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A Study on the Changes in the Number of Participating Athletes in the National Disabled Games between 2008 and 2012, Using the Latent Growth Model

Cheng-Lung Wu, Department of Marine and Recreation, National Penghu University of Science and Technology, Taiwan

ABSTRACT

This study employed the Latent Growth Model (LGM) to analyze changes in the number of participating athletes in the National Disabled Games from all cities and counties in Taiwan between 2008 and 2012. The aim was to examine the changes and dynamic process of the participating athletes at different times. The result of the study indicates that between 2008 and 2012, the initial average of the number of participating athletes in the National Disabled Games is 53.23, and the average growth is 3.93; the respective t values are 6.78 and 2.81, which are both statistically significant (*p<.05). In other words, the average number of participating athletes in the National Disabled Games in 2008 was 53.23, and continued to grow at an average rate of 3.93 persons per year. There was significant growth in the number of participating athletes between 2008 and 2012 in all cities and counties. In addition, there was significant difference in the growth rates among different cities and counties. Keywords: Latent Growth Model (LGM), physical and mental impairments, National Disabled Games

INTRODUCTION

It has become a global trend to improve the welfare of the physically and mentally challenged. The degree to which a country is capable of providing adequate care and opportunities for its physically and mentally challenged citizens is also an important index in evaluating its overall development. Engaging in sports has multiple health benefits. For the physically and mentally challenged, engaging in sports not only improves their health, but also enhances their social adaptability (Yeh, 2010). Wu (2000) points out that “adapted sports” is the integration of medical treatment, special education and sports. Lin (1997) has identified five benefits of participating in sports for the physically and mentally challenged: (1) to better understand their own impairment; (2) to overcome their impairments; (3) to enhance their physical capacity and help them develop cognitive and comprehensive abilities: (4) to develop their ability to control muscle strength appropriately; (5) to provide them with opportunities to learn new skills and comprehend the importance of safety. Consequently, it is necessary to examine the development in adaptive sports for the physically and mentally challenged. Yeh (2009) points out that the National Disabled Games is associated with values of care, health and happiness. The first sports event for the physically and mentally challenged was held in 1978, then called the “Taiwan Area Self-Empowerment Event for the Disabled.” Up to 1992, there had been a total of eight such events held by the then Taiwan Province, Taipei City, and Kaohsiung City. In 1994, the event was renamed the “Taiwan Area Disabled Citizens Games”, and was held in Kaohsiung City. In 2000, the name was once again changed, to “National Disabled Games” and was held in Taipei City. Thereafter, the event has been held in Pingtung, Hsinchu, Yilan, Hualien, and Chiayi. From 1991 to 1998, ball sports

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of the Games included: , , , table tennis, tennis, badminton, , lawn , , floor , , croquet, and billiard ball; other sports included: , judo, , shooting, weightlifting, , , , athletics, , ice skating, , dance, mountain climbing, hiking, competitions for fun, , physical , bicycle, etc. (Lin, 1997). In order to meet international standards, the National Disabled Games later added sports included in the , the , the Deaflympic Games and the Special (see Table 1). In terms of the number of participating athletes, in 1994, the number was 1,274; in 1996, the number was 1,043; in 1998, the number was 1,254. Thereafter, there has been a steady increase in the number of participants (Yeh, 2010). For a complete list of the number of participants from 2000 to 2012, see Table 2. This study employed the Latent Growth Model (LGM) to analyze the changes in the number of participating athletes in the three National Disabled Games held from 2008 to 2012, in order to examine the changes and dynamic process of the participants. The purpose was to understand the overall trajectory of growth for all participants, the trajectory of growth for individual athletes and the predictor variables for the individual trajectory and their degree of influence (Kaplan, 2009; Preacher,2010; Wu, West & Taylor, 2009).

Table 1: List of National Disabled Games Sports from 2002 to 2012 Year Sports Athletics, Swimming, Badminton, Table Tennis, Tennis, Powerlifting, Judo, Shooting, Bowling, 2002 Archery, Basketball (men), Goalball (men) Athletics, Swimming, Badminton, Table Tennis, Tennis, Judo, Shooting, Bowling, Archery, 2004 Basketball, Powerlifting, Goalball for the Visually Challenged (men), Wheelchair Billiards, Athletics, Swimming, Badminton, Table Tennis, Tennis, Powerlifting, Judo, Shooting, Bowling, 2006 Archery, Goalball, Billiards, Bocce, Boccia Athletics, Swimming, Badminton, Table Tennis, Tennis, Powerlifting, Judo, Shooting, Archery, 2008 Basketball, Goalball, Billiards, Bowling, Bocce, Boccia Athletics, Swimming, Badminton, Table Tennis, Tennis, Powerlifting, Shooting, Basketball, 2010 Bowling, Archery, Goalball, Billiards, Boccia, Bocce, Inline , Special Olympics Table Tennis, Special Olympics Badminton Athletics, Swimming, Badminton, Table Tennis, , Powerlifting, Shooting, , Bowling, Archery, Boccia, Goalball, Wheelchair Billiards, Special 2012 Olympics Badminton, Special Olympics Bowling, Bocce, Special Olympics Source: cited from Yeh(2010)

Table 2: List of Places and Number of Participating Athletes in the National Disabled Gamesfrom 2000 to 2012 Year Place Number of Participating Athletes 2000 Taipei City 1,474 2002 Pingtung County 1,328 2004 Hsinchu City 1,585 2006 Yilan County 1,820 2008 Hualien County 2,253 2010 Chiayi County 2,078 2012 Kaohsiung City 2,208 Source: adapted from Yeh (2010)

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RESEARCH METHODOLOGY

Scope of the study This study focused on the cities and counties that participated in the National Disabled Games. The observational variable was the number of participating athletes (both male and female) in the covered areas. This study aimed to examine and analyze the changes in the growth of number with respect to the participating athletes in the National Disabled Games from 2008 to 2012.

Latent growth model The Latent linear growth model was employed to test the latent growth of the number of participating athletes in the three National Disabled Games held between 2008 and 2012. There were three observed indices (see Figure 1) that represent the number of participating athletes calculated repeatedly three times. The other two variables were the starting point of the study (ICEPT, ηI) and the rate of growth (SLOPE, ηS), which were assumed to be correlated (ψSI) and affect the three observed indices (Hou, 2009). The factor leading coefficients (λ) of the growth rate to observed variables were assumed to be 0, 1, 2, 3, 4 and 5, respectively, as the growth of the number of participating athletes was assumed to be linear in this study. The starting point was the intercept of simple regression; therefore all coefficients were assumed to be 1 (Hou, 2009; Bollen & Curran, 2006;Duncan, Duncan & Strycker, 2006).

Research hypothesis The Latent Growth Model (LGM) was employed to examine whether the number of participating athletes in the National Disabled Games demonstrated growth. The research hypothesis was that there was a significant growth in the number of participating athletes in the National Disabled Games between 2008 and 2012.

RESULTS

Test for normality with single variable Testing for normality was conducted. In this study, the test for skewness was between 1.46 and 1.59, and for kurtosis it was between 1.70 and 2.16. This demonstrates a normal distribution of the data in this study (Kline, 1998).

Table 3: Normal Hypotheses Identification Variable min max skewness c.r. kurtosis c.r. 2012 7.00 226.00 1.46 3.85 1.70 2.24 2010 3.00 223.00 1.71 4.53 2.57 3.40 2008 4.00 219.00 1.59 4.20 2.16 2.86

Data analysis Testing for goodness of fit was conducted. In this study, TLI (NNFI) was 1.00 (greater than .90); IFI was 1.00 (greater than .90), CFI was 1.00 (greater than .90), and SRMR was .00 (smaller than 0.05). Therefore, the results indicated good fit.

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Table 4: Goodness of Fit of the Research Model Goodness-of-Fit Index Criteria Model of the Study Model Fit Id entification χ2 Thhe smaller the better 0.55 Pass TLI(NNFI) >0.9 1.00 Pass IFI >0.9 1.00 Pass CFI >0.9 1.00 Pass SRMR <0.05 0.00 Pass

Innterpretation of model parameters The intercept indicated that the average number of participating athletes was 53.23. The slope shhowed the growth of number to be 3.93 between 2008 and 2012.

Figure 1: Latent Growth Model for the Number of Participating Athletes in the National Disabled Games between 2008 and 2012

Table 5: Estimated Model Parameters Estimate Inntercept Average number of participating athletes in the National Disabled Games in 2008 53.23 Average growth in the number of participating athletes in the National Disabled Slope 3.93 Games between 2008 and 2012

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Average growth in the number of participating athletes in the National Disabled Games between 2008 and 2012 Table 6 shows that the initial average number of participating athletes between 2008 and 2012 was 53.23, and the average growth curve was 3.93. The t values for the two parameters were 6.78 and 2.81, respectively. This demonstrated a significant difference at p<.05. In other words, the average number of participating athletes in 2008 was 53.23 people, and the average growth in the number thereafter was 3.93 people. In addition, the results indicated a significant difference in the growth rates among different cities and counties between 2008 and 2012. Therefore, the hypothesis that there was a significant growth in the number of participating athletes in the National Disabled Games between 2008 and 2012 was validated. The intercept of variance was 2603.21, and the t value was 4.26, which indicates statistical significance. However, the slope estimate was 127.67, and the t value was 1.21, which was below the significance threshold. Consequently, this study did not conduct conditional LGM analysis.

Table 6: Parameter Estimates in LGM for Participating Athletes in the National Disabled Gamesbetween 2008 and 2012 Estimate Std. Error C.R. P Average Intercept 53.23 7.85 6.78 *** Slope 3.93 1.40 2.81 0.01 Variance Intercept 2603.21 611.11 4.26 *** Slope 127.67 105.64 1.21 0.23 E1 -94.57 207.29 -0.46 0.65 E2 220.55 114.48 1.93 0.05 E3 -98.15 215.67 -0.46 0.65 Covariance and Correlation Beginning Number and Growth Covariance -75.04 124.82 -0.60 0.55 Beginning Number and Growth Correlation -0.13

CONCLUSION AND SUGGESTIONS

Conclusion Research has found that the benefits of engaging in recreational activities for the physically and mentally challenged include therapy, rehabilitation, promotion of self-confidence and social adaptability, prevention and mental counseling, and improvement in the quality of life (Yeh, 2010). In recent years, adaptive sports for the physically and mentally challenged have received considerable attention and have developed swiftly. The National Disabled Games is the highest level of sports event in Taiwan for the physically and mentally challenged. Therefore, this study employed LGM to analyze the changes in the number of participating athletes in the three National Disabled Games held between 2008 and 2012. The purpose was to examine the changes and dynamic process in the number of participating athletes at different times. The results found goodness of fit between the latent linear growth model of the number and the observed data. In addition, there was significant difference in the number of participating athletes among different cities and counties in 2008; there was also significant difference in the growth of numbers among different cities and counties. The results matched that of Yeh (2010), which stated that the number of participating athletes in the National Disabled Games demonstrated consistent increase. The results of this study are also in accordance with the proposal in Healthy People 2020 published by the

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Department of Health, the Executive Yuan (now Ministry of Health and Welfare) in 2009, which stated that the “sports rights” of the physically and mentally challenged were often restricted due to their comparative disadvantage in physical, mental, economic and social conditions, and should therefore be given particular attention. This indicates that both the central government and local governments have given support and attention to the National Disabled Games, which in turn led to the steady increase in the number of participating athletes.

Suggestions 1. Suggestions for Future Policy Implementation The results of the study show significant difference in the number of participating athletes among different cities and counties in 2008; in addition, there was significant difference in the growth rate among different cities and counties. Therefore, this study suggests that the central government and local governments should continue to pay attention to the sports rights of the physically and mentally challenged, and to provide necessary facilities and software support in order to lower the threshold for participation. In particular, for offshore islands and remote areas where resources and public works are less adequately provided, the local governments should especially see to the needs of the physically and mentally challenged citizens. The hosting government of the National Disabled Games should also aim for better and more professional game quality in order to provide safe venues, fair rules and professional service quality. 2. Suggestions for Future Research Results of the study indicate significant growth in the number of participating athletes in the National Disabled Games between 2008 and 2012. Therefore, this study suggests that future research take into account factors such as difference in sports and areas, and investigate whether they have significant impact on the change in the number of participating athletes.

REFERENCES

Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation perspective. New York: Wiley. Duncan, T. E., Duncan, S. C., & Strycker, L. A.(2006). An Introduction to latent variable growth curve modeling: Concepts issues and applications (2nd ed.). Mahwah, NJ: Lawrence Erlbaum. Hou, Y. L. (2009). A longitudinal study of preschool children's flow experience in hands-on science activities: The analysis of latent growth curve model. Bulletin of Special Education, 34(3), 81-105. Kaplan, D. (2009). Structural equation modeling: Foundations and extensions. Thousand Oaks, CA: Sage. Kline, R. B. (1998). Principles and practice of structural equation modeling. New York: Guilford Press. Lin, M. (1997). Theory and practice of special sports: 1998 Taipei special physical education teacher workshop. Taipei, Taiwan: Taipei Education Center. Preacher, K. J. (2010). Latent growth curve models. In G. R. Hancock & R. O. Mueller (Eds.), The reviewer's guide to quantitative methods in the social sciences (pp. 199-208). New York: Routledge Wu, S. (2000). The development and direction of the adapted physical activity. Adapted Physical Activity Quarterly, 29(2), 105-113. Wu, W., West, S. G., & Taylor, A. B. (2009). Evaluating model fit for growth curve models: integration of fit indices from sem and mlm frameworks. Psychological Methods, 14(3), 183-201. doi: 10.1037/a0015858 Yeh, H. F. (2010). A study of satisfaction and service quality for the 2010 National Disabled Games. Unpublished master thesis, National Taiwan Normal University. Yeh, K. T. (2009). Mega events management. Taipei: Far Du Publishing.

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