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MathidiaMathematics Academy
Statistical foundations
Lesson 41 of 75
Introduction

Data and study design

Objective. Distinguish observational, experimental and sampling structures.

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  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Study design concerns how data is collected and determines what conclusions can validly be drawn from it. In an observational study, researchers record variables without intervening, which can reveal association but never confirms causation due to possible confounding variables. In a controlled experiment, researchers actively assign treatments, ideally through randomisation, which balances confounders across groups and allows causal claims. Sampling structure also matters: a simple random sample gives every individual equal selection chance, while stratified sampling divides the population into subgroups before sampling within each, improving precision when subgroups differ. A study linking exercise to lower heart disease rates is observational unless participants are randomly assigned to exercise or control groups.

Worked example

A researcher divides a population into age groups then randomly samples within each group. Identify this sampling data design and its main advantage.

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Illustrated card showing ?
  1. 1Note that the population is split into distinct subgroups before sampling.
  2. 2Recognise that random sampling then occurs separately within each subgroup.
  3. 3Identify this structure as stratified sampling by definition.
  4. 4State the key benefit: it ensures representation across subgroups, improving precision.

Answer: Stratified sampling; it improves precision by guaranteeing subgroup representation

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Common mistake. Students treat a strong association found in an observational study as proof of causation; without random assignment, confounding variables can produce the same pattern, so only experiments can support causal claims.

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