Diversity represents a major issue in all fields of educational theory and practice (e.g., Conners & Capell, 2021). From a social research perspective, it has been defined as “the distribution of population elements along a continuum of homogeneity to heterogeneity with respect to one or more variables” (Teachman, 1980). In educational intervention research, we have, for example, “interventions for diverse people” (e.g., Tincani et al., 2009), diversity as a “research strategy” (e.g., Bent-Goodley, 2021), or “design specifications” for diversity interventions (Vinkenburg, 2017). Diversity in educational intervention research is related to different facets like a research agenda, an evidence-based orientation, exploration and innovation, expanded effectiveness, interdisciplinary focus, error reduction, or statistical quality. For example, as a general social research strategy on diversity, multiple more or less stable personality characteristics should be measured that correlate with the dependent variables (control variables), that are related to the independent variables (interactions) or that might be related to alternative explanations (validation, exploration). In respect to data analysis and statistics, diversity has to be described, controlled, structured, and tested. Although diversity and related variability as well as variance represent the nucleus of statistical analyses in social research, strategies on how diversity can systematically be integrated into data analysis processes in educational intervention studies are still missing (e.g., Astleitner, 2020). Our goal in this paper is to identify, collect, and evaluate statistical concepts related to diversity which are essential in educational intervention research. Our perspective is one of quantitative social researchers who have comprehensive experience in the field of educational intervention studies. Our theoretical focus is based on the concept of diversity in social research settings (Schuelka et al., 2019) and on (methodological) models of educational intervention research (McBride, 2016).

Our method is a review of statistical methods (e.g., Tipton & Osen, 2018). First, we have reviewed literature and collected statistical concepts which are relevant for diversity and educational intervention research. Second, we have conceptually structured these concepts based on statistical procedures, definitions and goals, software for computations as well as potential use in intervention research. Third, we have formulated implications that allow to guide research and statistical analysis in educational intervention research in the future.

We have found statistical concepts (as well as statistical software) on diversity related to dispersion indices (e.g., range), outliers (e.g., multivariate outliers), diversity indices (e.g., Simpson´s diversity index), or social cohesion indices (e.g., Herfindahl-Hirschman Index), analysis of covariance, aptitude-treatment-interaction-analysis, recursive partitioning methods, cluster analysis, latent class (clustering) analysis, and homogeneity of variance tests (e.g., Budescu & Budescu, 2012; Doove et al., 2014; Huitema, 2011; Kent et al., 2014; Leys et al., 2013; Schaeffer, 2016). Using these concepts in a review of literature allows to identify numerous significant implications which can guide future activities in educational intervention research. We discuss issues related to educational interventions like changes in variances as side effects of interventions, disequalizing effects, handling outliers, diversity indices as sources for theory building, discovering different effectiveness patterns in different people, exploring participants who were particularly responsive or finding groups of people with similar characteristics before and after an intervention. Within this paper, we present, up to our knowledge for the first time, a collection of well and less well-known statistical concepts and related implications that are important for handling diversity in educational intervention research. We have promoted a constructive, methodologically critical view of educational intervention research based on the concept of diversity (e.g., Mellenbergh, 2019). Our work aims to encourage the reflection and use of diversity-related tests as a standard in educational intervention studies as has been the case in other research disciplines (e.g., Magurran, 2003).

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