Practice Observational vs Experimental Studies in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
An observational study records data without imposing treatments, while an experiment deliberately manipulates a variable. Only experiments with random assignment can establish causation; observational studies can only show association.
Observational: you watch people who already smoke and compare their lung cancer rates to non-smokers. Experimental: you randomly assign people to smoke or not (unethical, but illustrates the point). The observational study might find that smokers differ from non-smokers in many ways (diet, exercise, stress)—so you can't be sure smoking caused the cancer. The experiment controls for everything else.
Example 1
mediumClassify each study and state what conclusions can be drawn: (a) Researchers record which students eat breakfast and compare their grades. (b) Students are randomly assigned to eat breakfast or skip it for 30 days, then grades are measured.
Example 2
hardAn observational study finds smokers have 10x the lung cancer rate of non-smokers. Critics say this could be due to a genetic confounder that causes both smoking and cancer. How did scientists eventually establish smoking CAUSES cancer?
Example 3
easyA researcher asks 500 adults about their exercise habits and mental health. Is this observational or experimental? What is the strongest conclusion possible from this study?
Example 4
hardWhy is it impossible to conduct a fully randomized experiment to test the effect of poverty on health outcomes? What study design limitations result from this constraint?