Investigating the Efficiency of Teaching Mathematics to Students by Using the Double Ranked Set Sampling

Gorgees Shaheed Mohammad

doi:10.29333/ejmste/102422

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Gorgees Shaheed Mohammad ¹ ^*

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¹ University of AL-Qadisiyah, College of Education, Department of Mathematics, IRAQ^* Corresponding Author

Abstract

The main objective of this paper is to evaluate the efficacy of double ranked set sampling method in teaching mathematics to the students. The notion of ranked set sampling for estimating the mean of a population and its advantage over the use of a simple random sampling for the sampling is established in the literature. Furthermore, the double ranked set sampling has proven to be even more efficient than RSS. In this research, we review the use of the DRSS to estimate the intercept, the slope, and the standard deviation of the error terms as parameters of a simple linear regression model of teaching mathematics to students, when replications exist at each value of the predictor. Finally, we illustrate the proposed procedure by applying it when the underlying distribution of the error terms is normal or Laplace. Regardless of the assumed number of replications in the experiment, we observe a substantial gain in relative precision while using DRSS procedure over using RSS technique.

Keywords

education
mathematics
regression model
teaching

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2019, Volume 15, Issue 3, Article No: em1671

https://doi.org/10.29333/ejmste/102422

Publication date: 28 Dec 2018

Article Views: 1903

Article Downloads: 983

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References

Adatia, A. (2000). Estimation of parameters of the half – logistic distribution using generalized ranked set sampling. Computational Statistics and Data Analysis, 33, 1–13. https://doi.org/10.1016/S0167-9473(99)00035-3.
Al-saleh, M. F., & Al Kadiri, M. (2000). Double ranked set sampling. Statistics and probability Letters, 48, 205–212. https://doi.org/10.1016/S0167-7152(99)00206-0.
Barabesi, L., & El Sharaawi, A. (2001). The efficiency of ranked set sampling for parameter estimation. Statistics and probability Letters, 53, 189–199. https://doi.org/10.1016/S0167-7152(01)00078-5.
Barreto, M. C. M., & Barnett, V. (1999). Best linear unbiased estimators for the simple linear regression model using ranked set sampling. Environmental and Ecological Statistics, 6, 119–133. https://doi.org/10.1023/A:1009609902784.
Bhoj, D. S. (1997). Estimation of parameters of the extreme value distribution using ranked set sampling. Communications in Statistics, Part A – Theory and Methods, 26(3), 653–667. https://doi.org/10.1080/.
03610929708831940.
Bohn, L. L. (1996). A review of nonparametric ranked set sampling methodology. Communications in Statistics, Part A – Theory and Methods, 25, 2675–2685. https://doi.org/10.1080/03610929608831863.
Browder, D. M., Spooner, F., Ahlgrim-Delzell, L., Harris, A. A., & Wakemanxya, S. (2008). A meta-analysis on teaching mathematics to students with significant cognitive disabilities. Exceptional children, 74(4), 407-432. https://doi.org/10.1177/001440290807400401.
Chen, Z. (2000). Ranked – set sampling with regression – type estimators. Journal of Statistical Planning and Inference, 92, 181–192. https://doi.org/10.1016/S0378-3758(00)00077-X.
Dell, T. R., & Clutter, J. L. (1972). Ranked set sampling theory with order statistics background. International Biometric Society, 28, 545–555. https://doi.org/10.2307/2556166.
Gluzman, N. A., Sibgatullina, T. V., Galushkin, A. A., & Sharonov, I. A. (2018). Forming the Basics of Future Mathematics Teachers’ Professionalism by Means of Multimedia Technologies. EURASIA Journal of Mathematics, Science and Technology Education, 14(5), 1621-1633. https://doi.org/10.29333/ejmste/85034.
Granato, D., de Araújo Calado, V. M., & Jarvis, B. (2014). Observations on the use of statistical methods in food science and technology. Food Research International, 55, 137-149. https://doi.org/10.1016/j.foodres.2013.10.024.
Kaur, A., Patil, G. P., Shirk, S. J., & Taillie, C. (1996). Environmental sampling with a concomitant variable: a comparison between ranked set sampling and stratified simple random sampling. Journal of Applied Statistics, 23(2&3), 231–225. https://doi.org/10.1080/02664769624224.
Kalimullin, A. M., & Utemov, V. V. (2017). Open Type Tasks as a Tool for Developing Creativity in Secondary School Students. Interchange, 48, 129-144. https://doi.org/10.1007/s10780-016-9295-5.
Kim, Y. H., & Arnold, B. C. (1999). Parameter estimation under generalized ranked set sampling. Statistics and Probability Letters, 42, 353–360. https://doi.org/10.1016/S0167-7152(98)00225-9.
Kozlova, E. V., & Sakhieva, R. G. (2017). Specific Features of Training School Students for Final Certification in Mathematics for the Course of Basic School in the Context of a Complex Training System. EURASIA Journal of Mathematics, Science and Technology Education, 13(8), 4363-4378. doi: https://doi.org/10.12973/eurasia.2017.00932a.
Krutikhina, M. V., Vlasova, V. K., Galushkin, A. A., & Pavlushin, A. A. (2018). Teaching of Mathematical Modeling Elements in the Mathematics Course of the Secondary School. EURASIA Journal of Mathematics, Science and Technology Education, 14(4), 1305-1315. https://doi.org/10.29333/ejmste/83561.
Lam, K., Sinha, B. K., & Wu, Z. (1994) Estimation of parameters in a two – parameters in a two parameter exponential distribution using ranked set sample. Annals of the Institute of Statistical Mathematics, 46, 723–736. https://doi.org/10.1007/BF00773478.
Lloyd, E. H. (1952). Least – square estimation of location and scale parameters using order statistics. International Biometric Society, 39, 88–95. https://doi.org/10.1093/biomet/39.1-2.88.
MacEachern, S. N. (2002). A new ranked set sample estimator of variance. J.R. Statist. Journal of the Royal Statistical Society. Series B (Statistical Methodology), 64(2), 177–188. https://doi.org/10.1111/1467-9868.00331.
Mclntyre, G. A. (1952). A method of unbiased selective sampling using ranked sets. Australian Journal of Agricultural Research, 3, 385–390. https://doi.org/10.1071/AR9520385.
Mode, N., Conquest, L., & Marker, D. (1999). Ranked set sampling for ecological research, accounting for the total cost of sampling. Environ metrics, 10, 179–194. https://doi.org/10.1002/(SICI)1099-095X(199903/04)10:2<179::AID-ENV346>3.0.CO;2-#.
Raqab, M. Z., Kouider, E., & AlShboul, Q. M. (2002). Best linear invariant estimators using ranked set sampling procedure: comparative study. Computational Statistics and Data Analysis, 39, 97–105. https://doi.org/10.1016/S0167-9473(01)00051-2.
Stokes, S. L. (1995). Parametric ranked set sampling Annals of the Institute of Statistical Mathematics. Australian Journal of Agricultural, 47, 465–482.
Taylan, P., Weber, G. W., & Beck, A. (2007). New approaches to regression by generalized additive models and continuous optimization for modern applications in finance, science and technology. Optimization, 56(5-6), 675-698. https://doi.org/10.1080/02331930701618740.
Thibaut, L., Ceuppens, S., De Loof, H., De Meester, J., Goovaerts, L., Struyf, A., Boeve-de Pauw, J., …, Depaepe, F. (2018). Integrated STEM Education: A Systematic Review ofInstructional Practices in Secondary Education. European Journal of STEM Education, 3(1), 02. https://doi.org/10.20897/ejsteme/85525.
Utemov, V. V., & Masalimova, A. R. (2017). Differentiation of Creative Mathematical Problems for Primary School Students. EURASIA Journal of Mathematics, Science and Technology Education, 13(8), 4351-4362. https://doi.org/10.12973/eurasia.2017.00931a.
Yu, P. L. H., & Lam, K. (1997). Regression estimator in ranked set sampling. International Biometric Society, 53, 1070–1080. https://doi.org/10.2307/2533564.
Zelenina, N. A., & Khuziakhmetov, A. N. (2017). Formation of Schoolchildren’s Creative Activity on the Final Stage of Solving a Mathematical Problem. EURASIA Journal of Mathematics, Science and Technology Education, 13(8), 4393-4404. https://doi.org/10.12973/eurasia.2017.00934a.

How to cite this article

APA

Mohammad, G. S. (2019). Investigating the Efficiency of Teaching Mathematics to Students by Using the Double Ranked Set Sampling. Eurasia Journal of Mathematics, Science and Technology Education, 15(3), em1671. https://doi.org/10.29333/ejmste/102422

Vancouver

Mohammad GS. Investigating the Efficiency of Teaching Mathematics to Students by Using the Double Ranked Set Sampling. EURASIA J Math Sci Tech Ed. 2019;15(3):em1671. https://doi.org/10.29333/ejmste/102422

AMA

Mohammad GS. Investigating the Efficiency of Teaching Mathematics to Students by Using the Double Ranked Set Sampling. EURASIA J Math Sci Tech Ed. 2019;15(3), em1671. https://doi.org/10.29333/ejmste/102422

Chicago

Mohammad, Gorgees Shaheed. "Investigating the Efficiency of Teaching Mathematics to Students by Using the Double Ranked Set Sampling". Eurasia Journal of Mathematics, Science and Technology Education 2019 15 no. 3 (2019): em1671. https://doi.org/10.29333/ejmste/102422

Harvard

Mohammad, G. S. (2019). Investigating the Efficiency of Teaching Mathematics to Students by Using the Double Ranked Set Sampling. Eurasia Journal of Mathematics, Science and Technology Education, 15(3), em1671. https://doi.org/10.29333/ejmste/102422

MLA

Mohammad, Gorgees Shaheed "Investigating the Efficiency of Teaching Mathematics to Students by Using the Double Ranked Set Sampling". Eurasia Journal of Mathematics, Science and Technology Education, vol. 15, no. 3, 2019, em1671. https://doi.org/10.29333/ejmste/102422