Perhaps first among the important methodological innovations of educational psychology was the development and application of factor analysis by Charles Spearman. Factor analysis is mentioned here as one example of the many multivariate statistical methods used by educational psychologists. Factor analysis is used to summarize relationships among a large set of variables or test questions, develop theories about mental constructs such as self-efficacy or anxiety, and assess the reliability and validity of test scores. Over one hundred years after its introduction by Spearman, factor analysis has become a research staple figuring prominently in educational psychology journals.
Because educational assessment is fundamental to most quantitative research in the field, educational psychologists have made significant contributions to the field of psychometrics. For example, alpha, the widely used measure of test reliability was developed by educational psychologist Lee Cronbach. The reliability of assessments are routinely reported in quantitative educational research. Although, originally, educational measurement methods were built on classical test theory, item response theory and Rasch models are now used extensively in educational measurement worldwide. These models afford advantages over classical test theory, including the capacity to produce standard errors of measurement for each score or pattern of scores on assessments and the capacity to handle missing responses.
Meta-analysis, the combination of individual research results to produce a quantitative literature review, is another methodological innovation with a close association to educational psychology. In a meta-analysis, effect sizes that represent, for example, the differences between treatment groups in a set of similar experiments, are averaged to obtain a single aggregate value representing the best estimate of the effect of treatment. Several decades after Pearson's work with early versions of meta-analysis, Glass published the first application of modern meta-analytic techniques and triggered their broad application across the social and biomedical sciences. Today, meta-analysis is among the most common types of literature review found in educational psychology research.
Other quantitative research issues associated with educational psychology include the use of nested research designs (e.g., a student nested within a classroom, which is nested within a school, which is nested within a district, etc.) and the use of longitudinal statistical models to measure change.
