Robust Inference and Management Prioritisation of Sub-Basin Water-Quality Heterogeneity in the Pra River Basin, Ghana
Frank B. K. Twenefour *
Department of Mathematics, Statistics and Actuarial Science, Takoradi Technical University, Takoradi, Ghana and Department of Mathematical Science, University of Mines and Technology, Tarkwa, Ghana.
Henry Otoo
Department of Mathematical Science, University of Mines and Technology, Tarkwa, Ghana.
Eric Neebo Wiah
Department of Mathematics, Statistics and Actuarial Science, Takoradi Technical University, Takoradi, Ghana.
*Author to whom correspondence should be addressed.
Abstract
Aims: River-basin averages may conceal management-relevant differences among tributary systems. This study quantified the magnitude, precision, and management relevance of differences in Water Quality Index (WQI) among the Birim, Offin, and Pra sub-basins of the Pra River Basin, Ghana.
Study Design: Secondary quantitative analysis of an existing cross-sectional, station-level WQI dataset.
Place and Duration of Study: The study covered 150 georeferenced monitoring stations distributed across the Birim, Offin, and Pra sub-basins of the Pra River Basin, Ghana. The secondary statistical analysis was conducted in 2026 using previously developed station-level WQI data.
Methodology: The study did not re-derive the WQI or repeat spatial interpolation. Descriptive statistics and 95% confidence intervals were used to summarise sub-basin WQI patterns. Distributional characteristics were assessed using the Shapiro-Wilk test. Overall differences among sub-basins were evaluated using Welch's one-way analysis of variance, followed by Games-Howell post hoc pairwise comparisons. Effect-size measures were estimated to assess the practical magnitude of observed differences.
Results: Mean WQI was highest in Offin \((120.57 \pm 15.67)\), followed by Birim \((93.33 \pm 10.82)\) and Pra \((74.17 \pm 7.22)\). Welch's test showed significant differences among the sub-basins, \(F(2,89.96)=198.36, p<0.001\). Variance-partition effect sizes were very large \(\left(\eta^2=0.728 ; \omega^2=0.723\right)\), while Games-Howell comparisons showed very large to extremely large standardised differences across all pairwise contrasts.
Conclusion: WQI differed substantially among the three sub-basins, indicating that basin-wide averages may obscure spatial differences relevant to water-quality management. Offin emerged as the highest priority for surveillance and source investigation, Birim as a corrective-monitoring priority, and Pra as a preventive-protection priority. The study provides decision-oriented evidence by quantifying uncertainty and practical effect magnitude while avoiding unsupported attribution of pollution to specific sources.
Keywords: Effect size, heteroscedasticity, management prioritisation, Pra River Basin, robust inference, water quality index, Welch ANOVA