Improve estimator variance and allocation formulas

[XavierCLL]

Summary

This PR fixes two estimator-calculation issues found while reviewing the AcATaMa equation table against the implementation and cited estimator formulas.

1. Post-stratified area variance

The simple/systematic post-stratified estimator previously built the variance component with only the contribution from samples belonging to a reference class:

n_hj * (1 - n_hj / n_h+)^2 / (n_h+ - 1)

For a binary class indicator inside a post-stratum, the sample variance must include both successes and failures. Algebraically:

s_hj^2 = [n_hj(1 - p_hj)^2 + (n_h+ - n_hj)(0 - p_hj)^2] / (n_h+ - 1)
       = n_hj(1 - p_hj) / (n_h+ - 1)

where p_hj = n_hj / n_h+.

This PR usea a shared post_stratified_variance_table helper with:

n_hj * (1 - n_hj / n_h+) / (n_h+ - 1)

This avoids underestimating post-stratified standard errors and confidence intervals, especially when p_hj is high.

2. Stratified sample allocation

The stratified sample-size helper already computed total sample size using the weighted stratum standard deviations:

n = (sum_i W_i S_i / S(OA))^2
S_i = sqrt(U_i(1 - U_i))

However, per-stratum allocation used only mapped area proportions:

n_i = round(W_i * n)

This meant the conjectured user accuracy U_i affected total sample size but not the relative allocation among strata. This PR updates allocation to:

n_i = round((W_i S_i / sum_k W_k S_k) * n)

so per-stratum sample counts now use both mapped area proportion and expected stratum variability.

Files changed

• AcATaMa/gui/accuracy_assessment_results.py
  • Adds a shared helper for post-stratified class-indicator variance components.
• AcATaMa/utils/sampling_utils.py
  • Keeps the existing total sample-size equation.
  • Updates per-stratum allocation to weight by W_i S_i rather than W_i alone.

Verification

No test suite was run, per request.

Performed only non-test verification:

• Static LSP diagnostics on changed files: clean.
• Syntax-only compile checks with python -m py_compile on both changed modules.
• Manual standalone formula checks confirming:
  • the post-stratified binary sample-variance identity matches the implemented expression;
  • stratified allocation now changes when S_i differs across strata, as expected.

Notes

Stratified sampling fixtures may also change when area-based allocation is regenerated, because per-stratum counts now include S_i in the allocation weights.

[XavierCLL]

Affected table item	Before	After
STR — Sample size and allocation	Sᵢ = √[Uᵢ(1−Uᵢ)]; n ≈ (Σᵢ WᵢSᵢ/S(Ô))²; nᵢ ≈ round(Wᵢn), with minimum-per-stratum override	Sᵢ = √[Uᵢ(1−Uᵢ)]; n ≈ (Σᵢ WᵢSᵢ/S(Ô))²; nᵢ ≈ round((WᵢSᵢ / ΣₖWₖSₖ)n), with minimum-per-stratum override
Post-Stratified designs — Area estimation and CI	p̂₊ⱼᴾˢ = Σₕ Wₕᴾˢ(nₕⱼ/nₕ₊); AcATaMa applies its implemented post-stratified variance	p̂₊ⱼᴾˢ = Σₕ Wₕᴾˢ(nₕⱼ/nₕ₊); variance uses the corrected post-stratum class-indicator component: sₕⱼ² = nₕⱼ(1−nₕⱼ/nₕ₊)/(nₕ₊−1)

Note: the STR change affects sample allocation only. The Post-Stratified-design change affects standard error, confidence intervals, coefficient of variation, and uncertainty for post-stratified simple/systematic estimators.