Pixel Counting Can Be Biased — Interactive Demo

Overview. Estimating area by simply counting positive pixels can be biased when the grid is coarse, boundaries are oblique/complex, or the map has classification error. A design-based, post-stratified estimator—using a probability sample of reference points within map strata (map=1 vs map=0)—yields unbiased area estimates and valid confidence intervals. This demo contrasts naïve pixel counting with the recommended stratified estimator following best practices described by Olofsson et al. (2014).

• Pixel-count area: #positive cells × cell area. This can be biased with coarse grids and oblique/complex boundaries (especially with any-touched).
• Corrected area (post-stratified): Unbiased estimator using point samples. Split the map by the raster prediction (map class 1 vs 0); sample n points per stratum; label each by the polygon (1 inside, 0 outside). With stratum means p̂₁, p̂₀ and area weights W₁, W₀, the estimated proportion is P̂ = W₁·p̂₁ + W₀·p̂₀ and the corrected area is  = P̂ × (total area). CI uses Var(P̂) = W₁²·p̂₁(1−p̂₁)/n₁ + W₀²·p̂₀(1−p̂₀)/n₀.