Essential Benefits and Disadvantages of Using Discrete Bayesian Methods in Educational Research

Author(s):

Petri Nokelainen

Conference:

ECER 2009

Network:

9. Assessment, Evaluation, Testing and Measurement

Format:

Paper

Session Information

09 SES 03 C, Testing Theory and Methodology

Paper Session

Time:

2009-09-28

14:00-15:30

Room:

HG, Elise Richter

Chair:

Tobias C. Stubbe

Contribution

In this paper, I will first discuss the typical problems of using parametric frequentistic statistical techniques, such as t-test, to answer educational science research questions. After that I will present the Bayesian modeling approach and discuss about its advances and limitations from educational researcher's point of view. The discussion is based on practical experiences on empirical studies that I have carried out with Bayesian methods during the past ten years. The problem of rational inference under uncertainty has been the subject of considerable attention since the systematic study of the probability theory began in the eighteenth century. Many different theories of inference have been proposed, and there has hardly been a time when inference under uncertainty was not a matter of real controversy. It seems that educational research community (among many other fields using applied statistics) has been largely unaware of such controversies, and used what is known as classical, frequentistic or Gaussian inference (Hastings, 1997). Since 1960’s there has been a steady revival of interest in an alternative way of reasoning with probabilities called Bayesian inference (Berger, 1985, Bernardo & Smith, 2000). Many applied fields including astrophysics (Loredo, 1990), medicine (Smith, Spiegelhalter & Parmar, 1996), econometrics (Zellner, 1971), archaeology (Buck, Cavanagh & Litton, 1996) and political sciences have adopted Bayesian techniques, but the penetration of Bayesian inference into educational research has not been particularly influential. According to Tirri (1999), this is somewhat surprising as quantitative analysis in education exhibits all the features where Bayesian approaches excel: small data sets with many measured issues, emphasis on hierarchical models, models involving latent structures, and data sets with discrete (nominal) values. When an educational researcher wants to study dependencies between observed and/or latent variables, the assumptions for the data may become quite challenging in traditional frequentistic statistical analysis. Examples of such assumptions are the continuous measurement level, multivariate normality and linearity of both the data and phenomena under investigation. Bayesian modeling approach, named after English reverend Thomas Bayes (1701-1761), is a viable alternative to frequentistic statistical techniques addressing all the abovementioned modeling problems. Bayesian theory of probability (e.g., Bernardo & Smith, 2000) is interested in probability of certainty that a given fact or proposition is true. Bayesian approach is often labeled as ”subjective probability”, as its probability values dependent on how much weight we are willing to lay on both the evidence and prior information available.

Method

As this is a theoretical paper, earlier research body and my own empirical studies (and the reports based on them) are the information sources. For example, I have written several comparative methodological articles/chapters on frequentistic and bayesian methods.

Expected Outcomes

The essential benefits of discrete Bayesian methods are summarized as follows: 1) Theoretical minimum sample size is zero; 2) It allows prediction with the data; 3) It answers directly to the research questions as the model is constructed from the data P(M|D); 4) Researcher is able to input a priori (expert) knowledge to the model; 5) It is designed to analyze categorical variables; 6) It is able to analyze both linear and non-linear dependencies between variables. There are also issues applying discrete Bayesian methods that researchers should be aware of: 1) All data is categorized for the analysis. In practice this means that no matter how ’quantitative’ the data originally is (e.g., continuous indicator measured on ratio scale), it is categorized and the order of the classes is destroyed; 2) Small sample size is a fallacy as it leads to reduced power, making Type II error more probable.

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Author Information

Petri Nokelainen

University of Tampere

Department of Education

Tuulos

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