gtheory-app: a Shiny app for generalizability theory analyses

Generalizability theory (G-theory) extends classical reliability theory by partitioning measurement error into multiple, separable sources, thereby supporting the design of more dependable measurement procedures. Existing software for G-theory — most notably the GENOVA Suite and EduG — is widely used but predates contemporary R-based reproducible workflows and lacks interactive exploration of decision (D) study trade-offs. We introduce gtheory-app, a free and open-source Shiny application that brings G-theory analysis into the browser. The application accepts long-format data uploads with auto-detected delimiters or score-only files paired with a user-specified design, supports balanced and unbalanced data, and handles fully crossed, nested, and mixed (random + fixed) designs with an arbitrary number of facets. Variance components are estimated via lme4 (REML) with a classical ANOVA cross-check available for balanced data. The application then reports universe-score variance, relative and absolute error variances, the generalizability coefficient (Eρ²), the index of dependability (Φ), Φ(λ) for criterion-referenced decisions, a G-facets sensitivity table, and an interactive 3D surface graph over any pair of user-selected facets with the resulting D-study. Every numerical output is paired with a context-sensitive, plain-language interpretation that names the user's actual facets, places reliability values in conventional bands, and identifies the largest single error term as a target for redesign. We illustrate the application on three classes of designs: a fully crossed three-facet design, a nested-items design, and a multi-facet chain-nested design. We argue that gtheory-app fills a clear gap in the open-source psychometric software ecosystem and lowers the barrier to G-theory for applied researchers, educators, and assessment professionals.