯发展奠定坚实基础。
Badminton is a skill-driven category of net confrontation item group, its main form of movement is to use a variety of technical movements and tactical changes to break through the opponent's defense and score points, physical fitness is an important guarantee to get the initiative and win the victory [ 3 ] [ 3 ] ^([3]){ }^{[3]} . Physical fitness and skills are complementary to each other, and they are unified in the word "energy": practicing physical fitness is to reserve energy, practicing skills is to save energy, and the level of the sport depends on the level of the combined energy of the above two aspects [ 4 ] [ 4 ] ^([4]){ }^{[4]} . Different physical fitness qualities may produce interference effects, strength and aerobic endurance training at the same time on the development of muscular strength has interference effects [ 5 ] [ 5 ] ^([5]){ }^{[5]} , athletes are difficult to achieve a high level of all physical fitness qualities, so to establish a suitable physical fitness development goals, to help athletes in the multi-dimensional physical fitness qualities to achieve a balanced progress, so as to optimize the efficiency of the training, and to promote the overall performance of the sport. The rapid development of badminton has led to higher demands on athletes' fitness in competitive badminton [ 5 − 9 ] [ 5 − 9 ] ^([5-9]){ }^{[5-9]} . The National Junior Badminton Team (hereinafter referred to as the National Junior Team) is an important group aimed at cultivating national junior badminton reserves, which is built by the China Badminton Association in cooperation with local governments or related organizations. The National Junior Team, as the first ladder for players to go to the national team, is an initial attempt to start the systematic cultivation of their national team careers and contact with high-level competitive platforms, and its selection criteria are the athletes who are in the top 16 of the singles competitions of the national U series of badminton tournaments U12-U14, as well as those who are in the top 4 of the doubles competitions. From the perspective of physical fitness, the differences in physical fitness between the selected athletes and the non-selected athletes were explored in depth, laying a solid foundation for the subsequent career development.
青少年时期是各项素质发展的关键阶段 [ 10 ] [ 11 ] [ 10 ] [ 11 ] ^([10][11]){ }^{[10][11]}，同时青少年的身体素质发展存在特定的敏感期，且不同身体素质的敏感期存在差异。身体素质发展＂敏感期＂是能够取得最佳训练效果的时期 [ 12 ] [ 12 ] ^([12]){ }^{[12]}。Balyi（2005）提出的 LTAD 模式（Long-term Athlete Develo-opment Model）中指出正式训练阶段（男生 12-16 岁，女生 11-15 岁）是对刺激和训练产生生理反应的阶段，因此要把握敏感时期从而提升训练适应 [ 13 ] [ 15 ] [ 13 ] [ 15 ] ^([13][15]){ }^{[13][15]}。Lloyd 强调该阶段为发育高峰期，应把握好发展运动素质的时机窗口，一个 12 到 13 岁的孩子应该把他们的训练主要集中在力量，爆发力，速度，敏捷性和运动专项技能的发展上 [ 16 ] [ 16 ] ^([16]){ }^{[16]}。
Adolescence is a critical stage for the development of various qualities [ 10 ] [ 11 ] [ 10 ] [ 11 ] ^([10][11]){ }^{[10][11]} , and there are specific sensitive periods for the development of physical fitness in adolescents, which vary from one fitness level to another. The "sensitive period" of physical development is the period in which the best training results can be achieved [ 12 ] [ 12 ] ^([12]){ }^{[12]} . The LTAD model (Long-term Athlete Development Model) proposed by Balyi (2005) points out that the formal training phase (12-16 years old for boys and 11-15 years old for girls) is the most important period of training for the adolescents. Lloyd emphasizes that this is the peak developmental period and that there is a window of opportunity to develop athletic qualities. A 12- to 13-year-old should focus his or her training on the development of strength, explosiveness, speed, agility, and sport-specific skills [ 13 ] [ 15 ] [ 13 ] [ 15 ] ^([13][15]){ }^{[13][15]}
目前针对青少年羽毛球运动员体能敏感指标的研究尚显不足，特别是在运用科学方法进行指标篮选和评估方面。因此，本研究旨在通过 ROC 曲线法，探索青少年羽毛球运动员的体能标准，在多维度体能素质间筛选出使运动员均衡进步的敏感指标，以此为基础更准确地评估运动员的体能水平，预测其未来发展趋势。为运动员制定个性化的训练计划提供有力的支持，对我国羽毛球项目及其他球类项目的体能训练提供科学的参考依据。
Currently, there are insufficient studies on the sensitive indicators of physical fitness of young badminton players, especially in the use of scientific methods for indicator basket selection and assessment. Therefore, this study aims to explore the physical fitness standard of young badminton players through the ROC curve method, to screen out the sensitive indicators of balanced progress among multi-dimensional physical fitness qualities, and to more accurately assess the physical fitness level of athletes and predict the future development trend on the basis of the ROC curve method. This will provide a strong support for athletes to make personalized training plans, and provide a scientific reference basis for the physical training of badminton and other ball sports in China.

1 研究对象与方法  1 Objects and methods of study

1.1 研究对象  1.1 Subject of the study

以构建青少年羽毛球运动员体能敏感指标阈值为研究对象，依据青少年羽毛球运动员体能敏感指标阈值预测国少队优选资格的诊断评估。选取2022—2024年参加全国U系列羽毛球比
To construct the thresholds of physical fitness sensitivity indexes of junior badminton players as the research object, and to predict the diagnostic assessment of the preferential qualification of the national junior team based on the thresholds of physical fitness sensitivity indexes of junior badminton players. Selected to participate in the national U series badminton competition in 2022-2024
赛 U12－U14 综合素质测试的所有运动员为调查对象，共 1241 名运动员纳入本研究，其中男运动员 657 名，女运动员 584 名。
A total of 1241 athletes were included in this study, including 657 male athletes and 584 female athletes.

1．2数据来源  1.2 Data sources

运动员在参加全国 U 系列羽毛球比赛中均需进行赛前综合素质测试，测试合格者方可继续进行参加比赛。本研究收集的 2022－2024 年所有单打运动员的体能测试数据，国少单打运动员优选结果均来自 2022－2024 年全国 U 系列羽毛球比赛 U12－U14 的赛前综合素质测试和单打比赛成绩（图 1）。测试项目包括 20 次低重心四点跑，三分钟双摇跳绳，垂直纵跳， 30米 × 5 × 5 xx5\times 5往返跑和立定跳远 5 项体能素质指标。测试在比赛前由中国羽毛球协会指派测试专家，按照竞赛规程的测试项目标准，办法进行，测试流程具有权威性，专业性，规范性的特点，测试数据官方，可靠。这些测试项目能够全面反映青少年羽毛球运动员的灵敏性，协调性，力量，速度和耐力等关键体能要素。
Athletes are required to take pre-competition general fitness test in national U-series badminton tournaments, and those who pass the test can continue to participate in the tournaments. The physical fitness test data of all singles players in 2022-2024 collected in this study, and the preferred results of national junior singles players were all from the pre-competition comprehensive quality test and singles competition results of U12-U14 in the national U-series badminton tournaments in 2022-2024 (Fig. 1). The test items include 20 times of low center of gravity four-point run, three-minute double-swing rope skipping, vertical jump, 30-meter × 5 × 5 xx5\times 5 back-and-forth run and standing long jump, which are five physical fitness indicators. Test before the game by the China Badminton Association assigned test experts, according to the competition regulations of the test program standards, methods, test process has authority, professionalism, standardized characteristics, test data official, reliable. These test items can fully reflect the sensitivity, coordination, strength, speed and endurance and other key physical elements of young badminton players.
图1 数据收集整理流程  Figure 1 Data collection and organization process
Figure 1 Data Collection and Processing Flow
在此基础上，运用箱型图理论对测试数据进行异常值检验，进一步检查异常值产生原因，替换因数据录入错误产生的异常值，最终样本量不变（表 1）。确认所有数据均符合正态分布，为后续科学，有效的统计分析奠定了坚实基础。
On this basis, the box plot theory was applied to the test data for the outlier test, to further check the causes of outliers, to replace the outliers caused by data entry errors, and to keep the final sample size unchanged (Table 1). It was confirmed that all the data conformed to normal distribution, laying a solid foundation for subsequent scientific and effective statistical analysis.
表1样本量汇总表  Table 1 Summary of sample size
Table 1 Summary of Sample Size
比赛时间  competition time 级别  (military) rank 最终样本量  Final sample size
男运动员（名）  Male athletes (names) 女运动员（名）  Female athletes (names) 总运动员数（名）  Total number of athletes (names)
2022 年  2022 U12 67 57
U13 56 48 345
U14 63 54
2023 年  2023 U12 61 57
U13 83 75 404
U14 69 59
2024 年  2024 U12 86 87 492
比赛时间 级别 最终样本量 男运动员（名） 女运动员（名） 总运动员数（名） 2022 年 U12 67 57 U13 56 48 345 U14 63 54 2023 年 U12 61 57 U13 83 75 404 U14 69 59 2024 年 U12 86 87 492| 比赛时间 | 级别 | 最终样本量 | | | | :---: | :---: | :---: | :---: | :---: | | | | 男运动员（名） | 女运动员（名） | 总运动员数（名） | | 2022 年 | U12 | 67 | 57 | | | | U13 | 56 | 48 | 345 | | | U14 | 63 | 54 | | | 2023 年 | U12 | 61 | 57 | | | | U13 | 83 | 75 | 404 | | | U14 | 69 | 59 | | | 2024 年 | U12 | 86 | 87 | 492 |

1． 3 统计分析  1.3 Statistical analysis

ROC 曲线（Receiver Operating Characteristic curve，即受试者工作特征，以下简称为 ROC曲线）分析是评价诊断性实验优劣及确定阈值的一种方法 [ 16 − 18 ] [ 16 − 18 ] ^([16-18]){ }^{[16-18]} 。其原理是根据每个阈值的真阳性率和假阳性率来判断最佳阈值点，是医学诊断中设立病症阳性阈值的重要方法 [ 19 ] [ 19 ] ^([19]){ }^{[19]} 。在体育领域中，建立健康体力活动参考标准 [ 16 ] [ 20 ] [ 16 ] [ 20 ] ^([16][20]){ }^{[16][20]} 和运动员体能水平的参考标准 [ 19 ] [ 19 ] ^([19]){ }^{[19]} 的分析中，已经取得了较好的应用成效。
ROC curve (Receiver Operating Characteristic curve, hereinafter referred to as ROC curve) analysis is a method of evaluating the advantages and disadvantages of diagnostic experiments and determining the threshold [ 16 − 18 ] [ 16 − 18 ] ^([16-18]){ }^{[16-18]} . The principle is to determine the optimal threshold point based on the true positive and false positive rates for each threshold, and is an important method for establishing a positive threshold for a condition in medical diagnosis [ 19 ] [ 19 ] ^([19]){ }^{[19]} . In the field of sports, the establishment of the reference standard of healthy physical activity [ 16 ] [ 20 ] [ 16 ] [ 20 ] ^([16][20]){ }^{[16][20]} and the reference standard of athletes' physical fitness level [ 19 ] [ 19 ] ^([19]){ }^{[19]} have been analyzed in the analysis, and have achieved better application results.
采用 SPSS25.0 进行数据分析，Graphpad Prism 8 进行统计作图。使用独立样本 T 检验，单因素方差分析，检验体能测试指标在是否入选国少队以及年龄组间是否存在显著差异；通过 ROC 曲线法建立体能敏感指标与阈值，诊断指标（自变量）为 20 次低重心四点跑，三分钟双摇跳绳，垂直纵跳， 30 米 × 5 × 5 xx5\times 5往返跑，立定跳远；结局指标（因变量）为是否入选国少队的二分类变量。之后进行二元逻辑回归分析，诊断评估体能敏感指标阈值对国少队优选资格预测。将运动员分为是否满足 ROC 中阈值的二分类变量作为自变量，满足赋值为 1 ，不满足赋值为 0 ，入选国少队结果作因变量。最后通过纵向对比同年龄段不同敏感指标成绩分析优选国少队的体能成绩发展趋势（图2）。 
图2 数据分析流程  Fig. 2 Data analysis process

2 结果与分析  2 Results and analysis

2.1 运动员体能素质表现评估  2.1 Assessment of Athletes' Physical Fitness Performance

本研究中将调查对象按照近三年国少队优选条件，分为优选组与淘汰组。优选组指在每年 U12－U14 比赛中达到全国比赛单打前 16 名的运动员，淘汰组指未在比赛中进入前 16 名的运动员。
In this study, the respondents were categorized into a preferred group and an eliminated group according to the preferred conditions of the National Junior Team in the last three years. The preferred group refers to the athletes who reached the top 16 in the singles of the national tournament in the U12-U14 tournament every year, and the eliminated group refers to the athletes who did not reach the top 16 in the tournament.

2．1．1 优选组与淘汰组差异分析  2.1.1 Difference analysis between preferred and eliminated groups

通过对体能素质成绩进行分析，优选组成绩均大于淘汰组成绩。在不同年龄组中 5 项指标的优选组与淘汰组均存在显著性差异（表 2，表 3）。在男运动员体能素质成绩中，除 U12 组垂直纵跳，U13 组 30 米 × 5 × 5 xx5\times 5 往返跑，U14 组 20 次低重心四点跑和垂直纵跳指标外，其他不同年龄组的各项指标在优选组与淘汰组均存在显著差异。在女运动员体能素质成绩中，在垂直纵跳指标成绩上，U12，U14 组的优选运动员与淘汰组运动员之间不存在显著差异，其余四项指标在优选组与淘汰组之间均存在显著差异。全国 U 系列羽毛球比赛 U12－U14 综合素质体能测试能够区分优选组与淘汰组之间的差异。
By analyzing the physical fitness scores, the scores of the preferred group were greater than the scores of the eliminated group. There was a significant difference between the preferred group and the eliminated group in all 5 indicators in different age groups (Table 2, Table 3). In the physical fitness performance of male athletes, except for vertical jump in group U12, 30 meters × 5 × 5 xx5\times 5 back and forth run in group U13, 20 times of low center of gravity four-point run and vertical jump in group U14, there is a significant difference between the preferred group and the eliminated group in all the indicators in different age groups. In the female athletes' physical fitness performance, there is no significant difference between the preferred athletes of U12 and U14 groups and the eliminated group in vertical jump index, and there is significant difference between the preferred group and the eliminated group in the other four indexes. National U Series Badminton Competitions U12-U14 Comprehensive Quality Physical Fitness Test can distinguish the difference between the preferred group and the eliminated group.
表2 男运动员优选组与淘汰组差异分析  Table 2 Analysis of differences between the preferred and eliminated groups of male athletes
Table 2 Analysis of Differences between the Preferred Group and the Eliminated Group of Male Athletes
年龄组  age groups 指标  norm 优选组（ n 1 n 1 n_(1)\mathrm{n}_{1} ）  Preferred group ( n 1 n 1 n_(1)\mathrm{n}_{1} ) 淘汰组 ( n 2 ) n 2 (n_(2))\left(\mathrm{n}_{2}\right)  Elimination group ( n 2 ) n 2 (n_(2))\left(\mathrm{n}_{2}\right) t
U 12 ( n 1 = 48 , n 2 = 166 ) U 12 n 1 = 48 , n 2 = 166 {:[U12],[(n_(1)=48,n_(2)=166)]:}\begin{gathered} \mathrm{U} 12 \\ \left(\mathrm{n}_{1}=48, \mathrm{n}_{2}=166\right) \end{gathered} 20 次低重心四点跑／s  20 low center of gravity four point runs/s 34.77 ± 2.05 34.77 ± 2.05 34.77+-2.0534.77 \pm 2.05 36.47 ± 2.70 36.47 ± 2.70 36.47+-2.7036.47 \pm 2.70 －4．001＊＊  -4.001**
三分钟双摇跳绳／次  Three-minute double-rope skipping/repeat 3 2 4 . 8 1 ± 4 2 . 3 8 3 2 4 . 8 1 ± 4 2 . 3 8 324.81+-42.38\mathbf{3 2 4 . 8 1} \pm \mathbf{4 2 . 3 8} 296.48 ± 47.77 296.48 ± 47.77 296.48+-47.77296.48 \pm 47.77 3．678＊＊  3. 678**
垂直纵跳／cm  Vertical longitudinal jump／cm 35.12 ± 6.07 35.12 ± 6.07 35.12+-6.0735.12 \pm 6.07 33.77 ± 5.95 33.77 ± 5.95 33.77+-5.9533.77 \pm 5.95 1.374
30 米 × 5 × 5 xx5\times 5 往返跑／s  30 meters × 5 × 5 xx5\times 5 Round trip/s 29.47 ± 1.98 29.47 ± 1.98 29.47+-1.9829.47 \pm 1.98 3 0 . 7 8 ± 2.03 3 0 . 7 8 ± 2.03 30.78+-2.03\mathbf{3 0 . 7 8} \pm 2.03 －3．918＊＊  -3.918**
立定跳远/m  Standing long jump/m 2.08 ± 0.14 2.08 ± 0.14 2.08+-0.142.08 \pm 0.14 2.01 ± 0.15 2.01 ± 0.15 2.01+-0.152.01 \pm 0.15 2．916＊＊  2. 916**
U 13 ( n 1 = 48 , n 2 = 166 ) U 13 n 1 = 48 , n 2 = 166 {:[U13],[(n_(1)=48,n_(2)=166)]:}\begin{gathered} \mathrm{U} 13 \\ \left(\mathrm{n}_{1}=48, \mathrm{n}_{2}=166\right) \end{gathered} 20 次低重心四点跑/s  20 low center of gravity four point run/s 33.90 ± 1.92 33.90 ± 1.92 33.90+-1.9233.90 \pm 1.92 36.04 ± 7.00 36.04 ± 7.00 36.04+-7.0036.04 \pm 7.00 －2．089＊  -2.089*
三分钟双摇跳绳／次  Three-minute double-rope skipping/repeat 3 1 6 . 5 8 ± 3 9 . 7 7 3 1 6 . 5 8 ± 3 9 . 7 7 316.58+-39.77\mathbf{3 1 6 . 5 8} \pm \mathbf{3 9 . 7 7} 297.41 ± 49.68 297.41 ± 49.68 297.41+-49.68297.41 \pm 49.68 2.773 ∗ ∗ 2.773 ∗ ∗ 2.773^(****)2.773^{* *}
垂直纵跳/cm  Vertical longitudinal jump/cm 40.36 ± 8.85 40.36 ± 8.85 40.36+-8.8540.36 \pm 8.85 35.49 ± 6.42 35.49 ± 6.42 35.49+-6.4235.49 \pm 6.42 3．553＊＊  3.553**
30 米 × 5 × 5 xx5\times 5往返跑/s  30 meters × 5 × 5 xx5\times 5 Round trip/s 28.63 ± 1.69 28.63 ± 1.69 28.63+-1.6928.63 \pm 1.69 31.25 ± 20.96 31.25 ± 20.96 31.25+-20.9631.25 \pm 20.96 －0．862  -0.862
立定跳远/m  Standing long jump/m 2 . 3 0 ± 0 . 1 7 2 . 3 0 ± 0 . 1 7 2.30+-0.17\mathbf{2 . 3 0} \pm \mathbf{0 . 1 7} 2 . 1 5 ± 0 . 1 6 2 . 1 5 ± 0 . 1 6 2.15+-0.16\mathbf{2 . 1 5} \pm \mathbf{0 . 1 6} 5．883＊＊  5. 883**
U14 ( n 1 = 48 , n 2 = 181 )  U14  n 1 = 48 , n 2 = 181 {:[" U14 "],[(n_(1)=48,n_(2)=181)]:}\begin{gathered} \text { U14 } \\ \left(\mathrm{n}_{1}=48, \mathrm{n}_{2}=181\right) \end{gathered} 20 次低重心四点跑/s  20 low center of gravity four point run/s 32.42 ± 4.77 32.42 ± 4.77 32.42+-4.7732.42 \pm 4.77 35.66 ± 24.70 35.66 ± 24.70 35.66+-24.7035.66 \pm 24.70 －0．893  -0.893
三分钟双摇跳绳／次  Three-minute double-rope skipping/repeat 3 2 2 . 5 4 ± 4 0 . 1 6 3 2 2 . 5 4 ± 4 0 . 1 6 322.54+-40.16\mathbf{3 2 2 . 5 4} \pm \mathbf{4 0 . 1 6} 305.54 ± 48.08 305.54 ± 48.08 305.54+-48.08305.54 \pm 48.08 2．250＊  2. 250*
垂直纵跳/cm  Vertical longitudinal jump/cm 40.75 ± 8.00 40.75 ± 8.00 40.75+-8.0040.75 \pm 8.00 39.70 ± 7.16 39.70 ± 7.16 39.70+-7.1639.70 \pm 7.16 0.877
30 米 × 5 × 5 xx5\times 5往返跑/s  30 meters × 5 × 5 xx5\times 5 Round trip/s 28.01 ± 1.32 28.01 ± 1.32 28.01+-1.3228.01 \pm 1.32 28.78 ± 2.04 28.78 ± 2.04 28.78+-2.0428.78 \pm 2.04 －2．507 ∗ ∗ ^(**){ }^{*}  -2.507 ∗ ∗ ^(**){ }^{*}
立定跳远/m  Standing long jump/m 2.38 ± 0.15 2.38 ± 0.15 2.38+-0.152.38 \pm 0.15 2.29 ± 0.17 2.29 ± 0.17 2.29+-0.172.29 \pm 0.17 3．120＊＊  3. 120**
年龄组 指标 优选组（ n_(1) ） 淘汰组 (n_(2)) t "U12 (n_(1)=48,n_(2)=166)" 20 次低重心四点跑／s 34.77+-2.05 36.47+-2.70 －4．001＊＊ 三分钟双摇跳绳／次 324.81+-42.38 296.48+-47.77 3．678＊＊ 垂直纵跳／cm 35.12+-6.07 33.77+-5.95 1.374 30 米 xx5 往返跑／s 29.47+-1.98 30.78+-2.03 －3．918＊＊ 立定跳远／m 2.08+-0.14 2.01+-0.15 2．916＊＊ "U13 (n_(1)=48,n_(2)=166)" 20 次低重心四点跑／s 33.90+-1.92 36.04+-7.00 －2．089＊ 三分钟双摇跳绳／次 316.58+-39.77 297.41+-49.68 2.773^(****) 垂直纵跳／cm 40.36+-8.85 35.49+-6.42 3．553＊＊ 30 米 xx5 往返跑／s 28.63+-1.69 31.25+-20.96 －0．862 立定跳远／m 2.30+-0.17 2.15+-0.16 5．883＊＊ " U14 (n_(1)=48,n_(2)=181)" 20 次低重心四点跑／s 32.42+-4.77 35.66+-24.70 －0．893 三分钟双摇跳绳／次 322.54+-40.16 305.54+-48.08 2．250＊ 垂直纵跳／cm 40.75+-8.00 39.70+-7.16 0.877 30 米 xx5 往返跑／s 28.01+-1.32 28.78+-2.04 －2．507 ^(**) 立定跳远／m 2.38+-0.15 2.29+-0.17 3．120＊＊| 年龄组 | 指标 | 优选组（ $\mathrm{n}_{1}$ ） | 淘汰组 $\left(\mathrm{n}_{2}\right)$ | t | | :---: | :---: | :---: | :---: | :---: | | $\begin{gathered} \mathrm{U} 12 \\ \left(\mathrm{n}_{1}=48, \mathrm{n}_{2}=166\right) \end{gathered}$ | 20 次低重心四点跑／s | $34.77 \pm 2.05$ | $36.47 \pm 2.70$ | －4．001＊＊ | | | 三分钟双摇跳绳／次 | $\mathbf{3 2 4 . 8 1} \pm \mathbf{4 2 . 3 8}$ | $296.48 \pm 47.77$ | 3．678＊＊ | | | 垂直纵跳／cm | $35.12 \pm 6.07$ | $33.77 \pm 5.95$ | 1.374 | | | 30 米 $\times 5$ 往返跑／s | $29.47 \pm 1.98$ | $\mathbf{3 0 . 7 8} \pm 2.03$ | －3．918＊＊ | | | 立定跳远／m | $2.08 \pm 0.14$ | $2.01 \pm 0.15$ | 2．916＊＊ | | $\begin{gathered} \mathrm{U} 13 \\ \left(\mathrm{n}_{1}=48, \mathrm{n}_{2}=166\right) \end{gathered}$ | 20 次低重心四点跑／s | $33.90 \pm 1.92$ | $36.04 \pm 7.00$ | －2．089＊ | | | 三分钟双摇跳绳／次 | $\mathbf{3 1 6 . 5 8} \pm \mathbf{3 9 . 7 7}$ | $297.41 \pm 49.68$ | $2.773^{* *}$ | | | 垂直纵跳／cm | $40.36 \pm 8.85$ | $35.49 \pm 6.42$ | 3．553＊＊ | | | 30 米 $\times 5$ 往返跑／s | $28.63 \pm 1.69$ | $31.25 \pm 20.96$ | －0．862 | | | 立定跳远／m | $\mathbf{2 . 3 0} \pm \mathbf{0 . 1 7}$ | $\mathbf{2 . 1 5} \pm \mathbf{0 . 1 6}$ | 5．883＊＊ | | $\begin{gathered} \text { U14 } \\ \left(\mathrm{n}_{1}=48, \mathrm{n}_{2}=181\right) \end{gathered}$ | 20 次低重心四点跑／s | $32.42 \pm 4.77$ | $35.66 \pm 24.70$ | －0．893 | | | 三分钟双摇跳绳／次 | $\mathbf{3 2 2 . 5 4} \pm \mathbf{4 0 . 1 6}$ | $305.54 \pm 48.08$ | 2．250＊ | | | 垂直纵跳／cm | $40.75 \pm 8.00$ | $39.70 \pm 7.16$ | 0.877 | | | 30 米 $\times 5$ 往返跑／s | $28.01 \pm 1.32$ | $28.78 \pm 2.04$ | －2．507 ${ }^{*}$ | | | 立定跳远／m | $2.38 \pm 0.15$ | $2.29 \pm 0.17$ | 3．120＊＊ |
注：＊表示 P < 0.05 P < 0.05 P < 0.05P<0.05；＊＊表示 P < 0.01 P < 0.01 P < 0.01P<0.01；同下。
Note: * denotes P < 0.05 P < 0.05 P < 0.05P<0.05 ; ** denotes P < 0.01 P < 0.01 P < 0.01P<0.01 ; ibid.

表 3 女运动员优选组与淘汰组差异分析  Table 3 Analysis of differences between preferred and eliminated groups of female athletes

表 3 首选组和淘汰组女运动员差异分析  Table 3 Analysis of differences between female athletes in the preferred and eliminated groups
年龄组  age groups 指标  norm 优选组（ n 1 n 1 n_(1)\mathrm{n}_{1}）  Preferred group ( n 1 n 1 n_(1)\mathrm{n}_{1} ) 淘汰组（ n 2 n 2 n_(2)\mathrm{n}_{2}）  Elimination group ( n 2 n 2 n_(2)\mathrm{n}_{2} ) t
U 12 ( n 1 = 48 , n 2 = 153 ) U 12 n 1 = 48 , n 2 = 153 {:[U12],[(n_(1)=48,n_(2)=153)]:}\begin{gathered} \mathrm{U} 12 \\ \left(\mathrm{n}_{1}=48, \mathrm{n}_{2}=153\right) \end{gathered} 20 次低重心四点跑/s  20 low center of gravity four point run/s 34.62 ± 1.57 34.62 ± 1.57 34.62+-1.5734.62 \pm 1.57 36.39 ± 2.99 36.39 ± 2.99 36.39+-2.9936.39 \pm 2.99 －3．899＊＊  -3.899**
三分钟双摇跳绳／次  Three-minute double-rope skipping/repeat 3 3 7 . 5 5 ± 3 5 . 2 9 3 3 7 . 5 5 ± 3 5 . 2 9 337.55+-35.29\mathbf{3 3 7 . 5 5} \pm \mathbf{3 5 . 2 9} 303.77 ± 41.80 303.77 ± 41.80 303.77+-41.80303.77 \pm 41.80 5．021＊＊  5. 021**
垂直纵跳/cm  Vertical longitudinal jump/cm 33.16 ± 4.81 33.16 ± 4.81 33.16+-4.8133.16 \pm 4.81 32.67 ± 5.26 32.67 ± 5.26 32.67+-5.2632.67 \pm 5.26 0.567
30 米 × 5 × 5 xx5\times 5往返跑/s  30 meters × 5 × 5 xx5\times 5 Round trip/s 30.17 ± 1.39 30.17 ± 1.39 30.17+-1.3930.17 \pm 1.39 31.27 ± 1.71 31.27 ± 1.71 31.27+-1.7131.27 \pm 1.71 －4．028＊＊  -4.028**
立定跳远/m  Standing long jump/m 2.07 ± 0.12 2.07 ± 0.12 2.07+-0.122.07 \pm 0.12 1.98 ± 0.13 1.98 ± 0.13 1.98+-0.131.98 \pm 0.13 4．192＊＊  4. 192***
U 13 ( n 1 = 48 , n 2 = 150 ) U 13 n 1 = 48 , n 2 = 150 {:[U13],[(n_(1)=48,n_(2)=150)]:}\begin{gathered} \mathrm{U} 13 \\ \left(\mathrm{n}_{1}=48, \mathrm{n}_{2}=150\right) \end{gathered} 20 次低重心四点跑／s  20 low center of gravity four point runs/s 34.33 ± 2.01 34.33 ± 2.01 34.33+-2.0134.33 \pm 2.01 35.58 ± 3.54 35.58 ± 3.54 35.58+-3.5435.58 \pm 3.54 －2．322＊  -2.322*
三分钟双摇跳绳／次  Three-minute double-rope skipping/repeat 327.79 ± 43.79 327.79 ± 43.79 327.79+-43.79327.79 \pm 43.79 3 0 9 . 7 8 ± 42.46 3 0 9 . 7 8 ± 42.46 309.78+-42.46\mathbf{3 0 9 . 7 8} \pm 42.46 2．521＊  2.521*
垂直纵跳／cm  Vertical longitudinal jump／cm 35.61 ± 5.92 35.61 ± 5.92 35.61+-5.9235.61 \pm 5.92 33.29 ± 5.76 33.29 ± 5.76 33.29+-5.7633.29 \pm 5.76 2．398＊  2.398*
30 米 × 5 × 5 xx5\times 5 往返跑／s  30 meters × 5 × 5 xx5\times 5 Round trip/s 29.47 ± 1.07 29.47 ± 1.07 29.47+-1.0729.47 \pm 1.07 30.65 ± 1.24 30.65 ± 1.24 30.65+-1.2430.65 \pm 1.24 －5．892＊＊  -5.892**
立定跳远／m  Standing long jump/m 2 . 1 4 ± 0 . 1 1 2 . 1 4 ± 0 . 1 1 2.14+-0.11\mathbf{2 . 1 4} \pm \mathbf{0 . 1 1} 2.03 ± 0.13 2.03 ± 0.13 2.03+-0.132.03 \pm 0.13 5．242＊＊  5. 242**
U 14 ( n 1 = 48 , n 2 = 137 ) U 14 n 1 = 48 , n 2 = 137 {:[U14],[(n_(1)=48,n_(2)=137)]:}\begin{gathered} \mathrm{U} 14 \\ \left(\mathrm{n}_{1}=48, \mathrm{n}_{2}=137\right) \end{gathered} 20 次低重心四点跑／s  20 low center of gravity four point runs/s 34.27 ± 1.77 34.27 ± 1.77 34.27+-1.7734.27 \pm 1.77 3 5 . 2 5 ± 1 . 8 9 3 5 . 2 5 ± 1 . 8 9 35.25+-1.89\mathbf{3 5 . 2 5} \pm \mathbf{1 . 8 9} －3．046＊＊  -3.046**
三分钟双摇跳绳／次  Three-minute double-rope skipping/repeat 342.09 ± 36.15 342.09 ± 36.15 342.09+-36.15342.09 \pm 36.15 3 0 7 . 1 9 ± 50.27 3 0 7 . 1 9 ± 50.27 307.19+-50.27\mathbf{3 0 7 . 1 9} \pm 50.27 5.057 ∗ ∗ 5.057 ∗ ∗ 5.057****5.057 * *
垂直纵跳／cm  Vertical longitudinal jump／cm 36.02 ± 6.29 36.02 ± 6.29 36.02+-6.2936.02 \pm 6.29 33.99 ± 6.15 33.99 ± 6.15 33.99+-6.1533.99 \pm 6.15 1.908
30 米 × 5 × 5 xx5\times 5 往返跑／s  30 meters × 5 × 5 xx5\times 5 Round trip/s 29.52 ± 1.09 29.52 ± 1.09 29.52+-1.0929.52 \pm 1.09 30.25 ± 1.29 30.25 ± 1.29 30.25+-1.2930.25 \pm 1.29 －3．414＊＊  -3.414**
立定跳远／m  Standing long jump/m 2.15 ± 0.11 2.15 ± 0.11 2.15+-0.112.15 \pm 0.11 2.09 ± 0.13 2.09 ± 0.13 2.09+-0.132.09 \pm 0.13 2.771 ∗ ∗ 2.771 ∗ ∗ 2.771^(****)2.771^{* *}
年龄组 指标 优选组（ n_(1) ） 淘汰组（ n_(2) ） t "U12 (n_(1)=48,n_(2)=153)" 20 次低重心四点跑／s 34.62+-1.57 36.39+-2.99 －3．899＊＊ 三分钟双摇跳绳／次 337.55+-35.29 303.77+-41.80 5．021＊＊ 垂直纵跳／cm 33.16+-4.81 32.67+-5.26 0.567 30 米 xx5 往返跑／s 30.17+-1.39 31.27+-1.71 －4．028＊＊ 立定跳远／m 2.07+-0.12 1.98+-0.13 4．192＊＊ "U13 (n_(1)=48,n_(2)=150)" 20 次低重心四点跑／s 34.33+-2.01 35.58+-3.54 －2．322＊ 三分钟双摇跳绳／次 327.79+-43.79 309.78+-42.46 2．521＊ 垂直纵跳／cm 35.61+-5.92 33.29+-5.76 2．398＊ 30 米 xx5 往返跑／s 29.47+-1.07 30.65+-1.24 －5．892＊＊ 立定跳远／m 2.14+-0.11 2.03+-0.13 5．242＊＊ "U14 (n_(1)=48,n_(2)=137)" 20 次低重心四点跑／s 34.27+-1.77 35.25+-1.89 －3．046＊＊ 三分钟双摇跳绳／次 342.09+-36.15 307.19+-50.27 5.057**** 垂直纵跳／cm 36.02+-6.29 33.99+-6.15 1.908 30 米 xx5 往返跑／s 29.52+-1.09 30.25+-1.29 －3．414＊＊ 立定跳远／m 2.15+-0.11 2.09+-0.13 2.771^(****)| 年龄组 | 指标 | 优选组（ $\mathrm{n}_{1}$ ） | 淘汰组（ $\mathrm{n}_{2}$ ） | t | | :---: | :---: | :---: | :---: | :---: | | $\begin{gathered} \mathrm{U} 12 \\ \left(\mathrm{n}_{1}=48, \mathrm{n}_{2}=153\right) \end{gathered}$ | 20 次低重心四点跑／s | $34.62 \pm 1.57$ | $36.39 \pm 2.99$ | －3．899＊＊ | | | 三分钟双摇跳绳／次 | $\mathbf{3 3 7 . 5 5} \pm \mathbf{3 5 . 2 9}$ | $303.77 \pm 41.80$ | 5．021＊＊ | | | 垂直纵跳／cm | $33.16 \pm 4.81$ | $32.67 \pm 5.26$ | 0.567 | | | 30 米 $\times 5$ 往返跑／s | $30.17 \pm 1.39$ | $31.27 \pm 1.71$ | －4．028＊＊ | | | 立定跳远／m | $2.07 \pm 0.12$ | $1.98 \pm 0.13$ | 4．192＊＊ | | $\begin{gathered} \mathrm{U} 13 \\ \left(\mathrm{n}_{1}=48, \mathrm{n}_{2}=150\right) \end{gathered}$ | 20 次低重心四点跑／s | $34.33 \pm 2.01$ | $35.58 \pm 3.54$ | －2．322＊ | | | 三分钟双摇跳绳／次 | $327.79 \pm 43.79$ | $\mathbf{3 0 9 . 7 8} \pm 42.46$ | 2．521＊ | | | 垂直纵跳／cm | $35.61 \pm 5.92$ | $33.29 \pm 5.76$ | 2．398＊ | | | 30 米 $\times 5$ 往返跑／s | $29.47 \pm 1.07$ | $30.65 \pm 1.24$ | －5．892＊＊ | | | 立定跳远／m | $\mathbf{2 . 1 4} \pm \mathbf{0 . 1 1}$ | $2.03 \pm 0.13$ | 5．242＊＊ | | $\begin{gathered} \mathrm{U} 14 \\ \left(\mathrm{n}_{1}=48, \mathrm{n}_{2}=137\right) \end{gathered}$ | 20 次低重心四点跑／s | $34.27 \pm 1.77$ | $\mathbf{3 5 . 2 5} \pm \mathbf{1 . 8 9}$ | －3．046＊＊ | | | 三分钟双摇跳绳／次 | $342.09 \pm 36.15$ | $\mathbf{3 0 7 . 1 9} \pm 50.27$ | $5.057 * *$ | | | 垂直纵跳／cm | $36.02 \pm 6.29$ | $33.99 \pm 6.15$ | 1.908 | | | 30 米 $\times 5$ 往返跑／s | $29.52 \pm 1.09$ | $30.25 \pm 1.29$ | －3．414＊＊ | | | 立定跳远／m | $2.15 \pm 0.11$ | $2.09 \pm 0.13$ | $2.771^{* *}$ |

2．1．2 年龄组间差异分析  2.1.2 Analysis of differences between age groups

通过分析运动员在各年龄上的差异比较（表 4，表5），U14 组在各项指标中成绩最好，男运动员在垂直纵跳，立定跳远指标中三个年龄组互相均存在显著差异（U14＞U13＞U12）； 20 次低重心四点跑，三分钟双摇跳绳， 30 米 × 5 × 5 xx5\times 5 往返跑在年龄上不存在显著差异。在女运动员中三分钟双摇跳绳指标在年龄上不存在显著差异，在 20 次低重心四点跑和 30 米 × 5 × 5 xx5\times 5 往返跑成绩上 U12 组与 U13，U14 组存在显著差异（U12 < U 13 < U 13 < U13<\mathrm{U} 13 ，U14），在垂直纵跳成绩上 U14 显著高于 U12，在立定跳远成绩上三个年龄组均存在差异（U14＞U13＞U12）。
By analyzing the difference between the athletes in each age (Table 4, Table 5), U14 group has the best performance in each index, male athletes have significant difference between the three age groups in vertical jump and long jump (U14>U13>U12); there is no significant difference between U12 and U13 in 20 times of low center of gravity four-point run, three-minute double-crank rope skipping, and 30 meters × 5 × 5 xx5\times 5 back and forth run in terms of age. Among female athletes, there is no significant difference in age for the three-minute rope skipping index; there is a significant difference between the U12 group and the U13 and U14 groups for the 20 times low center of gravity four-point run and the 30-meter × 5 × 5 xx5\times 5 back and forth run (U12 < U 13 < U 13 < U13<\mathrm{U} 13 and U14); there is a significant difference between the U14 and U12 groups for the vertical jump; there is a significant difference between the three age groups for the vertical jump (U14 > U13); and there is a significant difference between the three age groups for the vertical jump (U14 > U13) and the three age groups for the vertical jump (U14 > U13). differences (U14 > U13 > U12).
表4男运动员在年龄上的差异比较  Table 4 Comparison of differences in age among male athletes in the
Table 4 Comparative Analysis of Age Differences Among Male Athletes
指标  norm U 12 ( n = 214 ) U 12 ( n = 214 ) U12(n=214)\mathrm{U} 12(\mathrm{n}=214) U 13 ( n = 214 ) U 13 ( n = 214 ) U13(n=214)\mathrm{U} 13(\mathrm{n}=214) U 14 ( n = 229 ) U 14 ( n = 229 ) U14(n=229)\mathrm{U} 14(\mathrm{n}=229) F F FF
20 次低重心四点跑／s  20 low center of gravity four point runs/s 36.09 ± 2.66 36.09 ± 2.66 36.09+-2.6636.09 \pm 2.66 35.56 ± 6.29 35.56 ± 6.29 35.56+-6.2935.56 \pm 6.29 34.9 ± 22.09 34.9 ± 22.09 34.9+-22.0934.9 \pm 22.09 0.363
三分钟双摇跳绳／次  Three-minute double-rope skipping/repeat 302.7 ± 48.01 302.7 ± 48.01 302.7+-48.01302.7 \pm 48.01 301.7 ± 48.22 301.7 ± 48.22 301.7+-48.22301.7 \pm 48.22 309 . ± 46.96 309 . ± 46.96 309.+-46.96309 . \pm 46.96 1.581
垂直纵跳／cm  Vertical longitudinal jump／cm 3 4 . 0 6 ± 5 . 9 9 3 4 . 0 6 ± 5 . 9 9 34.06+-5.99\mathbf{3 4 . 0 6} \pm \mathbf{5 . 9 9} 3 6 . 5 9 ± 7.30 a 3 6 . 5 9 ± 7.30 a 36.59+-7.30a\mathbf{3 6 . 5 9} \pm 7.30 \mathrm{a} 3 9 . 9 2 ± 7 . 3 4 3 9 . 9 2 ± 7 . 3 4 39.92+-7.34\mathbf{3 9 . 9 2} \pm \mathbf{7 . 3 4} 4 0 . 0 5 4 ∗ ∗ ∗ a b c 4 0 . 0 5 4 ∗ ∗ ∗ a b c 40.054^(******abc)\mathbf{4 0 . 0 5 4}^{* * * a b c}
指标 U12(n=214) U13(n=214) U14(n=229) F 20 次低重心四点跑／s 36.09+-2.66 35.56+-6.29 34.9+-22.09 0.363 三分钟双摇跳绳／次 302.7+-48.01 301.7+-48.22 309.+-46.96 1.581 垂直纵跳／cm 34.06+-5.99 36.59+-7.30a 39.92+-7.34 40.054^(******abc)| 指标 | $\mathrm{U} 12(\mathrm{n}=214)$ | $\mathrm{U} 13(\mathrm{n}=214)$ | $\mathrm{U} 14(\mathrm{n}=229)$ | $F$ | | :---: | :---: | :---: | :---: | :---: | | 20 次低重心四点跑／s | $36.09 \pm 2.66$ | $35.56 \pm 6.29$ | $34.9 \pm 22.09$ | 0.363 | | 三分钟双摇跳绳／次 | $302.7 \pm 48.01$ | $301.7 \pm 48.22$ | $309 . \pm 46.96$ | 1.581 | | 垂直纵跳／cm | $\mathbf{3 4 . 0 6} \pm \mathbf{5 . 9 9}$ | $\mathbf{3 6 . 5 9} \pm 7.30 \mathrm{a}$ | $\mathbf{3 9 . 9 2} \pm \mathbf{7 . 3 4}$ | $\mathbf{4 0 . 0 5 4}^{* * * a b c}$ |
30 米 × 5 × 5 xx5\times 5 往返跑 / s / s //s/ \mathrm{s}
30 meters × 5 × 5 xx5\times 5 Round trip / s / s //s/ \mathrm{s} 		30.49 ± 2.08 30.49 ± 2.08 30.49+-2.0830.49 \pm 2.08 30.66 ± 18.49 30.66 ± 18.49 30.66+-18.4930.66 \pm 18.49 28.62 ± 1.94 28.62 ± 1.94 28.62+-1.9428.62 \pm 1.94 2.512
立定跳远 / m / m //m/ \mathbf{m}  Standing long jump / m / m //m/ \mathbf{m} 2 . 0 2 ± 0 . 1 5 2 . 0 2 ± 0 . 1 5 2.02+-0.15\mathbf{2 . 0 2} \pm \mathbf{0 . 1 5} 2 . 1 8 ± 0 . 1 7 2 . 1 8 ± 0 . 1 7 2.18+-0.17\mathbf{2 . 1 8} \pm \mathbf{0 . 1 7} 2 . 3 1 ± 0 . 1 7 2 . 3 1 ± 0 . 1 7 2.31+-0.17\mathbf{2 . 3 1} \pm \mathbf{0 . 1 7} 1 6 9 . 6 4 8 ∗ ∗ abc 1 6 9 . 6 4 8 ∗ ∗ abc 169.648^(****abc)\mathbf{1 6 9 . 6 4 8}^{* * \mathrm{abc}}
30 米 xx5 往返跑 //s 30.49+-2.08 30.66+-18.49 28.62+-1.94 2.512 立定跳远 //m 2.02+-0.15 2.18+-0.17 2.31+-0.17 169.648^(****abc)| 30 米 $\times 5$ 往返跑 $/ \mathrm{s}$ | $30.49 \pm 2.08$ | $30.66 \pm 18.49$ | $28.62 \pm 1.94$ | 2.512 | | :---: | :---: | :---: | :---: | :---: | | 立定跳远 $/ \mathbf{m}$ | $\mathbf{2 . 0 2} \pm \mathbf{0 . 1 5}$ | $\mathbf{2 . 1 8} \pm \mathbf{0 . 1 7}$ | $\mathbf{2 . 3 1} \pm \mathbf{0 . 1 7}$ | $\mathbf{1 6 9 . 6 4 8}^{* * \mathrm{abc}}$ |
注：a 表示 U12 与 U13 具有显著差异；b表示U12 与 U14 具有显著差异；c 表示 U13 与 U14 具有显著差异；同下。
Note: a indicates that U12 is significantly different from U13; b indicates that U12 is significantly different from U14; c indicates that U13 is significantly different from U14; ibid.

表 5 女运动员在年龄上的差异比较  Table 5 Comparison of differences between female athletes in terms of age

Table 5 Comparative Analysis of Age Differences Among Female Athletes
指标  norm U 12 ( n = 201 ) U 12 ( n = 201 ) U12(n=201)\mathrm{U} 12(\mathrm{n}=201) U 13 ( n = 198 ) U 13 ( n = 198 ) U13(n=198)\mathrm{U} 13(\mathrm{n}=198) U 14 ( n = 185 ) U 14 ( n = 185 ) U14(n=185)\mathrm{U} 14(\mathrm{n}=185) F F FF
2 0 2 0 20\mathbf{2 0} 次低重心四点跑／s   2 0 2 0 20\mathbf{2 0} Sub-low center of gravity four point run/s 3 5 . 9 8 ± 2 . 8 2 3 5 . 9 8 ± 2 . 8 2 35.98+-2.82\mathbf{3 5 . 9 8} \pm \mathbf{2 . 8 2} 3 5 . 2 6 ± 3 . 2 6 3 5 . 2 6 ± 3 . 2 6 35.26+-3.26\mathbf{3 5 . 2 6} \pm \mathbf{3 . 2 6} 3 5 . 0 1 ± 1 . 9 1 3 5 . 0 1 ± 1 . 9 1 35.01+-1.91\mathbf{3 5 . 0 1} \pm \mathbf{1 . 9 1} 6 . 4 9 5 ∗ ab 6 . 4 9 5 ∗ ab 6.495^(**ab)\mathbf{6 . 4 9 5}{ }^{* \mathrm{ab}}
三分钟双摇跳绳／次  Three-minute double-rope skipping/repeat 3 1 1 . 6 ± 4 2 . 7 6 3 1 1 . 6 ± 4 2 . 7 6 311.6+-42.76\mathbf{3 1 1 . 6} \pm \mathbf{4 2 . 7 6} 3 1 4 . 3 3 ± 4 3 . 4 0 3 1 4 . 3 3 ± 4 3 . 4 0 314.33+-43.40\mathbf{3 1 4 . 3 3} \pm \mathbf{4 3 . 4 0} 3 1 5 . 8 7 ± 4 9 . 4 3 3 1 5 . 8 7 ± 4 9 . 4 3 315.87+-49.43\mathbf{3 1 5 . 8 7} \pm \mathbf{4 9 . 4 3} 0 . 4 2 6 0 . 4 2 6 0.426\mathbf{0 . 4 2 6}
垂直纵跳／cm  Vertical longitudinal jump／cm 3 2 . 7 9 ± 5 . 1 5 3 2 . 7 9 ± 5 . 1 5 32.79+-5.15\mathbf{3 2 . 7 9} \pm \mathbf{5 . 1 5} 3 3 . 8 8 ± 5 . 8 7 3 3 . 8 8 ± 5 . 8 7 33.88+-5.87\mathbf{3 3 . 8 8} \pm \mathbf{5 . 8 7} 3 4 . 5 0 ± 6 . 2 3 3 4 . 5 0 ± 6 . 2 3 34.50+-6.23\mathbf{3 4 . 5 0} \pm \mathbf{6 . 2 3} 4 . 3 7 4 ∗ b 4 . 3 7 4 ∗ b 4.374^(**b)\mathbf{4 . 3 7 4}^{* \mathrm{~b}}
3 0 3 0 30\mathbf{3 0} 米 × 5 × 5 xx5\times \mathbf{5} 往返跑／s
3 0 3 0 30\mathbf{3 0} meters × 5 × 5 xx5\times \mathbf{5} Round trip/s		 3 1 . 0 1 ± 1 . 7 0 3 1 . 0 1 ± 1 . 7 0 31.01+-1.70\mathbf{3 1 . 0 1} \pm \mathbf{1 . 7 0} 3 0 . 3 5 ± 1 . 3 0 3 0 . 3 5 ± 1 . 3 0 30.35+-1.30\mathbf{3 0 . 3 5} \pm \mathbf{1 . 3 0} 3 0 . 0 7 ± 1 . 2 8 3 0 . 0 7 ± 1 . 2 8 30.07+-1.28\mathbf{3 0 . 0 7} \pm \mathbf{1 . 2 8} 2 1 . 5 8 5 ∗ ∗ ab 2 1 . 5 8 5 ∗ ∗ ab 21.585^(****ab)\mathbf{2 1 . 5 8 5}^{* * \mathrm{ab}}
立定跳远／m  Standing long jump/m 2 . 0 0 ± 0 . 1 3 2 . 0 0 ± 0 . 1 3 2.00+-0.13\mathbf{2 . 0 0} \pm \mathbf{0 . 1 3} 2 . 0 6 ± 0 . 1 3 2 . 0 6 ± 0 . 1 3 2.06+-0.13\mathbf{2 . 0 6} \pm \mathbf{0 . 1 3} 2 . 1 1 ± 0 . 1 3 2 . 1 1 ± 0 . 1 3 2.11+-0.13\mathbf{2 . 1 1} \pm \mathbf{0 . 1 3} 3 2 . 3 0 2 ∗ a b a b 3 2 . 3 0 2 ∗ a b a b 32.302^(**abab)\mathbf{3 2 . 3 0 2}^{* \mathbf{a b a b}}
指标 U12(n=201) U13(n=198) U14(n=185) F 20 次低重心四点跑／s 35.98+-2.82 35.26+-3.26 35.01+-1.91 6.495^(**ab) 三分钟双摇跳绳／次 311.6+-42.76 314.33+-43.40 315.87+-49.43 0.426 垂直纵跳／cm 32.79+-5.15 33.88+-5.87 34.50+-6.23 4.374^(**b) 30 米 xx5 往返跑／s 31.01+-1.70 30.35+-1.30 30.07+-1.28 21.585^(****ab) 立定跳远／m 2.00+-0.13 2.06+-0.13 2.11+-0.13 32.302^(**abab)| 指标 | $\mathrm{U} 12(\mathrm{n}=201)$ | $\mathrm{U} 13(\mathrm{n}=198)$ | $\mathrm{U} 14(\mathrm{n}=185)$ | $F$ | | :---: | :---: | :---: | :---: | :---: | | $\mathbf{2 0}$ 次低重心四点跑／s | $\mathbf{3 5 . 9 8} \pm \mathbf{2 . 8 2}$ | $\mathbf{3 5 . 2 6} \pm \mathbf{3 . 2 6}$ | $\mathbf{3 5 . 0 1} \pm \mathbf{1 . 9 1}$ | $\mathbf{6 . 4 9 5}{ }^{* \mathrm{ab}}$ | | 三分钟双摇跳绳／次 | $\mathbf{3 1 1 . 6} \pm \mathbf{4 2 . 7 6}$ | $\mathbf{3 1 4 . 3 3} \pm \mathbf{4 3 . 4 0}$ | $\mathbf{3 1 5 . 8 7} \pm \mathbf{4 9 . 4 3}$ | $\mathbf{0 . 4 2 6}$ | | 垂直纵跳／cm | $\mathbf{3 2 . 7 9} \pm \mathbf{5 . 1 5}$ | $\mathbf{3 3 . 8 8} \pm \mathbf{5 . 8 7}$ | $\mathbf{3 4 . 5 0} \pm \mathbf{6 . 2 3}$ | $\mathbf{4 . 3 7 4}^{* \mathrm{~b}}$ | | $\mathbf{3 0}$ 米 $\times \mathbf{5}$ 往返跑／s | $\mathbf{3 1 . 0 1} \pm \mathbf{1 . 7 0}$ | $\mathbf{3 0 . 3 5} \pm \mathbf{1 . 3 0}$ | $\mathbf{3 0 . 0 7} \pm \mathbf{1 . 2 8}$ | $\mathbf{2 1 . 5 8 5}^{* * \mathrm{ab}}$ | | 立定跳远／m | $\mathbf{2 . 0 0} \pm \mathbf{0 . 1 3}$ | $\mathbf{2 . 0 6} \pm \mathbf{0 . 1 3}$ | $\mathbf{2 . 1 1} \pm \mathbf{0 . 1 3}$ | $\mathbf{3 2 . 3 0 2}^{* \mathbf{a b a b}}$ |

2.2 体能测试敏感指标阈值的确定与解读  2.2 Determination and Interpretation of Sensitive Indicator Thresholds for Physical Fitness Tests

分别得出不同年龄组的 20 次低重心四点跑，三分钟双摇跳绳，垂直纵跳， 30 米 × 5 × 5 xx5\times 5 往返跑，立定跳远的分析结果（表 6，表 7）。以 ROC 曲线下面积 AUC ⩾ 0.65 ⩾ 0.65 >= 0.65\geqslant 0.65 ，且 P < 0.05 P < 0.05 P < 0.05P<0.05 为条件，对分析结果进行筛选，可分别建立男，女运动员体能测试敏感指标与阈值（图3，图4）。ROC曲线下面积（AUC）可表明分类器的整体性能，AUC 值越高，表明分辨力越强。
The analysis results of 20 times of low center of gravity four-point run, three-minute double-swing rope skipping, vertical jump, 30m × 5 × 5 xx5\times 5 back and forth run, and standing long jump of different age groups were obtained respectively (Table 6 and Table 7). Taking the area under the ROC curve AUC ⩾ 0.65 ⩾ 0.65 >= 0.65\geqslant 0.65 and P < 0.05 P < 0.05 P < 0.05P<0.05 as the conditions, the analyzed results can be filtered to establish the sensitive indexes and thresholds of physical fitness test for male and female athletes respectively (Figs. 3 and 4).The area under the ROC curve (AUC) can indicate the overall performance of the classifier, and the higher the value of the AUC, the higher the discriminative power is.
在各项敏感指标成绩中除 30 米 × 5 × 5 xx5\times 5 往返跑是 U13 组阈值最高，其余指标均为 U14 组阈值最高。在男运动员中 20 次低重心四点跑 AUC 值最高（ 0.677 ∼ 0.710 0.677 ∼ 0.710 0.677∼0.7100.677 \sim 0.710 ），而女运动员是 30 米 × × xx\times 5 往返跑 AUC 值最高（0．699～0．770），男女运动员均在垂直纵跳成绩上 AUC 值最低，分别为 0.546 ∼ 0.643 , 0.527 ∼ 0.612 0.546 ∼ 0.643 , 0.527 ∼ 0.612 0.546∼0.643,0.527∼0.6120.546 \sim 0.643, ~ 0.527 \sim 0.612 。
The highest threshold values for each of the sensitivity measures were in the U14 group, except for the 30 m × 5 × 5 xx5\times 5 round trip, which was the highest threshold value in the U13 group. The 20 low center of gravity four-point run had the highest AUC value in male athletes ( 0.677 ∼ 0.710 0.677 ∼ 0.710 0.677∼0.7100.677 \sim 0.710 ), whereas in female athletes it was the 30 m × × xx\times 5-round trip that had the highest AUC value (0.699-0.770), and both male and female athletes had the lowest AUC values for vertical jump performance, 0.546 ∼ 0.643 , 0.527 ∼ 0.612 0.546 ∼ 0.643 , 0.527 ∼ 0.612 0.546∼0.643,0.527∼0.6120.546 \sim 0.643, ~ 0.527 \sim 0.612 , respectively.
表6 男运动员体能测试指标成绩 ROC 分析结果  Table 6 Results of ROC analysis of male athletes' performance in physical fitness test indicators
Table 6 ROC Analysis Results of Physical Fitness Test Indicators for Male Athletes
指标  norm 组别  groups 阈值  thresholds 敏感度  sensitivity 特异性  idiosyncrasy Youden 指数  Youden Index AUC
20 次低重心四点跑／s  20 low center of gravity four point runs/s U12 32.15 0.702 0.647 0.349 0．710＊＊  0.710**
U13 33.27 0.479 0.824 0.303 0．677＊＊  0.677**
U14 32.04 0.383 0.856 0.239 0．677＊＊  0.677**
三分钟双摇跳绳／次  Three-minute double-rope skipping/repeat U12 317 0.702 0.617 0.319 0.637 ∗ ∗ 0.637 ∗ ∗ 0.637^(****)0.637^{* *}
U13 274 0.917 0.301 0.218 0.612 ∗ ∗ 0.612 ∗ ∗ 0.612^(****)0.612^{* *}
U14 331 0.521 0.646 0.167 0.596 ∗ 0.596 ∗ 0.596^(**)0.596{ }^{*}
垂直纵跳／cm  Vertical longitudinal jump／cm U12 31.60 0.468 0.689 0.157 0.559
U13 39.55 0.583 0.753 0.336 0.643 ∗ ∗ 0.643 ∗ ∗ 0.643^(****)0.643^{* *}
指标 组别 阈值 敏感度 特异性 Youden 指数 AUC 20 次低重心四点跑／s U12 32.15 0.702 0.647 0.349 0．710＊＊ U13 33.27 0.479 0.824 0.303 0．677＊＊ U14 32.04 0.383 0.856 0.239 0．677＊＊ 三分钟双摇跳绳／次 U12 317 0.702 0.617 0.319 0.637^(****) U13 274 0.917 0.301 0.218 0.612^(****) U14 331 0.521 0.646 0.167 0.596^(**) 垂直纵跳／cm U12 31.60 0.468 0.689 0.157 0.559 U13 39.55 0.583 0.753 0.336 0.643^(****)| 指标 | 组别 | 阈值 | 敏感度 | 特异性 | Youden 指数 | AUC | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | 20 次低重心四点跑／s | U12 | 32.15 | 0.702 | 0.647 | 0.349 | 0．710＊＊ | | | U13 | 33.27 | 0.479 | 0.824 | 0.303 | 0．677＊＊ | | | U14 | 32.04 | 0.383 | 0.856 | 0.239 | 0．677＊＊ | | 三分钟双摇跳绳／次 | U12 | 317 | 0.702 | 0.617 | 0.319 | $0.637^{* *}$ | | | U13 | 274 | 0.917 | 0.301 | 0.218 | $0.612^{* *}$ | | | U14 | 331 | 0.521 | 0.646 | 0.167 | $0.596{ }^{*}$ | | 垂直纵跳／cm | U12 | 31.60 | 0.468 | 0.689 | 0.157 | 0.559 | | | U13 | 39.55 | 0.583 | 0.753 | 0.336 | $0.643^{* *}$ |
Figure 3 Sensitive Indicators and Thresholds for Physical Fitness Testing in Male Athletes
表 7 女运动员体能测试指标成绩 ROC 分析结果
Table 7 Results of ROC analysis of female athletes' performance in physical fitness test indicators
Table 7 ROC Analysis Results of Physical Fitness Test Indicators for Female Athletes
指标  norm 组别  groups 阈值  thresholds 敏感度  sensitivity 特异性  idiosyncrasy Youden 指数  Youden Index AUC
20 次低重心四点跑／s  20 low center of gravity four point runs/s U12 36.37 0.915 0.416 0.331 0.713 ∗ ∗ 0.713 ∗ ∗ 0.713^(****)0.713^{* *}
U13 35.21 0.813 0.567 0.380 0．723＊＊  0.723**
U14 35.14 0.756 0.507 0.263 0．652＊＊  0.652**
三分钟双摇跳绳／次  Three-minute double-rope skipping/repeat U12 316 0.787 0.604 0.391 0.744 ∗ ∗ 0.744 ∗ ∗ 0.744^(****)0.744^{* *}
U13 342 0.438 0.773 0.211 0．654＊  0.654*
U14 339 0.644 0.748 0.392 0.735 ∗ ∗ 0.735 ∗ ∗ 0.735^(****)0.735^{* *}
垂直纵跳／cm  Vertical longitudinal jump／cm U12 29.90 0.766 0.325 0.091 0.527
U13 30.50 0.792 0.397 0.189 0．612＊  0.612*
U14 39.50 0.444 0.793 0.237 0.595
30 米 × 5 × 5 xx5\times 5 往返跑／s  30 meters × 5 × 5 xx5\times 5 Round trip/s U12 30.41 0.66 0.701 0.361 0．699＊＊  0.699**
U13 29.39 0.542 0.887 0.429 0.770 ∗ ∗ 0.770 ∗ ∗ 0.770^(****)0.770^{* *}
U14 30.22 0.867 0.522 0.389 0.681 ∗ ∗ 0.681 ∗ ∗ 0.681^(****)0.681{ }^{* *}
指标 组别 阈值 敏感度 特异性 Youden 指数 AUC 20 次低重心四点跑／s U12 36.37 0.915 0.416 0.331 0.713^(****) U13 35.21 0.813 0.567 0.380 0．723＊＊ U14 35.14 0.756 0.507 0.263 0．652＊＊ 三分钟双摇跳绳／次 U12 316 0.787 0.604 0.391 0.744^(****) U13 342 0.438 0.773 0.211 0．654＊ U14 339 0.644 0.748 0.392 0.735^(****) 垂直纵跳／cm U12 29.90 0.766 0.325 0.091 0.527 U13 30.50 0.792 0.397 0.189 0．612＊ U14 39.50 0.444 0.793 0.237 0.595 30 米 xx5 往返跑／s U12 30.41 0.66 0.701 0.361 0．699＊＊ U13 29.39 0.542 0.887 0.429 0.770^(****) U14 30.22 0.867 0.522 0.389 0.681^(****)| 指标 | 组别 | 阈值 | 敏感度 | 特异性 | Youden 指数 | AUC | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | 20 次低重心四点跑／s | U12 | 36.37 | 0.915 | 0.416 | 0.331 | $0.713^{* *}$ | | | U13 | 35.21 | 0.813 | 0.567 | 0.380 | 0．723＊＊ | | | U14 | 35.14 | 0.756 | 0.507 | 0.263 | 0．652＊＊ | | 三分钟双摇跳绳／次 | U12 | 316 | 0.787 | 0.604 | 0.391 | $0.744^{* *}$ | | | U13 | 342 | 0.438 | 0.773 | 0.211 | 0．654＊ | | | U14 | 339 | 0.644 | 0.748 | 0.392 | $0.735^{* *}$ | | 垂直纵跳／cm | U12 | 29.90 | 0.766 | 0.325 | 0.091 | 0.527 | | | U13 | 30.50 | 0.792 | 0.397 | 0.189 | 0．612＊ | | | U14 | 39.50 | 0.444 | 0.793 | 0.237 | 0.595 | | 30 米 $\times 5$ 往返跑／s | U12 | 30.41 | 0.66 | 0.701 | 0.361 | 0．699＊＊ | | | U13 | 29.39 | 0.542 | 0.887 | 0.429 | $0.770^{* *}$ | | | U14 | 30.22 | 0.867 | 0.522 | 0.389 | $0.681{ }^{* *}$ |
U12 2.05 0.596 0.734 0.33 0.684 ∗ ∗ 0.684 ∗ ∗ 0.684^(****)0.684^{* *}
立定跳远 / m / m //m/ \mathrm{m}  Standing long jump / m / m //m/ \mathrm{m} U13 2.16 0.646 0.759 0.405 0.748 ∗ ∗ 0.748 ∗ ∗ 0.748^(****)0.748^{* *}
U14 2.18 0.467 0.770 0.237 0.664 ∗ ∗ 0.664 ∗ ∗ 0.664^(****)0.664^{* *}
U12 2.05 0.596 0.734 0.33 0.684^(****) 立定跳远 //m U13 2.16 0.646 0.759 0.405 0.748^(****) U14 2.18 0.467 0.770 0.237 0.664^(****)| | U12 | 2.05 | 0.596 | 0.734 | 0.33 | $0.684^{* *}$ | | :--- | :---: | :---: | :---: | :---: | :---: | :---: | | 立定跳远 $/ \mathrm{m}$ | U13 | 2.16 | 0.646 | 0.759 | 0.405 | $0.748^{* *}$ | | | U14 | 2.18 | 0.467 | 0.770 | 0.237 | $0.664^{* *}$ |
图4 女运动员体能测试敏感指标与阈值  Fig. 4 Sensitive Indicators and Thresholds for Physical Fitness Testing in Female Athletes

2.3 国少队优选预测的诊断评估  2.3 Diagnostic Assessment of Preferred Predictions for National Junior Teams

根据运动员体能敏感指标阈值（图 3，图4），将运动员分为两组后，进行二元逻辑回归。以进一步评估满足体能敏感指标阈值对于国少队运动员优选预测的影响。结果显示，男运动员符合体能敏感指标阈值要求的优选成功率是未达到体能敏感指标阈值要求的 2．4－4．8 倍 （
According to the athletes' physical fitness sensitivity index thresholds (Fig. 3, Fig. 4), binary logistic regression was performed after dividing the athletes into two groups. to further assess the effect of meeting the physical fitness sensitivity indicator thresholds on the prediction of national junior athletes' preference. The results showed that male athletes were 2.4-4.8 times more likely to be selected successfully if they met the fitness sensitivity thresholds than if they did not meet the thresholds ( O R = 2.456 ∼ 4.885 O R = 2.456 ∼ 4.885 OR=2.456∼4.885O R=2.456 \sim 4.885）；符合体能敏感指标阈值要求的女运动员优选成功率是未达到体能敏感指标阈值要求的 2．6－8．6 倍（ O R = 2.674 ∼ 8.690 O R = 2.674 ∼ 8.690 OR=2.674∼8.690O R=2.674 \sim 8.690）（表 8，表 9）。体能测试成绩对青少年羽毛球运动员的国少队优选资格有影响。
According to the athletes' physical fitness sensitivity index thresholds (Fig. 3, Fig. 4), binary logistic regression was performed after dividing the athletes into two groups. to further assess the effect of meeting the physical fitness sensitivity indicator thresholds on the prediction of national junior athletes' preference. The results showed that the preference success rate of male athletes who met the threshold of physical sensitivity was 2.4-4.8 times higher than that of female athletes who did not meet the threshold of physical sensitivity ( O R = 2.456 ∼ 4.885 O R = 2.456 ∼ 4.885 OR=2.456∼4.885O R=2.456 \sim 4.885 ), and the preference success rate of female athletes who met the threshold of physical sensitivity was 2.6-8.6 times higher than that of female athletes who did not meet the threshold of physical sensitivity ( O R = 2.674 ∼ 8.690 O R = 2.674 ∼ 8.690 OR=2.674∼8.690O R=2.674 \sim 8.690 ). The preferential success rate of female athletes who met the threshold of fitness sensitivity was 2.6-8.6 times higher than that of female athletes who did not meet the threshold of fitness sensitivity ( O R = 2.674 ∼ 8.690 O R = 2.674 ∼ 8.690 OR=2.674∼8.690O R=2.674 \sim 8.690 ) (Table 8, Table 9). Physical fitness test scores had an impact on the national junior team selection eligibility of junior badminton players.
表 8 男运动员基于截断值的二元逻辑回归结果 表 8 基于男运动员截断值的二元 Logistic 回归结果
Table 8 Binary Logistic Regression Results for Male Athletes Based on Cutoffs Table 8 Binary Logistic Regression Results for Male Athletes Based on Cutoffs
指标  norm 年龄组  age groups B B BB S E S E SES E O R O R ORO R 95 % CI 95 % CI 95%CI95 \% \mathrm{CI}
20 次低重心四点跑／s  20 low center of gravity four point runs/s U 12 1.299 1.014 3.667 0.502 ∼ 26.756 0.502 ∼ 26.756 0.502∼26.7560.502 \sim 26.756
U 1 3 U 1 3 U13\mathbf{U 1 3} 1 . 4 6 9 ∗ ∗ 1 . 4 6 9 ∗ ∗ 1.469^(****)\mathbf{1 . 4 6 9}^{* *} 0 . 3 5 4 0 . 3 5 4 0.354\mathbf{0 . 3 5 4} 4 . 3 4 6 4 . 3 4 6 4.346\mathbf{4 . 3 4 6} 2 . 1 7 2 ∼ 8 . 6 9 7 2 . 1 7 2 ∼ 8 . 6 9 7 2.172∼8.697\mathbf{2 . 1 7 2 \sim 8 . 6 9 7}
U14 1 . 3 0 8 ∗ ∗ 1 . 3 0 8 ∗ ∗ 1.308^(****)\mathbf{1 . 3 0 8}^{* *} 0 . 3 6 7 0 . 3 6 7 0.367\mathbf{0 . 3 6 7} 3 . 7 0 0 3 . 7 0 0 3.700\mathbf{3 . 7 0 0} 1 . 8 0 1 7 . 6 0 2 1 . 8 0 1 7 . 6 0 2 1.8017.602\mathbf{1 . 8 0 1 ~ 7 . 6 0 2}
指标 年龄组 B SE OR 95%CI 20 次低重心四点跑／s U 12 1.299 1.014 3.667 0.502∼26.756 U13 1.469^(****) 0.354 4.346 2.172∼8.697 U14 1.308^(****) 0.367 3.700 1.8017.602| 指标 | 年龄组 | $B$ | $S E$ | $O R$ | $95 \% \mathrm{CI}$ | | :---: | :---: | :---: | :---: | :---: | :---: | | 20 次低重心四点跑／s | U 12 | 1.299 | 1.014 | 3.667 | $0.502 \sim 26.756$ | | | $\mathbf{U 1 3}$ | $\mathbf{1 . 4 6 9}^{* *}$ | $\mathbf{0 . 3 5 4}$ | $\mathbf{4 . 3 4 6}$ | $\mathbf{2 . 1 7 2 \sim 8 . 6 9 7}$ | | | U14 | $\mathbf{1 . 3 0 8}^{* *}$ | $\mathbf{0 . 3 6 7}$ | $\mathbf{3 . 7 0 0}$ | $\mathbf{1 . 8 0 1 ~ 7 . 6 0 2}$ |
U12 1.586 ∗ ∗ 1.586 ∗ ∗ 1.586^(****)1.586^{* *} 0.379 4.885 2.324 ∼ 10.266 2.324 ∼ 10.266 2.324∼10.2662.324 \sim 10.266
30 米 × 5 × 5 xx5\times 5 往返跑 / s / s //s/ \mathrm{s}
30 meters × 5 × 5 xx5\times 5 Round trip / s / s //s/ \mathrm{s} 		U 13 1.374 ∗ ∗ 1.374 ∗ ∗ 1.374^(****)1.374^{* *} 0.344 3.950 2.014 ∼ 7.746 2.014 ∼ 7.746 2.014∼7.7462.014 \sim 7.746
U 14 0.966 ∗ 0.966 ∗ 0.966^(**)0.966^{*} 0.386 2.628 1.233 ∼ 5.603 1.233 ∼ 5.603 1.233∼5.6031.233 \sim 5.603
U 12 1.055 ∗ ∗ 1.055 ∗ ∗ 1.055^(****)1.055^{* *} 0.389 2.873 1.340 ∼ 6.160 1.340 ∼ 6.160 1.340∼6.1601.340 \sim 6.160
立定跳远 / m / m //m/ \mathrm{m}  Standing long jump / m / m //m/ \mathrm{m} U 13 1.122 ∗ ∗ 1.122 ∗ ∗ 1.122^(****)1.122^{* *} 0.337 3.070 1.586 ∼ 5.944 1.586 ∼ 5.944 1.586∼5.9441.586 \sim 5.944
U 14 0.898 ∗ 0.898 ∗ 0.898^(**)0.898^{*} 0.351 2.456 1.235 ∼ 4.882 1.235 ∼ 4.882 1.235∼4.8821.235 \sim 4.882
U12 1.586^(****) 0.379 4.885 2.324∼10.266 30 米 xx5 往返跑 //s U 13 1.374^(****) 0.344 3.950 2.014∼7.746 U 14 0.966^(**) 0.386 2.628 1.233∼5.603 U 12 1.055^(****) 0.389 2.873 1.340∼6.160 立定跳远 //m U 13 1.122^(****) 0.337 3.070 1.586∼5.944 U 14 0.898^(**) 0.351 2.456 1.235∼4.882 | | U12 | $1.586^{* *}$ | 0.379 | 4.885 | $2.324 \sim 10.266$ | | :---: | :---: | :--- | :--- | :--- | :--- | | 30 米 $\times 5$ 往返跑 $/ \mathrm{s}$ | U 13 | $1.374^{* *}$ | 0.344 | 3.950 | $2.014 \sim 7.746$ | | | U 14 | $0.966^{*}$ | 0.386 | 2.628 | $1.233 \sim 5.603$ | | | U 12 | $1.055^{* *}$ | 0.389 | 2.873 | $1.340 \sim 6.160$ | | 立定跳远 $/ \mathrm{m}$ | U 13 | $1.122^{* *}$ | 0.337 | 3.070 | $1.586 \sim 5.944$ | | | U 14 | $0.898^{*}$ | 0.351 | 2.456 | $1.235 \sim 4.882$ | | | | | | | |
表9 女运动员基于截断值的二元逻辑回归结果  Table 9 Results of binary logistic regression based on truncated values for female athletes
Table 9 Binary Logistic Regression Results for Female Athletes Based on Cut－off Values
Table 9 Binary Logistic Regression Results for Female Athletes Based on Cut-off Values
指标  norm 年龄组  age groups B S E S E SES E OR 95\％CI  95% CI
20 次低重心四点跑／s  20 low center of gravity four point runs/s U12 2.034 ∗ ∗ 2.034 ∗ ∗ 2.034****2.034 * * 0.548 7.644 2．613～22．365  2.613-22.365
U13 1．737＊＊  1. 737** 0.407 5.683 2．559～12．619  2.559-12.619
U14 1．158＊＊  1. 158*** 0.387 3.183 1．491～6．796  1.491-6.796
三分钟双摇跳绳／次  Three-minute double-rope skipping/repeat U12 1．730＊＊  1.730** 0.393 5.641 2．613～12．178  2.613-12.178
U13 0．983＊＊  0.983** 0.354 2.674 1．337～5．346  1.337-5.346
U14 1.693 ∗ ∗ 1.693 ∗ ∗ 1.693****1.693 * * 0.369 5.437 2．638～11．208  2.638 - 11.208
30 米 × 5 × 5 xx5\times 5 往返跑／s  30 meters × 5 × 5 xx5\times 5 Round trip/s U12 1．515＊＊  1.515** 0.355 4.549 2．270～9．115  2.270-9.115
U13 2．162＊＊  2. 162** 0.388 8.690 4．060～18．599  4.060-18.599
U14 1．960＊＊  1. 960*** 0.471 7.100 2．821～17．870  2.821-17.870
立定跳远／m  Standing long jump/m U12 1.365 ∗ ∗ 1.365 ∗ ∗ 1.365^(****)1.365{ }^{* *} 0.349 3.915 1．976～7．756  1.976-7.756
U13 1．668＊＊  1. 668** 0.373 5.301 2．550～11．018  2.550-11.018
U14 0．997＊＊  0.997** 0.363 2.710 1．330～5．520  1.330-5.520
指标 年龄组 B SE OR 95\％CI 20 次低重心四点跑／s U12 2.034**** 0.548 7.644 2．613～22．365 U13 1．737＊＊ 0.407 5.683 2．559～12．619 U14 1．158＊＊ 0.387 3.183 1．491～6．796 三分钟双摇跳绳／次 U12 1．730＊＊ 0.393 5.641 2．613～12．178 U13 0．983＊＊ 0.354 2.674 1．337～5．346 U14 1.693**** 0.369 5.437 2．638～11．208 30 米 xx5 往返跑／s U12 1．515＊＊ 0.355 4.549 2．270～9．115 U13 2．162＊＊ 0.388 8.690 4．060～18．599 U14 1．960＊＊ 0.471 7.100 2．821～17．870 立定跳远／m U12 1.365^(****) 0.349 3.915 1．976～7．756 U13 1．668＊＊ 0.373 5.301 2．550～11．018 U14 0．997＊＊ 0.363 2.710 1．330～5．520| 指标 | 年龄组 | B | $S E$ | OR | 95\％CI | | :---: | :---: | :---: | :---: | :---: | :---: | | 20 次低重心四点跑／s | U12 | $2.034 * *$ | 0.548 | 7.644 | 2．613～22．365 | | | U13 | 1．737＊＊ | 0.407 | 5.683 | 2．559～12．619 | | | U14 | 1．158＊＊ | 0.387 | 3.183 | 1．491～6．796 | | 三分钟双摇跳绳／次 | U12 | 1．730＊＊ | 0.393 | 5.641 | 2．613～12．178 | | | U13 | 0．983＊＊ | 0.354 | 2.674 | 1．337～5．346 | | | U14 | $1.693 * *$ | 0.369 | 5.437 | 2．638～11．208 | | 30 米 $\times 5$ 往返跑／s | U12 | 1．515＊＊ | 0.355 | 4.549 | 2．270～9．115 | | | U13 | 2．162＊＊ | 0.388 | 8.690 | 4．060～18．599 | | | U14 | 1．960＊＊ | 0.471 | 7.100 | 2．821～17．870 | | 立定跳远／m | U12 | $1.365{ }^{* *}$ | 0.349 | 3.915 | 1．976～7．756 | | | U13 | 1．668＊＊ | 0.373 | 5.301 | 2．550～11．018 | | | U14 | 0．997＊＊ | 0.363 | 2.710 | 1．330～5．520 |

2.4 国少运动员体能敏感指标成绩的变化  2.4 Changes in the performance of national junior athletes on fitness-sensitive indicators

本研究调查对象范围涉及 5 个年龄段运动员（即2008－2012年出生的运动员），为深入分析优选国少队的体能成绩发展趋势，特选取2009年（2022年U13—2023年U14），2010年（2022 年 U12—2024 年 U14），2011 年（2023 年 U12—2024 年 U13）出生的国少运动员连续两年或三年的体能敏感指标成绩进行对比。
The scope of this study involves 5 age groups of athletes (i.e., athletes born in 2008-2012). In order to deeply analyze the development trend of the physical performance of the preferred national junior teams, the physical performance of the national junior athletes born in 2009 (U13-2023 U14), 2010 (U12-2022 U14), and 2011 (U12-2024 U13) was selected for comparison in two or three consecutive years. -2024 U14), 2011 (2023 U12-2024 U13) born national junior athletes in two or three consecutive years of physical fitness sensitive index performance for comparison.

2．4．1 国少队—2009年出生运动员体能敏感指标成绩差异分析
2.4.1 Analysis of Variance in Performance on Fitness Sensitive Indicators for National Junior Teams - 2009 Birth Year Athletes

男运动员在 U13－U14 间，体能敏感指标成绩均不存在显著差异（ P > 0.05 P > 0.05 P > 0.05P>0.05）。女运动员在 20 次低重心四点跑指标上成绩下降明显， 13 岁时成绩显著高于 14 岁成绩（ P < 0.01 P < 0.01 P < 0.01P<0.01）（表 10）。
There were no significant differences in fitness-sensitive performance between U13 and U14 in male athletes ( P > 0.05 P > 0.05 P > 0.05P>0.05 ). Female athletes showed a significant decrease in performance on the 20 low center of gravity four-point run, with significantly higher performance at age 13 than at age 14 ( P < 0.01 P < 0.01 P < 0.01P<0.01 ) (Table 10).
表 10 国少队—2009年出生运动员体能敏感指标成绩差异分析 表10 国家未成年队2009年出生运动员体能敏感指标差异分析
Table 10 Analysis of Variance in Performance of National Minors - 2009 Birth Athletes on Fitness Sensitive Indicators Table 10 Analysis of Variance in Performance of National Minors - 2009 Birth Athletes on Fitness Sensitive Indicators
性别  distinguishing between the sexes 指标  norm 2022 年 U13  2022 U13 2023 年 U14  2023 U14 t
20 次低重心四点跑/s  20 low center of gravity four point run/s 33.02 ± 1.54 33.02 ± 1.54 33.02+-1.5433.02 \pm 1.54 33.92 ± 2.41 33.92 ± 2.41 33.92+-2.4133.92 \pm 2.41 -1.245
男  male 30 米 × 5 × 5 xx5\times 5往返跑/s  30 meters × 5 × 5 xx5\times 5 Round trip/s 28.10 ± 1.58 28.10 ± 1.58 28.10+-1.5828.10 \pm 1.58 27.91 ± 1.41 27.91 ± 1.41 27.91+-1.4127.91 \pm 1.41 0.351
立定跳远 / m / m //m/ \mathrm{m}  Standing long jump / m / m //m/ \mathrm{m} 2.37 ± 0.18 2.37 ± 0.18 2.37+-0.182.37 \pm 0.18 2.45 ± 0.11 2.45 ± 0.11 2.45+-0.112.45 \pm 0.11 -1.576
2 0 2 0 20\mathbf{2 0}次低重心四点跑/s   2 0 2 0 20\mathbf{2 0} Sub-low center of gravity four point run/s 3 3 . 5 0 ± 1 . 2 7 3 3 . 5 0 ± 1 . 2 7 33.50+-1.27\mathbf{3 3 . 5 0} \pm \mathbf{1 . 2 7} 3 5 . 1 0 ± 2 . 1 0 3 5 . 1 0 ± 2 . 1 0 35.10+-2.10\mathbf{3 5 . 1 0 \pm \mathbf { 2 . 1 0 }} − 2 . 5 5 7 ∗ − 2 . 5 5 7 ∗ -2.557^(**)\mathbf{- 2 . 5 5 7 ^ { * }}
三分钟双摇跳绳／次  Three-minute double-rope skipping/repeat 355.81 ± 28.05 355.81 ± 28.05 355.81+-28.05355.81 \pm 28.05 329.21 ± 50.00 329.21 ± 50.00 329.21+-50.00329.21 \pm 50.00 1.827
30 米 × 5 × 5 xx5\times 5往返跑/s  30 meters × 5 × 5 xx5\times 5 Round trip/s 29.05 ± 0.80 29.05 ± 0.80 29.05+-0.8029.05 \pm 0.80 29.80 ± 1.41 29.80 ± 1.41 29.80+-1.4129.80 \pm 1.41 -1.816
立定跳远 / m / m //m/ \mathrm{m}  Standing long jump / m / m //m/ \mathrm{m} 2.17 ± 0.53 2.17 ± 0.53 2.17+-0.532.17 \pm 0.53 2.12 ± 0.13 2.12 ± 0.13 2.12+-0.132.12 \pm 0.13 1.571
性别 指标 2022 年 U13 2023 年 U14 t 20 次低重心四点跑／s 33.02+-1.54 33.92+-2.41 -1.245 男 30 米 xx5 往返跑／s 28.10+-1.58 27.91+-1.41 0.351 立定跳远 //m 2.37+-0.18 2.45+-0.11 -1.576 20 次低重心四点跑／s 33.50+-1.27 35.10+-2.10 -2.557^(**) 三分钟双摇跳绳／次 355.81+-28.05 329.21+-50.00 1.827 30 米 xx5 往返跑／s 29.05+-0.80 29.80+-1.41 -1.816 立定跳远 //m 2.17+-0.53 2.12+-0.13 1.571| 性别 | 指标 | 2022 年 U13 | 2023 年 U14 | t | | :---: | :---: | :---: | :---: | :---: | | | 20 次低重心四点跑／s | $33.02 \pm 1.54$ | $33.92 \pm 2.41$ | -1.245 | | 男 | 30 米 $\times 5$ 往返跑／s | $28.10 \pm 1.58$ | $27.91 \pm 1.41$ | 0.351 | | | 立定跳远 $/ \mathrm{m}$ | $2.37 \pm 0.18$ | $2.45 \pm 0.11$ | -1.576 | | | $\mathbf{2 0}$ 次低重心四点跑／s | $\mathbf{3 3 . 5 0} \pm \mathbf{1 . 2 7}$ | $\mathbf{3 5 . 1 0 \pm \mathbf { 2 . 1 0 }}$ | $\mathbf{- 2 . 5 5 7 ^ { * }}$ | | | 三分钟双摇跳绳／次 | $355.81 \pm 28.05$ | $329.21 \pm 50.00$ | 1.827 | | | 30 米 $\times 5$ 往返跑／s | $29.05 \pm 0.80$ | $29.80 \pm 1.41$ | -1.816 | | | 立定跳远 $/ \mathrm{m}$ | $2.17 \pm 0.53$ | $2.12 \pm 0.13$ | 1.571 |
2．4．2 国少队—2010年出生运动员体能敏感指标成绩差异分析 2010年出生运动员分别对应 2022－2024 年全国 U 系列羽毛球比赛 U12—U14，随年龄增长，男运动员在 20 次低重心四点跑， 30 米
2.4.2 National Junior Team - 2010-born athletes physical sensitivity index performance difference analysis 2010-born athletes corresponded to the 2022-2024 national U series badminton tournament U12-U14, respectively, with age, male athletes in the 20 low center of gravity four-point run, the 30 meters × 5 × 5 xx5\times 5往返跑敏感指标上的成绩变化不存在显著差异 （ P > 0.05 P > 0.05 P > 0.05P>0.05）， 12 岁时立定跳远成绩与 13 岁， 14 岁成绩存在显著差异（ P < 0.05 P < 0.05 P < 0.05P<0.05），且逐年提高；女运动员 4 项敏感指标中均不存在显著差异（ P > 0.05 P > 0.05 P > 0.05P>0.05）（表11）。
2.4.2 National Junior Team - 2010-born athletes physical fitness sensitive indicators performance difference analysis 2010-born athletes correspond to the 2022-2024 national U series badminton tournament U12-U14, with the age of male athletes in the 20 low center of gravity four-point run, 30 m × 5 × 5 xx5\times 5 back and forth run sensitive indicators change does not exist a significant difference ( P > 0.05 P > 0.05 P > 0.05P>0.05 ), 12-year-old standing long jump performance and 13-year-old, 14-year-old performance in the standing long jump. There was no significant difference in the performance of male athletes in 20 times low center of gravity four-point run, 30 meters × 5 × 5 xx5\times 5 back and forth run ( P > 0.05 P > 0.05 P > 0.05P>0.05 ), and there was a significant difference between the standing long jump performance of male athletes at the age of 12 years old and that of male athletes at the age of 13 years old and 14 years old ( P < 0.05 P < 0.05 P < 0.05P<0.05 ) with the increase of the results of each year, and there was no significant difference between the performance of female athletes in the four sensitive indexes ( P > 0.05 P > 0.05 P > 0.05P>0.05 ) (Table 11).
表11国少队—2010年出生运动员体能敏感指标成绩差异分析 表11
Table 11 Analysis of differences in performance on fitness-sensitive indicators for National Junior Team-2010 birth athletes Table 11
2010年出生的国幼队运动员体能敏感指标差异分析
Analysis of differences in fitness sensitivity indexes among National Junior Team athletes born in 2010
性别  distinguishing between the sexes 指标  norm 2022 年 U12  2022 U12 2023 年 U13  2023 U13 2024 年 U14  2024 U14 F F FF
20 次低重心四点跑 / s / s //s/ \mathrm{s}  20 low center of gravity four point runs / s / s //s/ \mathrm{s} 34.00 ± 1.83 34.00 ± 1.83 34.00+-1.8334.00 \pm 1.83 34.10 ± 1.85 34.10 ± 1.85 34.10+-1.8534.10 \pm 1.85 31.53 ± 7.70 31.53 ± 7.70 31.53+-7.7031.53 \pm 7.70 1.536
男  male 30 米 × 5 × 5 xx5\times 5往返跑/s  30 meters × 5 × 5 xx5\times 5 Round trip/s 28.96 ± 2.77 28.96 ± 2.77 28.96+-2.7728.96 \pm 2.77 28.49 ± 1.27 28.49 ± 1.27 28.49+-1.2728.49 \pm 1.27 28.77 ± 1.31 28.77 ± 1.31 28.77+-1.3128.77 \pm 1.31 0.240
立定跳远/m  Standing long jump/m 2 . 0 9 ± 0 . 1 5 2 . 0 9 ± 0 . 1 5 2.09+-0.15\mathbf{2 . 0 9} \pm \mathbf{0 . 1 5} 2 . 2 7 ± 0 . 1 8 2 . 2 7 ± 0 . 1 8 2.27+-0.18\mathbf{2 . 2 7} \pm \mathbf{0 . 1 8} 2 . 3 1 ± 0 . 1 8 2 . 3 1 ± 0 . 1 8 2.31+-0.18\mathbf{2 . 3 1} \pm \mathbf{0 . 1 8} 7 . 1 3 5 ∗ ∗ ab 7 . 1 3 5 ∗ ∗ ab 7.135^(****ab)\mathbf{7 . 1 3 5}^{* * \mathrm{ab}}
次低重心四点跑/s  Sub-low center of gravity four point run/s 33.14 ± 1.74 33.14 ± 1.74 33.14+-1.7433.14 \pm 1.74 34.68 ± 2.74 34.68 ± 2.74 34.68+-2.7434.68 \pm 2.74 34.25 ± 1.56 34.25 ± 1.56 34.25+-1.5634.25 \pm 1.56 0.308
三分钟双摇跳绳／次  Three-minute double-rope skipping/repeat 334.5 ± 48.74 334.5 ± 48.74 334.5+-48.74334.5 \pm 48.74 317.69 ± 45.86 317.69 ± 45.86 317.69+-45.86317.69 \pm 45.86 346.13 ± 28.41 346.13 ± 28.41 346.13+-28.41346.13 \pm 28.41 1.856
30 米 × 5 × 5 xx5\times 5往返跑/s  30 meters × 5 × 5 xx5\times 5 Round trip/s 29.53 ± 1.25 29.53 ± 1.25 29.53+-1.2529.53 \pm 1.25 29.31 ± 1.13 29.31 ± 1.13 29.31+-1.1329.31 \pm 1.13 29.42 ± 1.12 29.42 ± 1.12 29.42+-1.1229.42 \pm 1.12 0.144
立定跳远 / m / m //m/ \mathrm{m}  Standing long jump / m / m //m/ \mathrm{m} 2.14 ± 0.14 2.14 ± 0.14 2.14+-0.142.14 \pm 0.14 2.16 ± 0.13 2.16 ± 0.13 2.16+-0.132.16 \pm 0.13 2.16 ± 0.12 2.16 ± 0.12 2.16+-0.122.16 \pm 0.12 0.215
性别 指标 2022 年 U12 2023 年 U13 2024 年 U14 F 20 次低重心四点跑 //s 34.00+-1.83 34.10+-1.85 31.53+-7.70 1.536 男 30 米 xx5 往返跑／s 28.96+-2.77 28.49+-1.27 28.77+-1.31 0.240 立定跳远／m 2.09+-0.15 2.27+-0.18 2.31+-0.18 7.135^(****ab) 次低重心四点跑／s 33.14+-1.74 34.68+-2.74 34.25+-1.56 0.308 三分钟双摇跳绳／次 334.5+-48.74 317.69+-45.86 346.13+-28.41 1.856 30 米 xx5 往返跑／s 29.53+-1.25 29.31+-1.13 29.42+-1.12 0.144 立定跳远 //m 2.14+-0.14 2.16+-0.13 2.16+-0.12 0.215| 性别 | 指标 | 2022 年 U12 | 2023 年 U13 | 2024 年 U14 | $F$ | | :---: | :---: | :---: | :---: | :---: | :---: | | | 20 次低重心四点跑 $/ \mathrm{s}$ | $34.00 \pm 1.83$ | $34.10 \pm 1.85$ | $31.53 \pm 7.70$ | 1.536 | | 男 | 30 米 $\times 5$ 往返跑／s | $28.96 \pm 2.77$ | $28.49 \pm 1.27$ | $28.77 \pm 1.31$ | 0.240 | | | 立定跳远／m | $\mathbf{2 . 0 9} \pm \mathbf{0 . 1 5}$ | $\mathbf{2 . 2 7} \pm \mathbf{0 . 1 8}$ | $\mathbf{2 . 3 1} \pm \mathbf{0 . 1 8}$ | $\mathbf{7 . 1 3 5}^{* * \mathrm{ab}}$ | | 次低重心四点跑／s | $33.14 \pm 1.74$ | $34.68 \pm 2.74$ | $34.25 \pm 1.56$ | 0.308 | | | | 三分钟双摇跳绳／次 | $334.5 \pm 48.74$ | $317.69 \pm 45.86$ | $346.13 \pm 28.41$ | 1.856 | | | 30 米 $\times 5$ 往返跑／s | $29.53 \pm 1.25$ | $29.31 \pm 1.13$ | $29.42 \pm 1.12$ | 0.144 | | | 立定跳远 $/ \mathrm{m}$ | $2.14 \pm 0.14$ | $2.16 \pm 0.13$ | $2.16 \pm 0.12$ | 0.215 |

2．4．3 国少队—2011年出生国少运动员体能敏感指标成绩差异分析
2.4.3 Analysis of Variance in Performance on Fitness Sensitive Indicators for National Junior Teams - 2011 Birth National Junior Athletes

2011 年出生的男运动员在 U2—U13 组中 20 次低重心四点跑， 30 米 × 5 × 5 xx5\times 5往返跑 2 项指标成绩不存在显著差异（ P > 0.05 P > 0.05 P > 0.05P>0.05），立定跳远成绩有显著提高（ P < 0.01 P < 0.01 P < 0.01P<0.01）；在女运动员中， 20次低重心四点跑，三分钟双摇跳绳， 30 米 × 5 × 5 xx5\times 5往返跑成绩有所下降，立定跳远成绩提高，但 4
Among the male athletes born in 2011, there was no significant difference in the performance of 20 times low center of gravity four-point run, 30m × 5 × 5 xx5\times 5 back and forth run ( P > 0.05 P > 0.05 P > 0.05P>0.05 ), and there was a significant improvement in standing long jump ( P < 0.01 P < 0.01 P < 0.01P<0.01 ) in the U2-U13 group; among the female athletes, there were no significant differences in the performance of 20 times low center of gravity four-point run, three-minute double-swing rope skipping, and 30m × 5 × 5 xx5\times 5 back and forth run ( × 5 × 5 xx5\times 5). ( P < 0.01 P < 0.01 P < 0.01P<0.01 ); among female athletes, the 20 low center of gravity four-point run, the three-minute double-crank rope skipping, and the 30-meter × 5 × 5 xx5\times 5 back-and-forth run declined, and the standing long jump improved but 4
项体能敏感指标在 12 − 13 12 − 13 12-1312-13岁之间均不存在显著差异（ P > 0.05 P > 0.05 P > 0.05P>0.05）（表 12）。 表 12 国少队一2011年出生运动员体能敏感指标成绩差异分析
) (Table 12). Table 12 Analysis of differences in the performance of National Junior Team I 2011-born athletes on fitness-sensitive indicators
表 12 2011年出生的运动员国家未成年队体能敏感指标差异分析
Table 12 Analysis of differences in fitness-sensitive indicators for national underage teams of athletes born in 2011
性别  distinguishing between the sexes 指标  norm 2023 年 U12  2023 U12 2024 年 U13  2024 U13 t
20 次低重心四点跑/s  20 low center of gravity four point run/s 34.80 ± 1.67 34.80 ± 1.67 34.80+-1.6734.80 \pm 1.67 34.59 ± 2.08 34.59 ± 2.08 34.59+-2.0834.59 \pm 2.08 0.307
男  male 30 米 × 5 × 5 xx5\times 5往返跑/s  30 meters × 5 × 5 xx5\times 5 Round trip/s 29.22 ± 1.11 29.22 ± 1.11 29.22+-1.1129.22 \pm 1.11 29.30 ± 2.00 29.30 ± 2.00 29.30+-2.0029.30 \pm 2.00 -0.137
立定跳远 / m / m //m/ \mathbf{m}  Standing long jump / m / m //m/ \mathbf{m} 2 . 0 9 ± 0 . 1 4 2 . 0 9 ± 0 . 1 4 2.09+-0.14\mathbf{2 . 0 9} \pm \mathbf{0 . 1 4} 2 . 2 6 ± 0 . 1 4 2 . 2 6 ± 0 . 1 4 2.26+-0.14\mathbf{2 . 2 6} \pm \mathbf{0 . 1 4} − 3 . 4 4 5 − 3 . 4 4 5 -3.445\mathbf{- 3 . 4 4 5}
20 次低重心四点跑/s  20 low center of gravity four point run/s 34.60 ± 1.25 34.60 ± 1.25 34.60+-1.2534.60 \pm 1.25 34.80 ± 1.56 34.80 ± 1.56 34.80+-1.5634.80 \pm 1.56 -0.388
三分钟双摇跳绳／次  Three-minute double-rope skipping/repeat 335.00 ± 24.76 335.00 ± 24.76 335.00+-24.76335.00 \pm 24.76 309.88 ± 42.77 309.88 ± 42.77 309.88+-42.77309.88 \pm 42.77 1.984
女  daughter 30 米 × 5 × 5 xx5\times 5往返跑 / s / s //s/ \mathrm{s}
30 meters × 5 × 5 xx5\times 5 Round trip / s / s //s/ \mathrm{s} 		29.75 ± 0.84 29.75 ± 0.84 29.75+-0.8429.75 \pm 0.84 30.04 ± 1.06 30.04 ± 1.06 30.04+-1.0630.04 \pm 1.06 -0.851
立定跳远 / m / m //m/ \mathrm{m}  Standing long jump / m / m //m/ \mathrm{m} 2.06 ± 0.12 2.06 ± 0.12 2.06+-0.122.06 \pm 0.12 2.10 ± 0.11 2.10 ± 0.11 2.10+-0.112.10 \pm 0.11 -0.969
性别 指标 2023 年 U12 2024 年 U13 t 20 次低重心四点跑／s 34.80+-1.67 34.59+-2.08 0.307 男 30 米 xx5 往返跑／s 29.22+-1.11 29.30+-2.00 -0.137 立定跳远 //m 2.09+-0.14 2.26+-0.14 -3.445 20 次低重心四点跑／s 34.60+-1.25 34.80+-1.56 -0.388 三分钟双摇跳绳／次 335.00+-24.76 309.88+-42.77 1.984 女 30 米 xx5 往返跑 //s 29.75+-0.84 30.04+-1.06 -0.851 立定跳远 //m 2.06+-0.12 2.10+-0.11 -0.969| 性别 | 指标 | 2023 年 U12 | 2024 年 U13 | t | | :---: | :---: | :---: | :---: | :---: | | | 20 次低重心四点跑／s | $34.80 \pm 1.67$ | $34.59 \pm 2.08$ | 0.307 | | 男 | 30 米 $\times 5$ 往返跑／s | $29.22 \pm 1.11$ | $29.30 \pm 2.00$ | -0.137 | | | 立定跳远 $/ \mathbf{m}$ | $\mathbf{2 . 0 9} \pm \mathbf{0 . 1 4}$ | $\mathbf{2 . 2 6} \pm \mathbf{0 . 1 4}$ | $\mathbf{- 3 . 4 4 5}$ | | | 20 次低重心四点跑／s | $34.60 \pm 1.25$ | $34.80 \pm 1.56$ | -0.388 | | | 三分钟双摇跳绳／次 | $335.00 \pm 24.76$ | $309.88 \pm 42.77$ | 1.984 | | 女 | 30 米 $\times 5$ 往返跑 $/ \mathrm{s}$ | $29.75 \pm 0.84$ | $30.04 \pm 1.06$ | -0.851 | | | 立定跳远 $/ \mathrm{m}$ | $2.06 \pm 0.12$ | $2.10 \pm 0.11$ | -0.969 |

3 讨论  3 Discussion

3.1 体能指标敏感度  3.1 Sensitivity of physical fitness indicators

通过对运动员的测试成绩进行分析，确立了各项体能敏感指标的阈值。这些阈值不仅为运动员的体能评估提供了明确的量化标准，也为教练员制定个性化的训练计划提供了科学依据。不同体能素质指标在运动员优选中的敏感度存在差异。具体而言，男运动员在 20 次低重心四点跑上的 AUC 值最高，表明该指标对于男运动员的体能评估具有较强的分辨力；而女运动员则在 30 米 × 5 × 5 xx5\times 5往返跑上的 AUC 值最高，反映出该指标对女运动员体能评估的重要性。相比之下，男女运动员在垂直纵跳上的 AUC 值均较低，这可能与羽毛球运动的特点有关。羽毛球运动更注重运动员的灵敏性，协调性和耐力等素质。
By analyzing the test scores of the athletes, the thresholds of various fitness-sensitive indicators were established. These thresholds not only provide a clear quantitative standard for athletes' physical fitness assessment, but also provide a scientific basis for coaches to formulate individualized training plans. There are differences in the sensitivity of different physical fitness indicators in athlete preference. Specifically, male athletes showed the highest AUC values in the 20 low center of gravity four-point run, indicating that this index has a strong discriminative power in the assessment of male athletes' physical fitness, while female athletes showed the highest AUC values in the 30-meter × 5 × 5 xx5\times 5 round-trip run, reflecting the importance of this index in the assessment of female athletes' physical fitness. In contrast, both male and female athletes had lower AUC values in vertical jump, which may be related to the characteristics of badminton. Badminton pays more attention to athletes' agility, coordination and endurance.
针对青少年羽毛球运动员，体能只是竞技能力构成的一个方面，各项体能测试结果中 AUC值在 0.527 ∼ 0.770 0.527 ∼ 0.770 0.527∼0.7700.527 \sim 0.770之间，未达到 0.9 以上，也反映了诸如技战术能力等其他因素对运动员运动表现的影响。
For young badminton players, physical fitness is only one aspect of the composition of the competitive ability, the results of the physical fitness test AUC values between 0.527 ∼ 0.770 0.527 ∼ 0.770 0.527∼0.7700.527 \sim 0.770 , did not reach more than 0.9, but also reflects the influence of other factors such as technical and tactical ability on the athletes' performance.

3.2 体能敏感指标与运动员优选的关系  3.2 Relationship between physical fitness sensitivity indicators and athlete preferences

本研究旨在通过体能敏感指标的筛选与评估，为青少年羽毛球运动员的优选提供科学依据。通过对优选组与淘汰组运动员的体能成绩进行对比分析，我们发现优选组成绩均显著优于淘汰组成绩，且在不同年龄组中均存在显著性差异。这一结果进一步验证了体能敏感指标在运动员优选中的重要性。在男运动员中，除 U 12 组垂直纵跳，U13 组 30 米 × 5 × 5 xx5\times 5往返跑，U14 组 20 次低重心四点跑和垂直纵跳指标外，其他不同年龄组的各项指标在优选组与淘汰组之间均存在显著差异。在女运动员中，除 U12，U14 组的垂直纵跳指标外，其余四项指标在优选组与淘汰组之间也存在显著差异。这些结果表明，体能敏感指标不仅能够反映运动员的体能水平，
The aim of this study is to provide a scientific basis for the preferential selection of young badminton players through the screening and evaluation of physical fitness sensitive indexes. By comparing and analyzing the physical performance of athletes in the preferred group and the eliminated group, we found that the performance of the preferred group was significantly better than that of the eliminated group, and there were significant differences in different age groups. This result further verifies the importance of physical sensitivity index in athlete selection. In male athletes, except for vertical jump in group U12, 30 meters × 5 × 5 xx5\times 5 back and forth run in group U13, 20 times of low center of gravity four-point run and vertical jump in group U14, there were significant differences between the selection and elimination groups in all the indicators in different age groups. In female athletes, except for vertical jump in U12 and U14 groups, there were also significant differences between the selected and eliminated groups in the other four indicators. These results indicate that the fitness-sensitive indexes can not only reflect the fitness level of athletes, but also
还能够作为运动员优选的重要依据。 此外，男运动员符合体能敏感指标阈值要求的优选成功率是未达到体能敏感指标阈值要求的 2．4－4．8 倍（
It can also be used as an important basis for athlete selection. In addition, male athletes were 2.4-4.8 times more successful in being selected for meeting the thresholds for fitness sensitivity indicators than those who did not meet the thresholds for fitness sensitivity indicators ( OR = 2.456 ∼ 4.885 OR = 2.456 ∼ 4.885 OR=2.456∼4.885\mathrm{OR}=2.456 \sim 4.885），女运动员则是 2．6－8．6 倍（ OR = 2.674 ∼ 8.690 OR = 2.674 ∼ 8.690 OR=2.674∼8.690\mathrm{OR}=2.674 \sim 8.690）。这一结果充分说明了体能敏感指标阈值在预测青少年羽毛球运动员优选资格中的重要性。体能素质优秀的运动员，在比赛中往往能够更占据优势。本研究提供的青少年羽毛球运动员的体能敏感指标阈值，与先前只提供运动员平均值的研究相比，对体能训练尤其是对平衡不同体能训练内容和整体训练计划的统筹安排更具参考价值，教练员可以根据运动员的体能测试结果，结合敏感指标阈值，在训练中正确设定训练目标值，当运动员某项体能素质达到目标值后，可即时变更训练计划，以达到事半功倍的效果。
It can also be used as an important basis for athlete selection. In addition, male athletes were 2.4-4.8 times more successful than those who did not meet the threshold of fitness sensitivity ( OR = 2.456 ∼ 4.885 OR = 2.456 ∼ 4.885 OR=2.456∼4.885\mathrm{OR}=2.456 \sim 4.885 ), and female athletes were 2.6-8.6 times more successful ( OR = 2.674 ∼ 8.690 OR = 2.674 ∼ 8.690 OR=2.674∼8.690\mathrm{OR}=2.674 \sim 8.690 ). This result fully illustrates the importance of physical fitness sensitivity index thresholds in predicting the preferred qualifications of junior badminton players. Athletes with excellent physical fitness qualities are often able to be more dominant in competitions. Compared with the previous study that only provided the average value of athletes, the physical fitness sensitive index thresholds provided by this study are more valuable for physical training, especially for balancing the different physical training contents and the overall training program, so that the coaches can correctly set the training target value in the training according to the athletes' physical fitness test results combined with the sensitive index thresholds, and the coaches can instantly set the target value of the athletes' physical fitness quality after they reach the target value. When an athlete's physical fitness reaches the target value, the training program can be changed instantly to achieve twice the result with half the effort.

3.3 国少运动员体能成绩的发展趋势  3.3 Trends in the physical performance of national junior athletes

本研究进一步对国少运动员的体能敏感指标成绩进行了纵向分析。青少年羽毛球运动员的体能敏感指标在不同年龄段呈现出不同的发展趋势。随着年龄的增长青少年羽毛球运动员的体能素质呈现逐步提升的一般规律。在 U12—U14 阶段中，男运动员立定跳远成绩在 U12—U13阶段成绩变化显著，这一阶段正是青少年男性下肢力量，爆发力和协调性快速发展的时期 [ 12 ] [ 12 ] ^([12]){ }^{[12]}。立定跳远作为评估下肢力量和身体协调性的重要指标，该指标成绩的提升不仅与训练强度的合理调整，训练方法的科学优化密切相关，更受到了运动员自身生长发育的自然推动。相比之下，女运动员在 20 次低重心四点跑这一指标上，U13至U14阶段成绩变化明显。20次低重心四点跑主要考察运动员的灵敏性，协调性和快速移动能力。根据 Faigenbaum 等人（1999）的研究，青少年女性在青春期前后，由于骨骼，肌肉及神经系统的快速变化，可能会对某些体能指标产生影响 [ 24 ] [ 24 ] ^([24]){ }^{[24]}。因此，女运动员在这一阶段 20 次低重心四点跑成绩的下降，可能与训练中忽视对这些特定能力的专门强化有关，也可能与女运动员自身的生长发育特点密切相关。其他体能敏感指标，虽然成绩也有所提升，但在不同年龄段之间并未呈现出显著差异。这与青少年身体素质长期发展的普遍规律相一致，即某些体能素质在特定年龄段可能出现快速增长，而其他素质则可能呈现更平稳的增长趋势。例如，汪君萍等人的研究表明，青少年在耐力，柔韧性和速度等方面的发展具有不同的年龄敏感期 [ 25 − 26 ] [ 25 − 26 ] ^([25-26]){ }^{[25-26]}。
The present study further analyzed longitudinally the performance of fitness-sensitive indicators of national junior athletes. The physical fitness sensitive indexes of junior badminton players showed different trends in different age groups. The physical fitness of junior badminton players showed a general pattern of gradual improvement with age. In the U12-U14 stage, the standing long jump performance of male athletes changed significantly in the U12-U13 stage, which is the period of rapid development of lower limb strength, explosive power and coordination of young male [ 12 ] [ 12 ] ^([12]){ }^{[12]} . As an important indicator of lower limb strength and coordination, the improvement of standing long jump is not only closely related to the reasonable adjustment of training intensity and scientific optimization of training methods, but also driven by the natural growth and development of athletes. In contrast, female athletes' performance in the 20-repetition low center of gravity four-point run changed significantly from U13 to U14. The 20-repetition low center of gravity four-point run mainly examines the athlete's agility, coordination and rapid movement ability. According to Faigenbaum et al. (1999), the rapid skeletal, muscular and neurological changes that occur in adolescent females around puberty may have an impact on some of the physical performance indicators [ 24 ] [ 24 ] ^([24]){ }^{[24]} . Therefore, the decline in performance in the 20 low center of gravity four-point run during this phase of female athletes' lives may be related to the neglect of specialized reinforcement of these specific abilities during training, or it may be closely related to the female athlete's own growth and developmental characteristics. Other fitness-sensitive indicators, although performance also improved, did not show significant differences between age groups. This is consistent with the general pattern of long-term development of physical fitness in adolescents, i.e., certain physical fitness qualities may show rapid growth at specific ages, while other qualities may show a smoother growth trend. For example, Wang Junping et al. showed that adolescents have different age-sensitive periods for the development of endurance, flexibility, and speed [ 25 − 26 ] [ 25 − 26 ] ^([25-26]){ }^{[25-26]} .

3.4 体能敏感指标对训练效率的优化作用  3.4 Optimization of training efficiency by fitness-sensitive indicators

本研究通过筛选与评估体能敏感指标，旨在为运动员制定个性化的训练计划提供科学依据，从而优化训练效率，促进运动员整体运动表现的提升，预测其未来发展趋势。运动员的体能成绩总体上随着年龄的增长而逐渐提高，但在年龄和性别上存在差异。在制定训练计划时，应根据运动员身体素质发展敏感期和青春期性别发育特点，针对不同体能素质指标，不同年龄段的运动员制定差异化的训练方案，从而优化训练效率，提高运动员的整体运动表现。在 U12中，男运动员在立定跳远等反映下肢力量和爆发力的指标上，成绩表现出较为显著的提升，这与该年龄段男性运动员下肢力量，爆发力和协调性的快速发展密切相关。相比之下，女运动员在这一阶段的体能发展相对平稳，但在 20 次低重心四点跑等反映灵敏性和协调性的指标上，表现出一定的提升。进入 U13 后，青少年羽毛球运动员的体能素质继续提升，但女运动员在某些指标上出现波动。例如，在 20 次低重心四点跑指标上的成绩出现下降，这可能与青春期
By screening and evaluating physical fitness sensitive indicators, this study aims to provide a scientific basis for athletes to formulate individualized training plans, so as to optimize the training efficiency, promote the improvement of athletes' overall sports performance, and predict their future development trend. Athletes' physical performance generally improves gradually with age, but there are differences in age and gender. When formulating training plans, differentiated training programs should be developed for athletes of different age groups according to the sensitive period of athletes' physical fitness development and the gender development characteristics of puberty, so as to optimize training efficiency and improve athletes' overall sports performance. In U12, male athletes showed significant improvement in the standing long jump and other indicators that reflect the strength and explosive power of the lower limbs, which is closely related to the rapid development of lower limb strength, explosive power and coordination of male athletes in this age group. In contrast, female athletes' physical development at this stage was relatively stable, but showed some improvement in the indicators of agility and coordination such as 20 times of low center of gravity four-point run. After entering the U13, the physical fitness of junior badminton players continued to improve, but female players showed fluctuations in certain indicators. For example, there is a decrease in the performance of 20 times low center of gravity four-point run, which may be related to puberty.
前后骨骼，肌肉及神经系统的快速变化对灵敏性和协调性训练的影响有关。在三分钟双摇跳绳等反映耐力和协调性的指标上，女运动员可能表现出更强的竞争力。此时，教练员需要密切关注运动员的生长发育特点，及时调整训练计划，以更好地适应运动员的体能发展需求。U14中，青少年羽毛球运动员的体能素质已经得到了较为全面的提升。在这一阶段，运动员的体能指标成绩往往呈现出稳定或继续提高的趋势。
Rapid changes in the anterior and posterior skeletal, muscular, and neurological systems are related to the effects of agility and coordination training. Female athletes may show stronger competitiveness in indicators reflecting endurance and coordination such as three-minute double-swing rope skipping. At this time, coaches need to pay close attention to the growth and development characteristics of the athletes and adjust the training program in time to better adapt to the physical development needs of the athletes.In U14, the physical fitness quality of junior badminton athletes has been improved in a more comprehensive way. At this stage, the athletes' performance in physical fitness indicators tends to show a trend of stabilization or continued improvement.
青少年羽毛球运动员的体能敏感指标在不同年龄段呈现出不同的发展趋势，这种趋势受到生长发育和训练安排双重因素的影响。因此，在制定训练计划时，教练员需要充分考虑运动员的年龄和性别特点，以及不同体能指标在不同年龄段的变化规律。通过精准识别体能敏感指标，并制定相应的训练策略，教练员可以更有效地提升运动员的体能水平，优化训练效率，为运动员的长期发展奠定坚实基础。
The physical sensitivity indexes of young badminton players show different development trends at different ages, and this trend is influenced by the dual factors of growth and development and training arrangements. Therefore, when developing training programs, coaches need to fully consider the age and gender characteristics of the athletes, as well as the changing patterns of different fitness indicators at different ages. By accurately identifying the sensitive indicators of physical fitness and formulating corresponding training strategies, coaches can more effectively improve the athletes' physical fitness level, optimize the training efficiency, and lay a solid foundation for the long-term development of athletes.

3.5 研究局限性  3.5 Research limitations

本研究选取的样本量有限，仅包括了 2022－2024 年全国 U 系列羽毛球比赛 U12－U14 组的运动员。虽然这些运动员具有一定的代表性，但样本量的限制可能影响到研究结果的准确性和普适性。同时，相同年龄段运动员体能素质存在个体差异。有些运动员可能在较早的年龄就展现出出色的体能素质，而另一些运动员则可能在较晚的年龄才逐渐崭露头角。这种生长发育的个体差异可能对本研究的结果产生一定影响。因此，在未来的研究中，需要进一步扩大样本量，涵盖更多年龄段和水平的运动员，以提高研究结果的可靠性和有效性。同时，本研究仅选取了五项体能指标进行 ROC 曲线分析，虽然这些指标在一定程度上能够反映运动员的体能素质水平，但可能仍有一些重要的体能指标被遗漏。因此，在未来的研究中，需要综合考虑更多与羽毛球运动相关的体能指标，以更全面地评估运动员的体能素质水平。
The sample size selected for this study was limited, including only athletes in the U12-U14 group of the National U Series Badminton Tournament in 2022-2024. Although these athletes are representative, the limitation of the sample size may affect the accuracy and generalizability of the results of the study. Meanwhile, there are individual differences in the physical fitness quality of athletes of the same age group. Some athletes may show excellent physical fitness at an earlier age, while others may come to prominence at a later age. Such individual differences in growth and development may have an impact on the results of this study. Therefore, it is necessary to further expand the sample size to cover athletes of more ages and levels in future studies to improve the reliability and validity of the findings. Meanwhile, only five physical fitness indicators were selected for ROC curve analysis in this study, and although these indicators can reflect the level of athletes' physical fitness quality to a certain extent, some important physical fitness indicators may still be omitted. Therefore, in future studies, more physical fitness indicators related to badminton need to be considered comprehensively to assess the physical fitness level of athletes more comprehensively.

4 结论  4 Conclusion

通过对 2022－2024 年全国 U 系列羽毛球比赛 U12－U14 组的运动员的体能测试数据进行深入分析，成功探究了青少年羽毛球运动员体能敏感指标的阈值和国少队优选结果地预测。研究结果表明，所选取的体能敏感指标间值能够较为准确区分优选组与淘汰组运动员之间的体能差异，此外，符合体能敏感指标要求的运动员在优选成功率上显著高于未达标运动员，这一规律在男女运动员中均得到了验证。同时，不同指标成绩在各年龄间呈现出一定差异。运动员在部分体能素质指标上的成绩呈现出稳定或提高的趋势，而在个别指标上则存在显著差异，这可能与运动员的生长发育，训练安排以及比赛经验等因素有关。本研究不仅揭示了青少年羽毛球运动员体能素质发展的敏感指标，也为为运动员的优选与个性化训练提供了有力的数据支持。
Through in-depth analysis of the fitness test data of players in the U12-U14 group of the 2022-2024 national U-series badminton tournament, the threshold values of the fitness sensitivity indexes of junior badminton players and the prediction of the results of the national junior team's preferential selection have been successfully explored. The results of the study showed that the selected values of the fitness sensitivity indexes could accurately distinguish the differences in fitness between the athletes in the preferred group and the eliminated group, and that the athletes meeting the requirements of the fitness sensitivity indexes were significantly higher than the athletes who did not meet the requirements in the preferred selection, and this law was verified in both male and female athletes. Meanwhile, the performance of different indexes showed some differences among ages. Athletes' performance in some physical quality indexes showed a stable or improving trend, while there were significant differences in individual indexes, which may be related to factors such as athletes' growth and development, training arrangements and competition experience. This study not only reveals the sensitive indicators of physical fitness development in junior badminton players, but also provides strong data support for the selection and individualized training of athletes.

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