Statistics Lecture – Data Sources, Sampling, Variable Types, & Study Design June 4

Data Storage & File Formats

• Computer files are recognised by their extensions (the characters after the final dot).
  • Common data‐table extensions used in the course:
  • .txt – plain text
  • .csv – comma-separated values (CSV = comma separated values)
  • Others: .xlsx, .sav, .json, etc.
• Rectangular (row × column) tables dominate introductory statistics workflows.
• Most course/lab datasets are supplied as CSV files via Moodle; ensure you know where the large “datasets” folder is located.

Study-Design Workflow (recap from previous lecture)

• 1 ▶ Identify the research question.
• 2 ▶ Choose the population of interest.
• 3 ▶ List the variables required to answer the question.
• 4 ▶ Collect data on those variables following an appropriate design.
• Bad data → bad analysis → bad conclusions (often undetectable by downstream readers!).
• Consulting a statistician before data collection is crucial – collection is usually the most expensive stage.

Types of Data Sources

1. Anecdotal Data

• Informal, casual observations or stories (single personal experiences).
• Subjective; not reliable for large-scale decision-making.
• Value: generates intuition/hypotheses (e.g. Newton’s apple, discovery of penicillin, microwave oven serendipity).
• Example given: “I felt more focused after coffee before last week’s lecture – therefore coffee improves concentration.”

2. Available (Secondary) Data

• Pre-existing data generated for purposes other than your current study.
• Examples:
  • Australian Bureau of Statistics (ABS) census tables.
  • Bureau of Meteorology (BoM) weather archives.
  • University enrolment records.
  • Smart-watch step counts/time logs.
• Advantage: inexpensive, instantly accessible.
• Caveat: variables, definitions, and quality were chosen for someone else’s objectives.

3. New / Collected / Simulated Data

• Gathered (or simulated) specifically for the research project.
• Mechanisms:
  • Surveys & questionnaires (e.g. Moodle student questionnaire).
  • Direct measurement/counting ("how many moths in my living room"; traffic counts).
  • Instrumentation/IoT (Raspberry Pi projects, sensors).
  • Computer simulation.
• Usually higher relevance & control, but costs time, money, ethics clearance.

Population, Sample & Census

• Population: all units (people, objects, events) you want information about.
  • Example: all UNSW students when studying average preparation time each morning.
• Sample: subset actually observed/measured.
  • Must be representative for valid inference.
• Census: attempt to obtain data on every population member (Australian census ≈ every 5 years).
  • Expensive, time-consuming, often ethically or logistically impossible.

Sampling Methods (people-focused)

• Sample Survey: ask questions of selected individuals.
• Voluntary Response Sample: participants self-select.
  • Typically biased (e.g. only highly motivated individuals respond).
• Convenience Sample: choose units that are easy to reach (e.g. stopping passers-by on Main Walkway).
  • May under-represent segments of the population.

Reasons to Sample Instead of Census

• Cost & time limitations.
• Practical/physical impossibility.
• Ethical/legal constraints (e.g. testing every student for tuberculosis; forcing smoking behaviour).
• Well-designed samples often yield high-accuracy estimates (e.g. election “quick counts”) without surveying 99 % of voters.

Variable Types

Categorical (Qualitative)

• Assigns cases to groups/levels.
• Arithmetic on codes is meaningless.
• Example: hemisphere {Northern, Southern}; file type; gender.

Quantitative (Numerical)

• Takes numerical values where arithmetic operations make sense.
• Must include units.
  • Example: temperature in ^{\circ}C, time in minutes, height in centimetres.

Pitfalls

• Simply recoding categories as numbers (e.g. Hemisphere 1 & 2) does not make them quantitative; averages, sums, etc. are nonsensical.
• A formal flowchart (omitted slide) asks: “Is there a natural order? Are arithmetic operations meaningful?”

Observational Studies vs Experiments

Association ≠ Causation

• Variables can be associated due to:
  1. Causation (A causes B).
  2. Common response to a third variable.
  3. Confounding with lurking variable(s).
• Spurious correlations abound (e.g. US science funding vs. suicides; per-capita cheese consumption vs. deaths tangled in bedsheets).
• Always ask: what other variable could explain both factors?

Lurking & Confounding Variables

• Lurking Variable: unobserved variable that influences interpretation; affects both explanatory & response variables.
• Confounding Variables:
  • Two variables are confounded when their effects on the response cannot be separated.
  • A confounding variable is an unobserved factor whose influence on the response is indistinguishable from that of the explanatory variable.
• Heavier concept – remember two criteria: (i) unobserved, (ii) impacts explanatory & response, making attribution difficult.

Classic Example (Fitness Study)

• Explanatory: weekly exercise time.
• Response: fitness level.
• Possible lurking/confounding variables:
  • Age – older people may be less fit and have less time/ability to exercise.
  • Genetics – influences fitness potential and maybe motivation/ability to exercise.

Example Case Studies

1. Hospital Size vs. Length of Stay

   • Large hospitals show longer average patient stays.
   • Likely explanation: severe/complex cases referred to large hospitals (confounding by illness severity).

2. Marital Status vs. Income

   • Married/ever-married men earn more than never-married men.
   • Age acts as a confounder: older individuals more likely to be married and have higher income.

3. Ice-Cream Sales vs. Heat Strokes

   • Both rise in hot weather.
   • Heat (temperature) is lurking variable; association arises via common response/confounding.

4. Tidal Height vs. Moon Position

   • Clear causal mechanism: lunar gravitational pull → tide cycle.
   • Demonstrates genuine causation.

5. Parent-Child Body Mass Index

   • Strong association.
   • Confounded by shared diet, lifestyle, environment, and genetics.

6. Smoking & Lung Cancer

   • Observed association strong; experimenting by forcing people to smoke/non-smoke is unethical.
   • Genetics, stress, socioeconomic status = potential lurking/confounding variables.
   • Evidence for causation eventually established via long-term cohort studies, biological mechanisms, and advanced causal inference.

Ethical & Practical Constraints in Experiments

• Randomised controlled trials ideal for causation but sometimes impossible (e.g. assigning smoking, withholding medical treatment).
• Alternative: prospective cohort studies, instrumental-variable techniques, natural experiments (field of causal inference).

Key Quantitative Formulae Quoted

• Body Mass Index:
  BMI = \frac{\text{Weight (kg)}}{\text{Height (m)}^2}

Big Picture – Why All This Matters

• Correct identification of variable types guides every later statistical method (see forthcoming “cheat-sheet” table of analyses).
• Solid study design prevents garbage-in/garbage-out, saving money and reputation.
• Understanding association, causation, lurking & confounding protects against invalid claims and mis-guiding policy or personal decisions.

Practical Pointers for the Course

• Whenever faced with data:
  1. Name the population and sample.
  2. Classify each variable (categorical vs. quantitative; explanatory vs. response).
  3. Decide whether the design is observational or experimental (look for “treatment”).
  4. Ask what lurking/confounding variables might exist.
• Use units for every quantitative measurement.
• Seek statistical advice before data collection.
• Remember: well-constructed samples can yield high-accuracy estimates without a full census.