A Research about Measurement Invariance of Attitude Participating in Field Hockey Sport

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1 A Research about Measurement Invariance of Attitude Participating in Field Hockey Sport Dr. Mao-Chun Chiu, Department of Leisure, Recreation & Health Business Management, Tajen University, Taiwan ABSTRACT The research goal is to test the measurement invariance of attitude participating in field hockey sport. By utilizing cluster sampling, three hundred and seventy-nine valid samples were selected and analyzed for descriptive analysis and structural equation model by statistical software SPSS2.0 and AMOS 6.0. Results revealed: First, there was no difference between the expected covariance equation and sample covariance. Second, there were no significant differences among measurement model, structural model, and covariance model after cross-validity analysis. At last, concrete suggestions are provided to government and other hockey sport organizations for further improvement. Keywords: Field hockey, attitude toward sport participation INTRODUCTION Doing exercise is effective for health improvement. With the economic growth in Taiwan, the awareness of leisure improves in the public, and the rapid increase of their participation in leisure and sports. Field hockey is an ancient sport with long history; the ball is small with high speed and is played in a spacious field with players high skills (Tsai, 996). Field hockey is suitable for eastern countries because of its limitlessness of body type and gender. Being included in the competition events in Asian Games, field hockey has potential for improvement in Taiwan. Ice hockey and field hockey are two kinds of hockey sport, and the latter is suitable to be promoted in Taiwan for its warm weather. The field, number of players, and game tactics are similar to those of soccer game; therefore, field hockey has become a popular leisure sport of the public. Myers (993) addressed that one s attitude is formed by his consciousness, emotion, and behavioral tendency. Attitude toward exercise is, regardless of results, one s or most people s gain to their health physically, satisfaction, happiness, and spirituality rely on adequate time and space with their independent willingness. Attitude refers to an individual s constancy and coherence tendency towards human affairs and his/her surroundings. This tendency could be predicted by one s external behavior, but the connotation not only means external behavior, attitude generally includes consciousness, emotion, and behavior (Chang, 989). Hence, for the measurement of attitude toward exercise, it could be individually analyzed one s attitude by feelings of doing exercise, belief, and tendency toward exercise; whether their attitude are positive or negative, liking or disliking, participating it or not. By realizing one s attitude researchers could predict his level of preference to the consciousness, favor and behavior of one matter (Wang, Chen, 2006). Ajzen and Fishbein s Reasoned Action Theory which addressed in 980 indicated that attitude plays an important role in constructing behavioral intention, and intention is a norm in predicting the occurrence of actual behavior. Ajen (988) considered attitude as a reflection tendency from some particular people whether they continuously like or dislike what they learned, Promoting sport The Journal of Human Resource and Adult Learning, Vol. 0, Num. 2, December, 204 issue 6

2 participating behavior has been a focus worldwide for decades, relevant theory indicated that attitude is a crucial factor affecting an individual s behavior and activity (Noland & Feldman, 985). The previous studies mainly focused on the impacts of participation hindrance to leisure behavior (Huang, Chen, 2005; Alexandris, Tsorbatoudis & Grouios, 2002; Alexandris & Carroll, 997; Alexandris & Carroll, 999). This research attempts to utilize a strict testing process to construct a model of attitude toward participating field hockey sport. Through a series of testing analysis on factor structure, a most parsimonious factor model is expected. Reliability, convergent validity, and discriminant validity of this factor model will be examined; also, the measurement invariance of attitude participating in field hockey sport will be tested by cross validity. RESEARCH METHOD Research Structure Based on relevant references, this research selected quantification research methods and tested the results by Structural Equation Modeling. Statistical Model is shown in diagram. e8 e7 e6 e5 e4 e3 e2 e e23 e22 e2 e20 B B2 B3 B4 B5 B6 B7 B8 A A2 A3 A4 Benefits Ability and skill Involvement Achievement and Satisfaction Diagram : Statistical Model I I2 I3 I4 I5 I6 I7 I8 I9 I0 I S S2 S3 S4 S5 e9 e0 e e2 e3 e4 e5 e6 e7 e8 e9 e24 e25 e26 e27 e28 Research Hypothesis Structural Equation Model (SEM) use co-variance model to estimate the mutual-support and correlative relationship among several Multi-Regression Equations. (Lee, Ko, Wu, Yu, 2004; Jöreskog & Sörbom,992) Chen (2007) emphasized that structural equation model adopted the covariant equation testing variable relationship among the variables, the diversity between the covariance equation and sample covariance equation of the received θ model ought to be smaller, the smaller the better. Chin (998) indicated that the goodness of fit of SEM is not allowed to be inferior. It refers to the obvious disparity between the model and the sample and the wrong model design, and will result in the following incorrect research outcomes. Hence, this research s first step is to advance the hypothesis to the goodness 62 The Journal of Human Resource and Adult Learning, Vol. 0, Num. 2, December, 204 issue

3 of fit of this model,,s-σ(θ)=0, S is the sample covariance equation, and Σ(θ) is the model expected covariance equation. H: There is no difference between the model expected covariance equation of the model and the sample covariance equation. H2: The model of attitude toward participating in filed hockey sport possesses measurement invariance. Research Tool () Questionnaire Design Two sections in this research questionnaire are: the scale about the model of attitude toward participating in field hockey sport and personal information.. Questionnaire Model about attitude participating in field hockey sport This questionnaire was revised from Yang and Ku s research and their scale of university students attitude toward leisure sport in This questionnaire includes twenty-eight questions in re sport benefit, sport involvement, ability and skill, achievement and satisfaction respectively. 2. Descriptive Statistics This questionnaire was revised from Yang and Ku s research and their scale of university students attitude toward leisure sport in A descriptive analysis includes gender, group, and annual income respectively. (2) Likert Scaling Bollen (989) indicated that seven-point Likert scale in SEM practically reveals the best performance, and therefore was selected for the questionnaire scoring. Four questionnaire items are benefits from sport, investment on sport, ability and skills, achievement and psychological satisfaction; and categories of this scale are rated from Strongly agree (seven points) to Strongly disagree (one point). Sampling The duration for data collection was from August, 5 th to 3 th, 204 with random sampling of subjects as participants in National Presidential In-door Hockey Cup in 204. Those participants were questioned an hour before the competitions which began in Changhua Stadium, and 400 questionnaires were collected. Sample Estimation and Statistical Power After settling the SEM model, the amount of samples needs to be determined before sample collection. Based on the RMSEA estimation method provided by MacCallum, Browne and Sugawara in 966, and by utilizing the minimum sample size computed by R language and the degree of freedom 344 in this survey for estimation, the minimum sample size is The effective sample size in this survey is 379 and it fits the suggested value mentioned above. Also, the statistical power is, which is bigger than the suggested value (Maxwell, Kelley, & Rausch, 2008) Results revealed that the statistical power is ideal. RESULTS Descriptive Statistics of Sample Characters Among the effective samples in this research, 52.2 percent of subjects are males and 47.8 percent are females; which refers to 98 and 8 respectively. In the case of group, 05 subjects were studying in elementary school, 26 in the junior high school, 87 in senior high school, and 6 in the adult group. The Journal of Human Resource and Adult Learning, Vol. 0, Num. 2, December, 204 issue 63

4 As for the item income, in 323 people s monthly salary is under twenty thousand dollars, 37 people are in the group between 20,00 to 30,000; only 9 people earn more than thirty thousand dollars. Table : Summary of Descriptive Statistics about Sample Characters Information Item Category Standard Sample size Percentage Gender Male Female Elementary School Group Junior High School Senior High School Adult 6 6. Under 20, Income 20,00-30,000 dollars Above 30, Measurement and Structural Model Analysis () Confirmation of Convergent Validity Confirmatory Factor Analysis (CFA) is a crucial step of SEM analysis. This survey, was amended based on the two-stage model from Kline in 2005, downsized the variables of CFA measurement model. First, test the measurement model before implementing the structural model evaluation. If the goodness of fit of the measured model is acceptable, complete SEM model evaluation will be conducted in the second stage. This research is aimed to conduct CFA analysis on the four aspects in this model as the benefits from sport, investment on sport, ability and skills, achievement and psychological satisfaction. Factor loading of all aspects are among 0.74 to 0.94; all reach the significant standard. Composite reliability is between the number of 0.95 to 0.98; and the average variance extracted is between the number of 0.78 to 0.83 (shown in Table 2), which fits the suggested value addressed by Hair, Anderson, Tatham and Black in 998, and by Fornell and Larcker in 98. Aspect Benefits Involvement Table 2: Reliability Analysis of Potential Aspects Norm Standar- Non-Stanarddized Loading dized Loading S.E. C.R. (t-value) P SMC C.R. AVE B B *** 0.77 B *** 0.82 B *** 0.74 B *** 0.88 B *** 0.88 B *** 0.88 B *** 0.8 I I *** 0.80 I *** 0.84 I *** 0.89 I *** 0.79 I *** 0.8 I *** 0.84 I *** 0.72 I *** The Journal of Human Resource and Adult Learning, Vol. 0, Num. 2, December, 204 issue

5 Ability and skill Achievement and Satisfaction I *** 0.72 I *** 0.82 A A *** 0.84 A *** 0.82 A *** 0.77 S S *** 0.84 S *** 0.82 S *** 0.82 S *** 0.84 (2)Confirmation of Discriminant Validity The aim of discriminant validity analysis is to confirm whether the difference occurs to two different aspects. This survey chose confidence interval method (Torkzadeh, Koufteros, Pflughoeft, 2003) to confirm the confidence interval of correlation coefficient between the two aspects. If the interval excludes (which reaches the complete correlation), discriminant validity exists between aspects. To establish a confidence interval of correlation coefficient in SEM under the circumstance of confidence level of 95%, this survey utilized Bootstrap estimation. If the confidence interval excludes, null hypotheses are refused, and the four aspects possess discriminant validity. Hancock and Nevitt (999) suggested that the number of Bootstrapping should be more than two hundred and fifty times when estimating the path coefficient. This survey, with a 95% confident level, repeatedly used sampling over one thousand times to retrieve the confidence interval of standardized correlation coefficient. AMOS bootstrap provides estimation for two confidence intervals, which are Bias-corrected Percentile Method and Percentile Method. Results of these two estimations are shown in Table 3-all standardized confidence interval of correlation coefficient exclude, which means discriminant validity exists between one aspect and another. Table 3: Bootstrap Correlation Coefficient 95% Confidence Interval Parameter Bias-corrected Percentile method Estimate Lower Upper Lower Upper Benefits <--> Ability and skill Benefits <--> Involvement Benefits <--> Achievement and Satisfaction Involvement <--> Ability and skill Ability and skill <--> Achievement and Satisfaction Involvement <--> Achievement and Satisfaction (3) Structural Model Analysis If the sample size of SEM is over 200, it normally causes bigger chi-squared value. (χ 2 =(n-)fmin). Fmin is the minimum value of difference between sample equation and expectation equation. The bigger the sample size it is, the higher the chi-squared value it becomes. P value therefore becomes easily be refused (Chang, 20). For this reason, Bollen and Stine addressed Bootstrape for amendment in 992. The chi value of Bollen-stine p correction is , and the original ML chi value is Because the chi-value became smaller, all goodness of fit requires computation again. Results are listed in Table 4. Structural model analysis includes model fitness and explanatory power of entire research model. This The Journal of Human Resource and Adult Learning, Vol. 0, Num. 2, December, 204 issue 65

6 research took Bagozzi and Yi (988), Bentler (995), and Hair (988) s opinions, using seven indexes for evaluation for goodness of fit of over-all model, including chi-value test (χ 2 ), χ 2 and ratio of degree of freedom, goodness of fit index (GFI), adjusted goodness of fit index (AGFI), root mean square error of approximation (RMSEA), comparative fit index (CFI), and normed fit index (NFI). Results are listed in Table 6. Bagozzi and Yi (988) emphasized that, taking χ 2 and ratio of degree of freedom to test the goodness of fit, the degree is ideal to be smaller. The ratio of this research is <3(.53); Hair, etc. (988) indicated that GFI and AGFI are ideal to close to, no absolute standard to judge the goodness of fit. Baumgartner and Homburg (996) recommended that the values of GFI and AGFI in the research need to be higher than GFI and AGFI in this research model are 0.97 and 0.96 respectively. Browne and Cudeck (993) explained a good model with reasonable fir if its RMSEA is lower than The RMSEA of this research model is 0.04, the allowable standard is >0.90. CFI in this research model is NFI value as least needs to be higher than 0.90, while the NFI is 0.97 in this research model. Over all, the fit indices are within the standard value, which showed the research results are acceptable. Also, the data of the samples in this research can be used to explain practical observation data. Table 4: Fitness Analysis of Research Model Fit Indices Allowable Range Research Model Judgment of model fit χ 2 (Chi-square) the smaller the better DF 378 χ 2 /DF <3.53 Fit GFI > Fit AGFI > Fit RMSEA < Fit CFI > Fit NFI > Fit.80 e8 B.77 e7 B e6 B e5.86 B e4 B e3 B e2 B e B8.85 e23 A e22 A e2 A e20 A4 Benefits Ability and skill Involvement.95 Achievement and Satisfaction.72 I.79 I I I I I6 I7 I8 I9 I0 I S S2 S3 S4 S e9 e0 e e2 e3 e4 e5 e6 e7 e8 e9 e24 e25 e26 e27 e28 Diagram 2: Model of Attitude Participating in Field Hockey Sport 66 The Journal of Human Resource and Adult Learning, Vol. 0, Num. 2, December, 204 issue

7 (4) Cross Validity This research is operated under the circumstance that the assumption of the research model is accurate, and two groups are compared after random sampling. (Cliff, 983; Cudeck & Broene, 983; Hairs, etc., 983) To deeply test the stability of this model, this research progressively restrict three coefficients, including path coefficient of the measured model, path coefficient of structure and structural covariance. If no obvious differences are found in this model, it owns a certain level of stability.. Set equal path coefficient to two groups, twenty four factor loadings in total are designed equally in structural model (DF=24) and Chi-square measure (CMIN) increased Besides, the test result p=.97 and failed to reach the significant level, which means setting twenty four factor loading equally is acceptable. 2. Besides remaining the restriction of the measurement model, plus setting ten structural path coefficient (DF=34-24=0), Chi-square measure (CMIN) increased 8.06 (CMIN= =8.06). The test result p=.62 and failed to reach the significant level; in other words, these ten structural path coefficient are acceptable, and are the same. 3. With the same restriction to the structural efficient model, and extra twenty eight set structural variances and covariances (DF=62-34=28). Chi-square measure increased (CMIN= =09.74).The test result p= 0.00 and has reached the significant level 0.05; which means making these twenty eight variances and covariances equal is unacceptable. These twenty eight variances and covariances are unequal. Chung and Rensvold (2002) brought up the practical significance of test based on CFI norm. Results showed ΔCFI 0.0 after the simulation, which means that no differences between the two nested structural model. Nevertheless, Little (997) addressed that ΔTLI 0.05 is the standard of having no difference among nested structural model. The invariance comparison of ΔCFI and ΔTLI both fit the suggested value mentioned as well as the requirement of congruent groups. This model is stable and fits the standard of cross validity. Table 5: Comparison of group interval invariance Model χ 2 df Δdf Δχ 2 P CFI ΔCFI TLI Measurement weights Structural covariances Measurement residuals CONCLUSION Most subjects in this survey are males, currently in junior high school, and monthly income lower than 20,000. This research includes three stages and questionnaires are analyzed by confirmatory factor analysis. Research results revealed that this questionnaire includes benefit, involvement, achievement and satisfaction, ability and skill, four factors with twenty eight questions in total. For the application of structural equation model, Bollen (989) considered that Likert seven-point scale is ideal to reduce the over-skewed results, and confirmatory research is suitable because the variance level is greater. Therefore, the questionnaire design selected was the seven-point scale. After analyzed by composite reliability, average variance extracted, this questionnaire possesses good convergent validity. With bootstrap confident interval, two estimated methods-bias-corrected Percentile Method and Percentile Method were used to estimate disterminant validity. Results showed The Journal of Human Resource and Adult Learning, Vol. 0, Num. 2, December, 204 issue 67

8 that every potential variable in this questionnaire is distinguishable. Seven scales in this research were evaluated for overall model fit, including χ 2 test, ratio of χ 2 and degree of freedom, goodness of fit (GFI), adjusted goodness of fit index (AGFI), root mean square error of approximation (RMSEA), and comparative fit index (CFI), parsimony-adjusted comparative fit index (PCFI), results showed good model fit. Therefore, the first hypothesis that there is no difference between the model expected covariance equation of the model and the sample covariance equation is valid. This research randomly conducted cross-validity confirmation of two groups, both ΔCFI and ΔTLI as the invariance comparison are smaller than the standard suggested by the scholars, and therefore fit the requirement of equal group interval. This model has stability and fit the cross-validity. As the result, the second hypothesis that the model of attitude toward participating in field hockey sport possesses measurement invariance is valid. SUGGESTIONS Academic contribution of this research In the past thirty years, structural equation model has become a widely used statistical technology. Researchers applied SEM to construction models and attempted to know the relationship among variables. By operating the model to test the relationship of hypotheses, and further collect data for evaluation. According to Schreiber (2008), McDonald and Ho (2002), Boomsma (2000), and Hoyle and Panter (995) s suggestions, well-designed SEM research articles must display sample size, statistical power, the version of statistical software used (AMOS 6.0), goodness of fit, Chi-square measurement, multi fit indices (GFI, AGFI, CFI, NFI, RMSEA ), parameter estimation of measurement and structure including standardized and non-standardized estimated value and the reports of significance, SMC and explainable variance, final statistical model diagram, and cross validity. Based on the recommendation, this research provided a more complete statistical analysis report for other researchers in the future. Statistical power evaluation is very crucial work, because sample size plays the key role while testing the model. (Bollen, 989) The degree of freedom in this research shows the minimum number of the sample size needs to be higher than 344; the valid sample size is 396 and has reached its standard. Under the request of statistical power, the general statistical power is ideal to be 0.8 (Maxwell, Kelley & Rausch, 2008), and the statistical power in this research is.0 and is ideal for statistical analysis. Suggestions for Field Hockey Sport Participation Field hockey sport helps relieve players study pressure and tension, this research recommends schools and relevant organizations to form field hockey clubs for promotion and pressure relief. Although the number of hockey players in Taiwan is lower than it in other countries; the researchers expect that by the active promotion of sports fair council can field hockey sport become popular in Taiwan and further produce positive impact on players skill and improvement. In the trend of globalization, the demarcation lines among nations are blurred and bring more frequent skill interactions in countries. Inviting coaches from other countries for player training in Taiwan to improve competition level is also highly recommended. 68 The Journal of Human Resource and Adult Learning, Vol. 0, Num. 2, December, 204 issue

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10 MacCallum, R.C., Browne, M. W., & Sugawara, H. M.(996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, (2), Maxwell, S. E., Kelley, K., & Rausch, J. R. (2008). Sample size planning for statistical power and accuracy in parameter estimation. Annual Review of Psychology, 59, McDonald, R. P., & Ho, M. H. R. (2002). Principles and practice in reporting structural equation analyses. Psychological Methods, 7, Myers, D. G. (993). Social Psychology(4th ed.). NY: McGraw-Hill. Noland, M. P. & Feldman, R. H. L.(985). An empirical investigation of leisure exercise behavior in adult women. Health Education, 6, Schreiber, J. B. (2008). Core reporting practices in structural equation modeling. Administrative Pharmacy, 4, Tsai, Y. M. (996). Physical application in Field Hockey. Taipei Physical Education College Press, 5, Torkzadeh, G., Koufteros, X., & Pflughoeft, K. (2003), Confirmatory analysis of computer self-efficacy. Structural Equation Modeling, 0(2), Wang, J. M., & Chen, C. C.(2006).The effects of coach efficacy and leadership on athletes' sport motivation and sport attitude. Bulletin of Sports and Exercise Psychology, 9, -8. Yang, L. M., & Ku, Y. C.(2004). The development and application of exercise attitude scale for university student. Physical Educational Journal, 37,49-6. Appendix : Covariance Matrix B B2 B3 B4 B5 B6 B7 B8 I I2 I3 I4 I5 I6 I7 I8 I9 I0 I A A2 A3 A4 S S2 S3 S4 S The Journal of Human Resource and Adult Learning, Vol. 0, Num. 2, December, 204 issue