Statistical Tools for Experimental Design, Inference and Process Optimisation in Mineral Processing: Review of ANOVA, Response Surface Methods and Data-Driven Models

Abstract

Mineral processing research concerns heterogeneous materials and strongly interacting operating variables, so experimental conclusions depend as much on design quality and statistical reasoning as on laboratory technique. This critical review examines the connected roles of descriptive analysis, analysis of variance (ANOVA), design of experiments (DOE), regression, response surface methodology (RSM), multivariate analysis, mixed-effects modelling and data-driven surrogate models in mineral processing. The discussion covers comminution, classification, gravity and dense-medium separation, magnetic separation, froth flotation, hydrometallurgy, dewatering and the beneficiation of lithium-bearing and other critical-mineral ores. Particular attention is given to experimental units, randomisation, replication, blocking, interaction effects, assumption diagnostics, effect sizes, model uncertainty, multiple-response optimisation and confirmation testing. ANOVA remains valuable for partitioning variation and testing designed effects, but p-values alone provide an incomplete basis for engineering decisions. Regression and RSM support prediction and optimisation when model form is adequate, while mixed and multivariate methods address hierarchical sampling structures and correlated responses. For nonlinear or stochastic systems, Gaussian-process, artificial-neural-network and ensemble models may improve prediction, provided that cross-validation, sensitivity analysis, interpretability and independent experimental verification accompany their use. The article proposes a sequential framework that links ore characterisation, DOE, statistical inference, predictive modelling, constrained optimisation and scale-up validation. It also presents a reporting checklist intended to improve reproducibility and comparability. The central conclusion is that mineral-processing statistics should function as an integrated research architecture rather than as a final software step performed after testwork. This approach can reduce unnecessary experiments, expose factor interactions, quantify uncertainty and produce more transferable process knowledge.