Evaluation of Audit-Sampling Sufficiency for Artificial Intelligence Agriculture Grant Disbursement Under Local Government Fiscal Stress: A Political Science Detection-Probability Bound for Misallocation

The problem is framed as a detection-probability bound: given a fixed audit budget, what cluster-level sample size is required to identify a misallocation of a given magnitude with acceptable power? The study is a design and power analysis of a before-after-control-impact (BACI) estimator, not an empirical audit. Under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64), power was estimated across 2000 replications per design cell for cluster counts of 8, 16, 24, and 32 and effect sizes of 3, 5, and 8 percentage points. The analysis indicates that 52 clusters are required to detect a 5-percentage-point misallocation at 80% power. At 32 clusters, power for a 5-point effect falls below the conventional threshold, and the minimum detectable effect at 80% power exceeds 6 percentage points. The intraclass correlation of 0.64 implies that cluster-level sampling dominates precision, and that audit designs treating grants as independent observations will overstate detection probability. The conclusion is that audit-sampling sufficiency for AI agriculture grants cannot be assessed without explicit modelling of the intraclass correlation and that fiscal stress raises the effective detection threshold.