Why an Observational Study Cannot Show Cause

Ice cream sales and drowning deaths rise and fall together across the year. Nobody thinks a cone causes a drowning. Both are driven by a third thing: hot weather. When it's hot, more people buy ice cream, and more people swim, so more drownings happen. Hot weather is a lurking variable: it isn't measured in the study, but it moves both variables in the same direction, creating an association between two things that never touch each other.

This is why a strong correlation in observational data never proves cause. In an observational study, the researcher just watches and records what subjects already do. Anyone in the ice cream group might differ from anyone in the no-ice-cream group in dozens of ways besides ice cream: income, climate, age, activity level. Any of those could be the real driver. You cannot rule out a lurking variable because you never controlled who ended up in which group.

To earn a cause-and-effect claim, the study design has to change: researchers need an experiment with random assignment. Flipping a coin to decide who gets the treatment spreads every lurking variable, known or unknown, evenly across the groups on average. Age, income, climate exposure, whatever might confound things gets balanced out, so if the groups end up different, the treatment is the only systematic difference left standing. That is the link between this topic and the next: observational studies describe the world, experiments can explain it.