The first problem of using parametric frequentistic statistical techniques in the research field of education is that they are based on frequencies produced by repeated measures. Widely applied multivariate methods, such as exploratory factor analysis or multivariate analysis of variance, require a researcher to collect about ten informants for each question that is to be analysed in the same process.
The second problem is that all parametric frequentistic analyses are based on the concept of normal distribution. If this assumption is met, it leads to a desirable state of multivariate normality allowing linear inter-item analysis. However, if the assumption is not met, for example, when the variables in the analysis have different shapes of distributions, the models based on normal distribution are not working correctly and produce false results.
The third problem is that indicators measurement level should be at least an interval (continuous) in order to meet the aforementioned multivariate normality assumption (leading to linear dependencies between variables). Although this assumption does not relate to grouping variables that are allowed to have nominal or ordinal measurement levels (e.g., linear discriminant analysis), most of the questionnaire items have typically a five-point ordinal "Likert scale". Statistical dependencies between such non-continuous items are not necessarily linear.
Typical solution when assumptions of parametric frequentistic statistical techniques are not met is to use frequentistic non-parametric techniques. Such techniques provide opportunity to apply, for example, Spearman’s rank order correlation instead of Pearson product moment correlation or Mann-Whitney U-test instead of Student’s t-test. However, such techniques are, although allowing smaller sample sizes than their parametric counterparts, still frequentistic techniques. These techniques are sometimes called ’distribution free’, but they are not ’assumption free’ as most of them expect simultaneously analysed distributions to have symmetrical and similar shapes.
Being a 'bayesian' allows us to address all of the aforementioned technical problems. First of all, Bayesian modeling is based on probabilities allowing theoretical minimum sample size of zero and prediction with the model. Further, discrete categorical variables are allowed, and finally, both linear and non-linear dependencies between variables are analyzed.
In this study, Bayesian methods were applied to study various professional growth and learning research questions. The results showed that Bayesian modeling should be applied when a discrete indicator sample is small, it contains other than linear dependencies, and/or predictive inference is needed to address research questions.
