Using Bayesian statistics to deal with small sample size: Reflection from a study of international education

Hiep-Hung Pham
EdLab Asia Center for Education Research and Development, 83 Nguyen Khang, Cau Giay, Hanoi 100000, Vietnam
Email: hiep@edlabasia.org
ORCID: https://orcid.org/0000-0003-3300-7770

September 4, 2022

Scholars in social sciences often face the recurrent problem of a small sample size. Under this circumstance, Bayesian inference is often recommended to ensure data estimation validity [1,2]. In this paper, I will reflect on my experience using Bayesian statistics to analyze a dataset of 49 samples and subsequently succeed in publishing my work in a qualified journal in international education [3]. The work is part of a larger project investigating the recent trend of international student mobilities in Asia and Vietnam [4-7].


https://www.tandfonline.com/doi/abs/10.1080/14767724.2022.2081536

Traditionally, Vietnam is regarded as a significant source of international students for major host countries such as the US, UK, Australia, or Japan. In the opposite direction, the understanding of international students in Vietnam remains very limited. Thus, my colleagues and I aimed to fulfill this research gap by examining factors impacting the outputs of international students at 49 tertiary education institutions in Vietnam. The study contributes to an emerging trend of research on international student mobilities in Asia.

One of the perennial problems scholars face in developing countries is the lack of available secondary data. Given this circumstance, we used primary data collected directly from Vietnam’s universities and colleges. A survey was distributed to 100 tertiary education institutions in Vietnam in February 2019. Nevertheless, after ten months of data collection, we could only receive 49 validated samples, which is insufficient for conventional frequentist analysis. Besides more accurate inference of the small dataset at hand than the frequentist method, Bayesian inference also allowed us to visualize beautiful credible intervals of estimated parameters. Credible intervals imply the region where unobserved parameter values fall with particular probabilities, which is theoretically more advantageous than the confidence intervals and p-value testing of frequentist approaches [8,9]. Thus, Bayesian statistics employing the bayesvl R package (version 0.8.5) was chosen for empirical analysis [10].

The analysis led to three main findings. First, we discovered that despite the small number, international students have become indispensable to Vietnamese tertiary education. While full-time international students in Vietnam mostly come from neighboring countries in Asia, short-time international students come from both Asia and other continents.

Second, Vietnamese universities and colleges have implemented various strategies (factors) to attract international students. These strategies (factors) can be categorized into two main types:

• Operation-related strategies (factors), such as having an in-charged unit to recruit international students, having a particular process to recruit international students, having separate classrooms for international students, having a separate dormitory for international students, and having a scholarship for international students.
• Academic-related strategies (factors), such as having a scholarship for international students, using a foreign language as the primary teaching language, being accredited by an international accreditation entity, having expatriate teachers, and implementing an international curriculum licensed by a partner university.

Third, our Bayesian analysis revealed that the strategies adopted by universities and colleges do not necessarily bring about equal effectiveness in attracting international students. In particular, four out of five operation-related factors (except having separate classrooms for international students) have some effect on international students’ outcomes. On the contrary, it is interesting that all academic-related factors (except for having a scholarship for international students) do not have associations with the success of Vietnamese universities and colleges in attracting international students.

Based on the presented findings, Vietnamese tertiary education institutions should implement appropriate and strategic measures to recruit international students, given the current intense competition in the international student market [11]. Vietnamese universities and colleges might consider sustaining their current market by relying on intra-regional for full-time international students, intra-regional and extra-regional for short-time international students, and international students whose primary purposes are not academic-related. Vietnamese universities and colleges should also consider expanding their current market into new segments.

Although the study has resulted in some insights for policymaking of international education in Vietnam, it has not fully adopted the advantages of the Bayesian approach, such as prior incorporation and multilevel modeling [12]. Future studies may benefit from these advantages using a full-fledged approach like the Bayesian Mindsponge Framework analytics [13].

References

[1] Rupp AA, Dey DK, Zumbo BD. (2004). To bayes or not to bayes, from whether to when: Applications of Bayesian methodology to modeling. Structural Equation Modeling, 11, 424–451.

[2] Kruschke JK, Aguinis H, Joo H. (2012). The time has come Bayesian methods for data analysis in the organizational sciences. Organizational Research Methods, 15, 722–752. https://journals.sagepub.com/doi/10.1177/1094428112457829

[3] Pham HH, et al. (2022). International education as an export sector: an investigation of 49 Vietnamese universities and colleges using Bayesian analysis. Globalization, Societies and Education, 1–19. https://www.tandfonline.com/doi/abs/10.1080/14767724.2022.2081536

[4] Pham HH. (2022). Further Understanding on International Student Mobilities in Asia is Needed. Journal of International Students, 12(2). https://www.ojed.org/index.php/jis/article/view/4898

[5] Pham HH, et al. (2021). A bibliometric review of research on international student mobilities in Asia with Scopus dataset between 1984 and 2019. Scientometrics, 126(6), 5201–5224. https://link.springer.com/article/10.1007/s11192-021-03965-4

[6] Pham HH, et al. (2021). The Southern world as a destination of international students: An analysis of 50 tertiary education institutions in Vietnam. Journal of Contemporary Eastern Asia, 20(1), 24–43. http://koreascience.or.kr/article/JAKO202123857269532.page

[7] Vuong QH, et al. (2021). Current trends and realities of international students in East and Southeast Asia: The cases of China, Hong Kong, Taiwan, and Malaysia. International Journal of Education and Practice, 9(3), 532–549.

[8] Halsey LG, et al. (2015). The fickle P value generates irreproducible results. Nature Methods, 12(3), 179-185. https://www.nature.com/articles/nmeth.3288

[9] Wagenmakers EJ, et al. (2017). Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications. Psychonomic Bulletin & Review, 25, 35-57. https://link.springer.com/article/10.3758/s13423-017-1343-3

[10] Vuong QH, et al. (2020). Bayesian analysis for social data: A step-by-step protocol and interpretation. MethodsX, 7, 100924. https://www.sciencedirect.com/science/article/pii/S2215016120301448

[11] Stein S, de Oliveira Andreotti V. (2017). Higher education and the modern/colonial global imaginary. Cultural Studies ? Critical Methodologies, 17(3), 173–181. https://journals.sagepub.com/doi/10.1177/1532708616672673

[12] Nguyen MH, et al. (2022). Introduction to Bayesian Mindsponge Framework analytics: An innovative method for social and psychological research. MethodsX, 9, 101808. https://www.sciencedirect.com/science/article/pii/S2215016122001881

[13] Vuong QH, Nguyen MH, La VP. (2022). The mindsponge and BMF analytics for innovative thinking in social sciences and humanities. De Gruyter. https://books.google.com/books/about?id=EGeEEAAAQBAJ