In Chile, La Araucanía records 13.0% extreme poverty; Magallanes, 4.2%. That is 8.8 percentage points of difference — and if a public agency at the central or local level (regional governments / municipalities) designs its intervention using only the national average (6.9%), or disregarding regional differences, it could get the allocation of resources or the distribution of its components wrong. This post documents a reproducible analysis of CASEN 2024 in Julia, with cross-validation of official public figures against BIDAT and good traceability of the flow in the repo. Three findings to start with — statistically robust: Extreme poverty: La Araucanía 13.0% 95% CI [11.8%, 14.1%] versus Magallanes 4.2% [3.1%, 5.2%] — a gap of 8.8 pp with non-overlapping CIs. FONASA coverage: La Araucanía 91.1% [90.2%, 92.0%] versus Metropolitana 75.9% [75.0%, 76.7%] — a gap of 15.2 pp with non-overlapping CIs. Completed higher education: Metropolitana 34.9% [34.0%, 35.7%] versus Maule 20.4% [19.2%, 21.6%] — a gap of 14.5 pp with non-overlapping CIs. The CIs are 95% and were computed by Taylor linearization (wiki) for CASEN's complex sampling design (stratified two-stage, expr weights). That the CIs do not overlap implies these regional differences are statistically significant at the conventional level. Tolerance to contrast, or checking against official data All results were checked against the official tables available in BIDAT. Table 1 — Official validation results (BIDAT, CASEN 2024) Parameter Value Validation status (national + regional, % + expanded) PASS Maximum tolerance in percentage points 1×10⁻⁵ pp Maximum tolerance in expanded values 1×10⁻⁶ Observed difference (pp) 2.98×10⁻⁶ pp Observed difference (expanded) 0.0 National rows compared 16 Regional rows compared 256 The maximum observed difference is below 3 millionths of a percentage point and within the preset tolerance. The results match the official tables within the predefined tolerances. Spoonful 1: sampling design and expansion without shortcuts CASEN 2024 has a probabilistic stratified two-stage design (BIDAT methodological note). For regional-level estimates, the correct factor is expr; for the municipal level expc is required — they are not interchangeable. This analysis uses expr and reports estimates by region with 95% CIs computed by Taylor linearization over the complex design (strata, PSU/UPM and weights/factors). Population represented in this run (sum of expr): 20.13 million people (a pending task is to assess the impact of the new 2024 Census instead of projections over the 2017 Census). # CASEN 2024 sampling design specification design = ( weight = :expr, # regional expansion factor strata = :estrato, # sampling stratum psu = :cod_upm, # primary sampling unit (PSU) domain = :region, # estimation domain ) Coverage by analyzed dimension: Table 2 — CASEN 2024 variables used and target population Dimension CASEN variable Target population Education educc People ≥ 18 years Health s13 Total population Poverty pobreza Total population Weighted national results The following percentages correspond to proportions weighted with expr, validated against official data in BIDAT. The difference from the official values is < 3×10⁻⁶ pp. Table 3 — Weighted national distribution (CASEN 2024, main categories) Dimension Category % national Education Complete secondary 30.9% Education Complete higher education 29.1% Education Incomplete higher education 12.5% Education Incomplete secondary 9.9% Education Incomplete primary 8.4% Education Other 7.7% Education No formal education 1.5% Health Public system FONASA 82.6% Health Isapre 13.2% Health None (private out-of-pocket) 2.0% Health Armed forces and police 1.8% Health Does not know 0.3% Health Other system 0.2% Poverty Non-poverty 82.7% Poverty Non-extreme poverty 10.4% Poverty Extreme poverty 6.9% Spoonful 2: the technical flow in Julia The pipeline runs end to end with julia --project=. scripts/run_all.jl (the orchestrator). The two most relevant pieces of code to reproduce and "audit" these results are the cell-allocation algorithm and the sampling-design specification, available in the public repository. Taylor linearization: SE and CI of the complex design A Taylor estimator was implemented for proportions in domains (regions). The linearized variable for the proportion $\hat{p}_d$ in domain $d$ is: $$z_j = \frac{1(j \in d)\,(1(\text{cat}_j = C) - \hat{p}_d)}{\hat{N}_d}$$ The variance is estimated with the stratified cluster-design formula: # Taylor linearization variance (stratified, PSU) # e_{hi} = sum of w_j * z_j over PSU i in stratum h var_total = sum over strata h: (n_h / (n_h - 1)) * sum_i (e_{hi} - mean(e_h))^2 se = sqrt(var_total) ci_lo = clamp(p̂ - 1.96 * se, 0.0, 1.0) ci_hi = clamp(p̂ + 1.96 * se, 0.0, 1.0) All PSUs of the design are used (including those outside the domain, with $z_j = 0$), which is correct for random-domain estimation. The median regional 95% CI width is 1.66 pp; the maximum is 5.76 pp (small regions with low-prevalence categories). Next entry, at some point 👀 — Jackknife and Bootstrap for CASEN as a contrast: TSL is an optimal first-order approximation for means and proportions, but for non-linear statistics (Gini, medians, quantile ratios) it can under-estimate the variance. The code repository includes the theory and the in-progress Julia code to contrast TSL with Jackknife (delete-1) and Bootstrap — a future entry in this series, which I have not reviewed in depth. Largest remainder: why it matters in a waffle chart A 100-cell waffle chart requires the proportions to add up to exactly 100 whole cells. Direct rounding introduces accumulated errors that make the sum 99 or 101. This flow uses the largest remainder algorithm, which guarantees the exact sum by introducing a slight imprecision for the sake of the visualization (take it as a purely visual nicety): """ Allocate `n_cells` whole cells to proportions `p` using largest-remainder. Guarantees that sum(cells) == n_cells exactly. """ function allocate_cells(p::AbstractVector{<:Real}, n_cells::Int = 100) raw = p .* n_cells floors = floor.(Int, raw) remain = raw .- floors deficit = n_cells - sum(floors) # Assign remaining cells to the proportions with the largest remainder idx = sortperm(remain, rev=true)[1:deficit] floors[idx] .+= 1 return floors end Validated with unit tests: allocate_cells([0.5, 0.3, 0.2], 100) == [50, 30, 20]. Reproducibility # Requirements: Julia 1.10+ git clone <repo> cd casen2024/julia_viz julia --project=. -e "using Pkg; Pkg.instantiate()" julia --project=. scripts/run_all.jl The flow generates plenty of artifacts (CSV tables, PNG charts, audit logs for each input). The Manifest.toml file pins the exact versions of all dependencies (I used Julia 1.10). Spoonful 3: visual evidence National composition (Charts 1–3) Each waffle represents 100 cells allocated by largest remainder over the weighted proportions. Regional gaps (Charts 4–6) Each panel uses an axis fitted to the range of its own category (not a shared global scale), which makes it possible to visualize differences that flatten out if all categories share the same axis. The horizontal bars are 95% CIs computed by Taylor linearization; the dashed vertical line marks the national estimate and the pale grey band its 95% CI. Gaps with 95% CIs — all statistically robust Table 4 — Regional gaps with 95% CIs by Taylor linearization (CASEN 2024) Dimension Category Gap (pp) Maximum 95% CI Minimum 95% CI Poverty Non-poverty 18.6 pp Magallanes 90.0% [88.5%, 91.5%] La Araucanía 71.4% [69.8%, 73.0%] Health Isapre 16.3 pp Metropolitana 20.6% [19.8%, 21.5%] Maule 4.3% [3.7%, 5.0%] Health FONASA 15.2 pp La Araucanía 91.1% [90.2%, 92.0%] Metropolitana 75.9% [75.0%, 76.7%] Education Complete higher education 14.5 pp Metropolitana 34.9% [34.0%, 35.7%] Maule 20.4% [19.2%, 21.6%] Poverty Extreme poverty 8.8 pp La Araucanía 13.0% [11.8%, 14.1%] Magallanes 4.2% [3.1%, 5.2%] In every case the CIs do not overlap: the gaps are statistically significant at 5%. CIs computed by Taylor linearization over the complex design (strata, PSU/UPM, expr). Closing: three questions for those who use the survey If you use CASEN 2024 for territorial characterization or other uses where regional-level variables matter, think twice before using a point estimate (without its confidence interval): Are your results validated against BIDAT and do they carry design-based CIs? A difference greater than 1×10⁻⁵ pp from the official tables is not technical: it is a process issue. And without complex-design CIs, an 8 pp gap can look like evidence when it is noise in small regions. Are you using the correct expansion factor? expr is the right one for regions; expc for municipalities. They are not interchangeable, and using the wrong one biases coverage estimates. Is your analysis reproducible? A flow that cannot be audited cannot be defended before a technical counterpart, nor updated when CASEN 2026 is released. The CIs incorporated here are complex-design (Taylor linearization), not simple asymptotic ones. They cover sampling variance but not non-response error or undercoverage. Causal inference between subpopulations requires additional design.