Observational Studies vs. Experiments

Key Distinction

• Observational study: Researchers observe and measure variables without attempting to influence responses. No treatment is imposed.
• Experiment: Researchers deliberately impose a treatment on individuals to observe the response.

Why It Matters: Causation

Only well-designed experiments can establish cause-and-effect relationships.

Observational studies can show association but cannot prove causation because of potential confounding variables.

Confounding Variables

A confounding variable is a variable that:

1. Is associated with the explanatory variable
2. Also affects the response variable

This makes it impossible to determine which variable is actually causing the observed effect.

Example: People who exercise more tend to weigh less. But people who exercise may also eat healthier. Diet is a confounding variable.

Types of Observational Studies

• Sample survey: Collects data at one point in time
• Retrospective study: Looks back at past data
• Prospective study: Follows subjects into the future

Lurking Variables

A lurking variable is not among the explanatory or response variables but may influence the relationship between them.

Simpson's Paradox

A trend that appears in several groups of data reverses when the groups are combined. This occurs because of a lurking variable.

Classic example: A treatment may appear better overall, but worse in every subgroup, due to unequal group sizes.

Key Vocabulary

| Term | Definition | |------|-----------| | Explanatory variable | The variable we think explains or causes changes | | Response variable | The variable we measure as an outcome | | Confounding | Two variables whose effects cannot be separated | | Lurking variable | A hidden variable that affects the relationship |

AP Tip: If asked "can we conclude causation?", the answer is NO for observational studies. Always mention confounding variables as the reason.