Statistics for N = 1

A Non-Parametric Bayesian Approach

Keywords: 95% Credible Interval, Percentage of All Non-Overlapping Data (PAND), Percentage of All Non-Overlapping Data Bayes (PAND-B), Single Case Design (SCD), Single Case Experimental Design (SCED)

Abstract

Research in education is often associated with comparing group averages and linear relations in sufficiently large samples and evidence-based practice is about using the outcomes of that research in the practice of education. However, there are questions that are important for the practice of education that cannot really be addressed by comparisons of group averages and linear relations, no matter how large the samples. Besides, different types of constraints including logistic, financial, and ethical ones may make larger-sample research unfeasible or at least questionable. What has remained less known in many fields is that there are study designs and statistical methods for research involving small samples or even individuals that allow us to address questions of importance for the practice of education. This article discusses one type of such situations and provides a simple coherent statistical approach that provides point and interval estimates of differences of interest regardless of the type of the outcome variable and that is of use in other types of studies involving large samples, small samples, and single individuals.

Downloads

Download data is not yet available.

Author Biography

Jimmie Leppink, University of York, York, North Yorkshire (NY), United Kingdom

PhD in Statistics Education, LLM in Forensics, Criminology and Law, and MSc in Psychology and Law from Maastricht University, the Netherlands; MSc in Statistics from Catholic University of Leuven, Belgium; currently Senior Lecturer in Medical Education and Director of Assessment at Hull York Medical School, University of York, United Kingdom.

References

Box GEP, Jenkins GM, Reinsel GC. Time series analysis: Forecasting and control. 3.rd ed. Upper Saddle River, NJ: Prentice Hall; 1994.

Brockwell PJ, Davis RA. Time series: Theory and methods. 2.nd ed. New York: Springer; 2009.

Leppink J. The art of modelling the learning process: Uniting educational research and practice. [Internet]. Cham: Springer; 2020 [citado 2020 Nov 13]. Disponível em: https://doi.org/10.1007/978-3-030-43082-5

Michiels B, Heyvaert M, Meulders A, Onghena P. Confidence intervals for single-case effect size measures based on randomization test inversion. Behav Res Meth [Internet]. 2017 [citado 2020 Nov 13];49:363-81. Disponível em: https://doi.org/10.3758/s13428-016-0714-4

Michiels B, Onghena P. Randomized single-case AB phase designs: Prospects and pitfalls. Behav Res Meth [Internet]. 2018 [citado 2020 Nov 13];51:2454-76. Disponível em: https://doi.org/10.3758/s13428-018-1084-x

Pérez-Fuster P, Sevilla J, Herrera G. Enhancing daily living skills in four adults with autism spectrum disorder through an embodied digital technology-mediated intervention. Res Aut Spect Dis [Internet]. 2019 [citado 2020 Nov 13];58:54-67. Disponível em: https://doi.org/10.1016/j.rasd.2018.08.006

Tanious R, De TK, Onghena P. A multiple randomization testing procedure for level, trend, variability, overlap, immediacy, and consistency in single-case phase designs. Behav Res Therap [Internet]. 2019 [citado 2020 Nov 13];119:103414. Disponível em: https://doi.org/10.1016/j.brat.2019.103414

Van de Schoot R, Milocević M. Small sample size solutions: A guide for applied researchers and practitioners [Internet]. OAPEN Home; 2020. [citado 2020 Nov 13]. Disponível em: http://library.oapen.org/handle/20.500.12657/22385

Cohen J. Statistical power analysis for the behavioural sciences. New York: Routledge; 1988.

Parker RI, Hagan-Burke S, Vannest KJ. Percentage of all non-overlapping data (PAND): An alternative to PND. J Spec Educ [Internet]. 2007 [citado 2020 Nov 13];40:194-204. Disponível em: https://doi.org/10.1177/00224669070400040101

Published
2020-12-17
How to Cite
Leppink, J. (2020). Statistics for N = 1: A Non-Parametric Bayesian Approach. Scientia Medica, 30(1), e38066. https://doi.org/10.15448/1980-6108.2020.1.38066
Section
Education in Health Sciences