Statistics helps us make decisions from data, but the type of study matters just as much as the numbers collected. In an experiment, researchers assign treatments to subjects so they can compare outcomes under controlled conditions. In an observational study, researchers measure or record what happens without assigning treatments.
This difference determines whether a study can support a cause and effect conclusion or only show an association.
Experiments are powerful because random assignment helps balance out other variables between groups. Observational studies are often useful when experiments would be unethical, impossible, too expensive, or too slow. However, observational data can be affected by lurking variables that explain the pattern.
Good statistical reasoning means matching the conclusion to the study design.
Key Facts
- Experiment: researchers assign treatments and compare responses.
- Observational study: researchers observe variables without assigning treatments.
- Random assignment helps reduce bias by making treatment groups similar on average.
- Association does not prove causation.
- A controlled experiment can support cause and effect if the design is valid.
- Relative difference = (group 1 rate - group 2 rate) / group 2 rate
Vocabulary
- Experiment
- A study in which researchers assign treatments to subjects and measure the resulting response.
- Observational Study
- A study in which researchers collect data without controlling or assigning treatments.
- Treatment
- A condition, action, or intervention applied to subjects in an experiment.
- Random Assignment
- A method of placing subjects into treatment groups using chance so the groups are comparable.
- Lurking Variable
- An unmeasured variable that may affect both the explanatory variable and the response variable.
Common Mistakes to Avoid
- Claiming causation from an observational study is wrong because the researchers did not assign treatments, so other variables may explain the difference.
- Confusing random sampling with random assignment is wrong because random sampling helps represent a population, while random assignment helps compare treatment groups fairly.
- Ignoring lurking variables is wrong because an outside factor may be responsible for the observed association.
- Assuming a larger sample automatically fixes a bad design is wrong because more data can still preserve bias if the study method is flawed.
Practice Questions
- 1 A researcher randomly assigns 120 students to either study with flashcards or study with notes, then compares test scores. Identify the study type and state whether it can support a cause and effect conclusion.
- 2 In an observational study of 800 adults, 300 of 500 coffee drinkers report high alertness, while 120 of 300 non coffee drinkers report high alertness. Find the alertness rate for each group and the difference in rates.
- 3 A study finds that students who eat breakfast have higher math scores than students who skip breakfast. Explain why this result alone does not prove that eating breakfast causes higher math scores.