Undergraduate students’ errors on interval estimation based on variance neglect

Budi Murtiyasa, Afifah Ma'rufi, Mohd Asrul Affendi bin Abdullah

Abstract


Interval estimation is an important topic, especially in drawing conclusions on an event. Mathematics education students must possess the skill to formulate and use interval estimation. The errors of mathematics education students in formulating wrong interval estimates indicate a low understanding of interval estimation. This study explores the errors of mathematics education students in interpreting the variance in the questions regarding selecting the proper test statistic to formulate the interval estimation of mean accurately. Respondents in this study involved 36 students of mathematics education (N = 9 males, N = 27 females). This research is qualitative research with a qualitative descriptive approach. Data collection was carried out using the respondents’ ability test and interviews. The respondents’ ability test instrument was tested on 36 students and declared valid where r-count > r-table with r-table of 0.3291, and declared reliable with a Cronbach Alpha value of 0.876 > 0.6. Through an exploratory approach, data were analyzed by categorizing, reducing, and interpreting to conclude students' abilities and thinking methods in formulating interval estimation of the mean based on the variance in questions. The results showed that mathematics education students neglected the variance, so they could not determine the test statistics correctly, resulting in error interval estimates. This study provides insight into the thinking methods of mathematics education students on variance in interval estimation problems in the hope of anticipating errors in formulating interval estimation problems.

Keywords


distribution test; interval estimation; statistical tests; variance

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References


Ahmad, S., Zulkurnain, N. N. A., & Khairushalimi, F. I. (2016). Assessing the validity and reliability of a measurement model in Structural Equation Modeling (SEM). Journal of Advances in Mathematics and Computer Science, 15(3), 1-8. https://www.journaljamcs.com/index.php/JAMCS/article/view/23445

Altman, D. G. (2005). Why do we need confidence intervals. World Journal of Surgery, 29(5), 554-556. https://doi.org/10.1007/s00268-005-7911-0

Budiarto, E. (2002). Biostatistika untuk kedokteran dan kesehatan masyarakat [Biostatistics for public health and medicine]. Kedokteran EGC.

Budiyono. (2016). Statistika untuk penelitian [Statistics for research]. UNS Press.

Cahyono, T. (2018). Statistika terapan [The applied statistics]. Deepublish.

Cumming, G., & Fidler, F. (2009). Confidence intervals: Better answers to better questions. Journal of Psychology, 217(1), 15-26. https://doi.org/10.1027/0044-3409.217.1.15

Damanik, E., & Simamora, E. (2019). Estimasi interval kepercayaan parameter selisih rata-rata IPK kelas pendidikan reguler dan ekstensi FMIPA angkatan 2010 UNIMED dengan boostrap persentil [The parameter confidence of interval estimation of GPA differences of regular education class and extension class of mathematics and Physics faculty in 2010 of UNIMED with bootstrap percentile]. Karismatika, 5(3), 1-9. https://jurnal.unimed.ac.id/2012/index.php/jmk/article/view/23354

Fieller, E. C. (1954). Some problems in interval estimation. Journal of the Royal Statistical Society: Series B (Methodological), 16(2), 175-185. https://doi.org/10.1111/j.2517-6161.1954.tb00159.x

Hobri, H., Tussolikha, D., & Oktavianingtyas, E. (2020). Pemecahan masalah dalam menyelesaikan soal jumping task ditinjau dari gaya kognitif [Problem-solving of jumping question tasks based on cognitive styles]. Jurnal elemen, 6(2), 183-198. https://doi.org/10.29408/jel.v6i2.1857

Hoekstra, R., Johnson, A., & Kiers, H. A. (2012). Confidence intervals make a difference: Effects of showing confidence intervals on inferential reasoning. Educational and Psychological Measurement, 72(6), 1039-1052. https://doi.org/10.1177/0013164412450297

Hoekstra, R., Morey, R., Rouder, J., & Wagenmakers, E. (2014). Robust misinterpretation of confidence intervals. Psychonomic bulletin & review, 21(5), 1157-1164. https://doi.org/10.3758/s13423-013-0572-3

Jarret, C. (2011). What is a confidence interval and why would you want one. In Uxmatters. https://www.uxmatters.com/mt/archives/2011/11/what-is-a-confidence-interval-and-why-would-you-want-one.php

Kalinowski, P. (2010). Identifying misconceptions about confidence intervals. Proceedings of the eighth international conference on teaching statistics (ICOTS8), 50.

Kadilar, C., & Cingi, H. (2005). A new ratio estimator in stratified random sampling. Communications in Statistics—Theory and Methods, 34(3), 597-602. https://doi.org/10.1081/STA-200052156

Lusiana, R. (2017). Analisis kesalahan mahasiswa dalam memecahkan masalah pada materi himpunan ditinjau dari gaya kognitif [Analysis of student errors in solving problems on set material in terms of cognitive style]. Jurnal Penelitian dan Pembelajaran Matematika, 10(1), 24-29. https://doi.org/10.30870/jppm.v10i1.1290

Murtiyasa, B., Perwita, W. R. G. (2020). Analysis of mathematics literation ability of students in completing PISA-oriented mathematics problems with changes and relationships content. Universal Journal of Educational Research, 8(7), 3160-3172. https://doi.org/10.13189/ujer.2020.080745

Murtiyasa, B., Wulandari, V. 2020. Analisis kesalahan siswa materi bilangan pecahan berdasarkan teori Newman [Analysis of student errors in fractional numbers based on Newman's theory]. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 9(3), 713-726. https://doi.org/10.24127/ajpm.v9i3.2795

Purnamasari, I., & Setiawan, W. (2019). Kemampuan pemecahan masalah matematis siswa SMP pada materi SPLDV ditinjau dari kemampuan awal matematika (KAM) [Mathematics problem-solving skills of JHS in SPLDV materials based on initial mathematics skills]. Journal of Maldives: Journal of Mathematics Education IKIP Veteran Semarang, 3(2), 207-215. https://doi.org/10.31331/medivesveteran.v3i2.771

Raupong, R., Saleh, A. F., & Taruma, H. S. (2015). Penaksiran rataan dan varians populasi pada sampel acak terstratifika dengan auxiliary variable [Estimation of population mean and variance on a stratified random sample with auxiliary variable]. Jurnal Matematika, Statistika dan Komputasi, 12(1), 9-18.

Strehl, A. L., & Littman, M. L. (2008). An analysis of model-based interval estimation for Markov decision processes. Journal of Computer and System Sciences, 74(8), 1309-1331. https://doi.org/10.1016/j.jcss.2007.08.009

Supena, I., Darmuki, A., & Hariyadi, A. (2021). The Influence of 4C (constructive, critical, creativity, collaborative) learning model on students' learning outcomes. International Journal of Instruction, 14(3), 873-892. https://doi.org/10.29333/iji.2021.14351a

Syamsuddin, A. (2020). Describing taxonomy of reflective thinking for field-dependent-prospective mathematics teacher in solving mathematics problem. International Journal of Scientific & Technology Research, 9(3), 4418-4421.

Tamba, K., Siahaan, M., & Appulembang, O. (2021). Kesalahan mahasiswa pendidikan matematika dalam menggunakan ukuran pemusatan: pengabaian variansi [Mathematics students' errors in using focused measurement: variance ignorance]. Jurnal Elemen, 7(1), 164-179. https://doi.org/10.29408/jel.v7i1.2806

Taherdoost, H. (2016). Validity and reliability of the research instrument: How to test the validation of a questionnaire/survey in a research. International Journal of Academic Research in Management. 5(3), 28-36. https://doi.org/10.2139/ssrn.3205040

Taqiyuddin, M., Sumiaty, E., & Jupri, A. (2016). Miskonsepsi siswa sekolah menengah pertama pada topik pertidaksamaan linear satu variable [Misconceptions of junior high school students on the topic of linear inequality of one variable]. Journal of Mathematics Education Research, 1(1), 64-81.

Ulpah, M. (2009). Belajar statistika: Mengapa dan bagaimana? [Learning statistics: Why and how?]. Insania: Jurnal Pemikiran Alternatif Pendidikan, 14(3), 325-435. https://doi.org/10.24090/insania.v14i3.354

Williams, C. (2007). Research methods. Journal of Business & Economics Research (JBER), 5(3), 65-71. https://doi.org/10.19030/jber.v5i3.2532




DOI: https://doi.org/10.29408/jel.v8i1.4529

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