การเปรียบเทียบประสิทธิภาพของสถิติพาราเมตริกและสถิตินอนพาราเมตริกในการทดสอบค่ากลางระหว่างประชากรหลายกลุ่มเมื่อข้อมูลเป็นแบบลิเคิร์ท 5 ระดับ
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Abstract
This research aimed to compare the efficiency of parametric and nonparametric statistics on central testing between population groups. The data were measured with five-level Likert-type scales. The testing statistics included one-way ANOVA (F test), Kruskal-Wallis test (K-W test), van der Waerden normal scores test (V-W test), and median test (M test). The conditions of problem simulation were three distributions of population including negative skewness and leptokurtic distribution, symmetric and platykurtic distribution, and positive skewness and leptokurtic distribution. The populations were divided into 3, 4 and 5 groups. The sample size was allocated to three levels; small size (n = 10), medium size (n = 25, 50), and large size (n = 100). Equal and unequal variances were determined. All situations were hypothesized at significant levels of 0.05 and 0.01. Each situation was simulated with 10,000 replications. For efficiency of testing statistics, the ability control type I error and the highest power of the test were taking into consideration for each situation. The results showed that when populations were having negative skewness and leptokurtic distribution (Sk = -1, K = 4), all testing statistics were found ineffective. For population with symmetric and platykurtic distribution (Sk = 0, K = 2), the highest effectiveness of test statistics for medium sample size was F test, while that for large sample size were F test, K-W test, and V-W test. In addition, for population with positive skewness and leptokurtic distribution (Sk = 1, K = 4), small sample size with equal variance found F test and K-W test as highest effective testing statistics whereas unequal variance found only F test as an effective testing statistics. For medium sample size, the highest effective test was K-W test for equal variance and V-W test for unequal variance. For large sample size, the highest effective tests were F test, K-W test and V-W test for equal variance and V-W test and K-W test for unequal variance.
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References
[2] Jarunratanakul, P. and Keeratiparadorn, P., 2018, Mediation effect of organizational identification on the relationship between person-organization fit and affective commitment to the political party, Kasetsart J. Soc. Sci. 39: 601-610.
[3] Tengpongsthorn, W., 2017, Factors affecting the effectiveness of police performance in Metropolitan Police Bureau, Kasetsart J. Soc. Sci. 38: 39-44.
[4] Chanjaraspong, T., 2017. Acceptance factors for the use of video call via smartphone by blind people, Kasetsart J. Soc. Sci. 38: 81-87.
[5] Promdee, S., Saratapun, N. and Hirunwong, A., 2017, Factors related to at-risk behavior to obesity of grade 6 students under the Office of Bangkok Metropolitan Primary Education, Kasetsart J. Soc. Sci. 38: 435-444.
[6] Sullivan, GM., and Artino, AR., 2013, Analyzing and interpreting data from Likert-type scales, J. Grad. Med. Edu. 5: 541-542.
[7] Songthong, M., 2014, Robustness and power of the test of parametric and nonparametric statistics in testing of central difference between two populations for Likert-type data 5 points, Thai Sci. Technol. J. 22: 605-619. (in Thai)
[8] Murray, J., 2013, Likert data: what to use, parametric or non-parametric?, Int. J. Bus. Soc. Sci. 4: 258-264.
[9] Glass, G.V., Peckham, P.D. and Sanders, J.R., 1972, Consequences of failure to meet assumptions underlying the fixed effects analyses of variance and covariance, Rev. Edu. Res. 42: 237-288.
[10] Kuzon, W.M., Urbanchek, M.G. and McCabe, S., 1996, The seven deadly sins of statistical analysis, Ann. Plast. Surg. 37: 265-272.
[11] Jamieson, S., 2004, Likert scales: How to (ab)use them, Med. Edu. 38: 1217-1218.
[12] Blaikie, N.W.H., 2003, Analyzing Quantitative Data: From Description to Explanation, Sage Publications, London.
[13] Sangthong, M., 2014, Principles of Statistics, Se-education, Bangkok, 456 p. (in Thai)
[14] Klubnual, P., 2018, The efficiency of parametric and non-parametric statistics on location testing with multiple population groups, RMUTSB Acad. J. 6: 84-100. (in Thai)
[15] Hecke, T.V., 2010. Power Study of ANOVA Versus Kruskal-Wallis Test, Available Source: https://www.tandfonline.com/doi /abs/10.1080/09720510.2012.10701623, June 1, 2018.
[16] Bowarnkitiwong, S. and Areekul, K., 2017, Robustness of f-test for heterogeneity of population variances, SDU Res. J. 13: 1-16. (in Thai)
[17] Sheskin, D.J., 2000, Handbook of Parametric and Nonparametric Statistical Procedures, 2nd Ed., Chapman and Hall/CRC, Boca Raton, FL.
[18] Chongcharoen, S., 2005, Nonparametric Statistical Analysis, The Academic Textbook Promotion Project of National Institute of Development Administration, Bangkok, 324 p. (in Thai)
[19] Ramberg, J.S., Dudewicz, E.J., Tadikamalla, P.R. and Mykytka, E.F., 1979, A probability distribution and its uses in fitting data, Technometrics 21: 201-214.
[20] Cochran, W.G., 1954, Some methods for strengthening the common χ2 tests, Biometrics 10: 417-451.