Demo Analyses
Cross-dataset case studies showcasing statistical rigour with uncertainty quantification
These analyses demonstrate methodological approach and uncertainty quantification. Data values are synthetic or simplified aggregates—not research claims. Real analyses would use full datasets, validate assumptions, adjust for confounders, and undergo peer review.
Case Study 1: Crime Rates by LGA
Joining SA crime statistics with ABS population estimates
Methodology
Question: Do crime rates differ significantly between Adelaide CBD and Port Adelaide Enfield?
Datasets: SA Police crime statistics (offence counts by LGA) + ABS 3218.0 Regional Population (ERP by LGA)
Method: Compute offence rate per 1,000 population. Wilson score intervals (95% CI) for proportions. Cohen's d for effect size.
Sample: n = 70 SA LGAs, year 2023
Interpretation
Adelaide CBD shows a higher reported offence rate (112.1 vs 29.5 per 1,000). Effect size: large (d ≈ 2.8, Cohen's d > 0.8). However, CBD rates are inflated by daytime population (workers, visitors) not captured in ERP. A fairer comparison would use daytime population or restrict to residential offences.
Case Study 2: Emergency Department Performance
SA Health ED wait times with uncertainty
Methodology
Question: What proportion of SA ED patients are seen within 4 hours?
Dataset: SA Health ED performance metrics, Q2 2024
Method: Wilson score interval for binomial proportion (patients seen ≤ 4h / total presentations)
Sample: n = 10,000 presentations across 7 major public hospitals
Interpretation
82.3% (95% CI: 81.5%–83.2%) of patients were seen within 4 hours in Q2 2024. The confidence interval is narrow due to large sample size (n = 10,000). Performance exceeds the national benchmark of 80%, though this aggregates across triage categories—Category 1 (life-threatening) and Category 5 (non-urgent) have different targets.
Limitation: Excludes private hospitals; wait times vary by time of day, day of week, and season (winter surge).
Case Study 3: Effect Size in Policy Interventions
Comparing two groups with Cohen's d
Methodology
Scenario: Hypothetical comparison of student test scores before and after an education intervention
Method: Independent samples t-test + Cohen's d effect size. Report effect size alongside p-value to distinguish statistical significance from practical importance.
Sample: n = 10 per group (small sample for illustration)
Why Effect Sizes Matter
A statistically significant result (p < 0.05) tells you the difference is unlikely due to chance, but not whether the difference is large enough to matter. Cohen's d quantifies the magnitude: d = 2.87 (large) means the groups differ by 2.9 standard deviations—a substantive gap. Always report both p-values and effect sizes.
Case Study 4: Data Consistency Checks
Do LGA-level totals reconcile with state totals?
Methodology
Question: When summing LGA-level population estimates, do we recover the published state total?
Datasets: ABS 3218.0 Regional Population (LGA series) + ABS 3101.0 National Population (state series)
Method: Sum ERP across all SA LGAs; compare to published SA total. Report difference and % discrepancy.
Expected result: Close match (within rounding) if geography definitions are aligned
Why This Matters
Cross-dataset consistency checks validate that datasets can be safely joined and compared. A large discrepancy would signal: (1) misaligned geographies (e.g., LGA boundaries changed), (2) different estimation methods, or (3) data quality issues. Here, the 0.001% difference is negligible—likely due to rounding in the published tables.
Methodological Standards Applied
- •Confidence intervals: Wilson score for proportions, t-intervals or bootstrap for means
- •Sample sizes: Stated for every estimate
- •Effect sizes: Cohen's d reported alongside comparisons
- •Assumptions: Documented and tested where possible
- •Limitations: Explicitly stated for each analysis
- •Reproducibility: All statistical functions are unit-tested and open-source (see GitHub)