W1 L1 Data & Evidence – Statistical Thinking (Comprehensive Notes)

Statistical Thinking

• Definition: A mindset for interpreting a complex world through simplified summaries that capture essential structure/function while explicitly acknowledging uncertainty.

• Core idea: Any estimate or description is accompanied by a degree of doubt—never $100\%$ certainty.

• Everyday illustration – Australian dog-ownership estimate:

  • Council registration records might suggest a total number of dogs, but unregistered pets introduce unknown error.

  • Emphasises the constant presence of uncertainty.

Example of Statistical Thinking in Practice – ABS Learning Graph

• Data source: Australian Bureau of Statistics (ABS) survey on formal & non-formal learning among individuals aged $15$–$74$ years.

• Key percentages:

  • Major-city residents in formal study: $21.8\%$.

  • Regional/remote residents in formal study: $17.3\%$.

• Interpretation:

  • The bar/column graph converts millions of raw records into two clear comparative statistics.

  • Demonstrates communication power of statistical summaries for decision-makers and the public.

Three Fundamental Tasks of Statistics

1. Describe – Convert raw complexity into concise metrics.

   • Example: "Australia’s population in $2017$ was $24\,600\,000$."

2. Decide – Make evidence-based choices/comparisons under uncertainty.

   • Example: "South Australia (SA) with $1\,700\,000$ people is projected to grow $0.1$–$0.9\%$ per year, slower than every state except Tasmania."
     • The comparison component (SA vs. others) constitutes a statistical decision.

3. Predict – Forecast future outcomes from past data.

   • Example: "National population projected to reach between $37.4$ and $49.2\text{ million}$ by $2066$."
     • Interval conveys uncertainty built into prediction models.

Learning From Data – The Empirical Cycle

• Previous Research ➔ Hypothesis ➔ Test / Collect New Data ➔ Compare.

• Take-away-food anecdote:

  • Prior reviews ("previous research") rated the restaurant highly.

  • Formed hypothesis: food would be excellent.

  • Actual tasting ("data") either supports or contradicts the hypothesis.

• Importance: Mirrors formal scientific method used throughout psychological science.

Aggregation

• Raw ratings example: $[4,5,3,5,2,4,5,1,4]$ are hard to interpret.

• Aggregated view (e.g., frequency table or average rating) instantly reveals overall sentiment.

• Principle: Summarise observations into meaningful categories/levels while retaining key information about distribution.

Uncertainty & Risk Illustration – Diabetes Risk Calculator

• Fictional individual scored $6$ on AUSDRISK.

  • Falls into "low" risk band.

  • Interpretation: Approximately $1$ in $50$ develop Type-2 diabetes within $5$ years.

• Range of plausible true risk depends on sampling error & model uncertainty:

  • Low-uncertainty scenario: $0$–$2$ per $50$.

  • High-uncertainty scenario: $0$–$8$ per $50$.

• Conceptual preview: later coursework will formalise confidence intervals & error margins.

Sampling Approaches

Population Illustration

• Hypothetical population composition: more red, fewer blue, fewest yellow individuals.

Representative (Probability-Based) Sample

• Draw individuals randomly such that sample colour proportions mirror true population.

• Supports valid generalisation; sampling error is purely random and quantifiable.

Convenience (Biased) Sample

• Participants self-select via ads, social media, campus flyers, etc.

• Over-represents certain demographics (e.g., WEIRD — Western, Educated, Industrialised, Rich, Democratic).

• Leads to systematic bias; limits external validity of psychological findings.

Causality vs. Correlation

• Motto: "Correlation $\neq$ Causation."

• Spurious-Correlation website example:

  • $r \approx 0.95$ between U.S. per-capita cheese consumption and deaths by bedsheet entanglement.

  • Absurd explanatory leap ("cheese ➔ nightmares ➔ fatal tangling") highlights danger.

• Guidelines for researchers:

  • Use language of "association" or "relationship" for observational designs.

  • Inferring causation typically requires experimental manipulation + rigorous controls, yet still warrants caution.

Ethical, Philosophical & Practical Implications (threaded throughout)

• Transparent reporting of uncertainty fosters honest science & informed policy.

• Awareness of sampling bias encourages equitable, inclusive research that truly represents populations.

• Misinterpreting correlation as causation can fuel misinformation, poor interventions, or harmful stereotypes.

• Statistical literacy empowers citizens to scrutinise media claims and make better personal decisions (e.g., health risk calculators, education enrolment rates, population projections).