Observational Studies and Confounding

Two ways to collect data

In an observational study the researcher records what happens without imposing any treatment; in an experiment the researcher assigns treatments to units. A retrospective study looks back at existing records (past smokers versus non-smokers); a prospective study follows a group forward in time. A census measures every unit of the population; a sample survey measures a part of it. Observational studies are the only option when a treatment cannot be assigned ethically or practically — you cannot randomly assign people to smoke.

Confounding

A variable is confounding when it is associated with both the explanatory variable and the response, so that its effect cannot be separated from the effect of the explanatory variable. Example: in one survey $70\%$ of heavy coffee drinkers smoked, against $20\%$ of non-drinkers, and heavy coffee drinkers had higher heart-disease rates. Smoking is confounded with coffee — the data cannot tell which one (if either) raises the risk. On the exam, naming a confounder earns credit only if you explain both links: how it relates to the explanatory variable and how it could affect the response.

What each design lets you say

An observational study, even a large and well-sampled one, shows association, not causation. Random selection still allows generalisation to the population. Only random assignment — the experiment — balances confounders across groups and licenses a causal claim. When the question says "explain why this study cannot show that A causes B", the answer is always: no random assignment, so a confounding variable could explain the association.