The “new” statistics: mixing Bayesian statistics in with Qualitative research method: demonstrated on an analysis of stereotyping in teacher decision-making

Year: 2019

Author: Low-Choy, Samantha, Riley, Tasha, Alston-Knox, Clair

Type of paper: Abstract refereed

Researchers currently find themselves within a social-media fuelled galvanisation of nearly a century of debate, which is outlawing certain “shortcuts” and superficial approaches to statistical thinking. Some researchers have been advocating a Bayesian approach as one solution to the logical inconsistencies of null hypothesis testing and/or assessing significance by thresholding p-values. Against this backdrop, our paper, in the special issue of The Digital in Education (2017, Educational Media International), showed how Bayesian statistics can help bridge, in at least five ways, with qualitative research method.

The motivation was analysis of a study with interwoven quantitative and qualitative components. A well-designed experiment was conducted to detect whether stereotyping behaviour was evident in decision-making by teachers, in a hypothetical situation. In parallel, teachers were also interviewed about their perceptions on stereotyping, and how it might influence their decision-making in general, and in the experiment. The online tool that linked the quantitative and qualitative components also prompted teachers to explain any decisions that were not aligned with the grades of hypothetical students. Potentially these were influenced by stereotyping according to gender or ethnicity.

The five bridges spanned practical and theoretical considerations. Initially, feasible computation dictated a Bayesian approach to quantitative analysis: the data structure rendered it unsuitable for analysis using classical item response theory. We soon identified other benefits. Bayesian modelling privileges the model, so that a conceptual model can be directly mapped to a statistical model. The rich information resulting from Bayesian inference allows drilling down—about individual teachers, hypothetical students or stereotyping issues—in a way that allows a direct link between the qualitative results (interviews) and model results. In later studies we can exploit the cycle of Bayesian updating knowledge: these results can define a “prior” model, updated by new data, to produce new “posterior” inferences. As noted earlier, a primary reason for Bayesian inference is that by “inverting” classical probability it is more intuitive, communicating the plausibility of any hypothesis, rather than the likelihood of the data under any specific hypothesis. This paper is one of the first to comment on ontological, axiological and epistemological aspects of mixing-in Bayesian and Qualitative approaches.