Randomized Experiments: Control Groups, Blinding, Blocking, and Matched Pairs
A lesson in randomized experiments that moves from intuition and definitions to worked reasoning, error correction, and independent practice.
Lesson Goals: Randomized Experiment
Random assignment supports a causal comparison by balancing lurking variables in the long run, while random sampling separately controls how far results can be generalized.
Random assignment
Random assignment in randomized experiment: State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization.
Worked reasoning
For Random assignment in randomized experiment, Design or critique a study in a commuter route study for randomized experiments, emphasizing random assignment.
When the idea is valid
For Random assignment in randomized experiment, Interference should be limited, treatment implementation consistent, and response measurement blind where feasible.
Misconception to remove
For Random assignment in randomized experiment, reject this error: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Control group
Control group in randomized experiment: State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization.
Worked reasoning
For Control group in randomized experiment, Design or critique a study in a commuter route study for randomized experiments, emphasizing control group.
When the idea is valid
For Control group in randomized experiment, Interference should be limited, treatment implementation consistent, and response measurement blind where feasible.
Misconception to remove
For Control group in randomized experiment, reject this error: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Placebo
Placebo in randomized experiment: State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization.
Worked reasoning
For Placebo in randomized experiment, Design or critique a study in a city bus arrival investigation for randomized experiments, emphasizing placebo.
When the idea is valid
For Placebo in randomized experiment, Interference should be limited, treatment implementation consistent, and response measurement blind where feasible.
Misconception to remove
For Placebo in randomized experiment, reject this error: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Single and double blinding
Single and double blinding in randomized experiment: State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization.
Worked reasoning
For Single and double blinding in randomized experiment, Design or critique a study in a city bus arrival investigation for randomized experiments, emphasizing single and double blinding.
When the idea is valid
For Single and double blinding in randomized experiment, Interference should be limited, treatment implementation consistent, and response measurement blind where feasible.
Misconception to remove
For Single and double blinding in randomized experiment, reject this error: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Blocking
Blocking in randomized experiment: State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization.
Worked reasoning
For Blocking in randomized experiment, Design or critique a study in a campus dining survey for randomized experiments, emphasizing blocking.
When the idea is valid
For Blocking in randomized experiment, Interference should be limited, treatment implementation consistent, and response measurement blind where feasible.
Misconception to remove
For Blocking in randomized experiment, reject this error: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Matched pairs
Matched pairs in randomized experiment: State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization.
Worked reasoning
For Matched pairs in randomized experiment, Design or critique a study in a seedling-growth comparison for randomized experiments, emphasizing matched pairs.
When the idea is valid
For Matched pairs in randomized experiment, Interference should be limited, treatment implementation consistent, and response measurement blind where feasible.
Misconception to remove
For Matched pairs in randomized experiment, reject this error: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Replication
Replication in randomized experiment: State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization.
Worked reasoning
For Replication in randomized experiment, Design or critique a study in a seedling-growth comparison for randomized experiments, emphasizing replication.
When the idea is valid
For Replication in randomized experiment, Interference should be limited, treatment implementation consistent, and response measurement blind where feasible.
Misconception to remove
For Replication in randomized experiment, reject this error: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Completely randomized design
Completely randomized design in randomized experiment: State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization.
Worked reasoning
For Completely randomized design in randomized experiment, Design or critique a study in a greenhouse germination experiment for randomized experiments, emphasizing completely randomized design.
When the idea is valid
For Completely randomized design in randomized experiment, Interference should be limited, treatment implementation consistent, and response measurement blind where feasible.
Misconception to remove
For Completely randomized design in randomized experiment, reject this error: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Worked designs
Worked designs in randomized experiment: State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization.
Worked reasoning
For Worked designs in randomized experiment, Design or critique a study in a water-filtration experiment for randomized experiments, emphasizing worked designs.
When the idea is valid
For Worked designs in randomized experiment, Interference should be limited, treatment implementation consistent, and response measurement blind where feasible.
Misconception to remove
For Worked designs in randomized experiment, reject this error: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Guided, Independent and Challenge Practice
Every question in Randomized Experiments: Control Groups, Blinding, Blocking, and Matched Pairs is newly written from the revised framework and the logic visible in public College Board materials. Constructed numerical settings are identified as instructional scenarios and are never represented as measurements from a real population. No released or secure question wording is reproduced.
Easy Practice
Easy 1: Placebo
Question P39-Easy-1. Design or critique a study in a campus dining survey for randomized experiments, emphasizing placebo.
Worked solution and validity check
Worked solution P39-Easy-1. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Easy 2: Single and double blinding
Question P39-Easy-2. Design or critique a study in a commuter route study for randomized experiments, emphasizing single and double blinding.
Worked solution and validity check
Worked solution P39-Easy-2. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Easy 3: Blocking
Question P39-Easy-3. Design or critique a study in a school library checkout study for randomized experiments, emphasizing blocking.
Worked solution and validity check
Worked solution P39-Easy-3. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Easy 4: Matched pairs
Question P39-Easy-4. Design or critique a study in a water-filtration experiment for randomized experiments, emphasizing matched pairs.
Worked solution and validity check
Worked solution P39-Easy-4. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Easy 5: Replication
Question P39-Easy-5. Design or critique a study in a commuter route study for randomized experiments, emphasizing replication.
Worked solution and validity check
Worked solution P39-Easy-5. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Easy 6: Completely randomized design
Question P39-Easy-6. Design or critique a study in a manufacturing fill-volume check for randomized experiments, emphasizing completely randomized design.
Worked solution and validity check
Worked solution P39-Easy-6. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Easy 7: Worked designs
Question P39-Easy-7. Design or critique a study in a public-parks visitor survey for randomized experiments, emphasizing worked designs.
Worked solution and validity check
Worked solution P39-Easy-7. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Easy 8: Random assignment
Question P39-Easy-8. Design or critique a study in a campus dining survey for randomized experiments, emphasizing random assignment.
Worked solution and validity check
Worked solution P39-Easy-8. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Easy 9: Control group
Question P39-Easy-9. Design or critique a study in a battery-life laboratory trial for randomized experiments, emphasizing control group.
Worked solution and validity check
Worked solution P39-Easy-9. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Easy 10: Placebo
Question P39-Easy-10. Design or critique a study in a tutoring-program evaluation for randomized experiments, emphasizing placebo.
Worked solution and validity check
Worked solution P39-Easy-10. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Easy 11: Single and double blinding
Question P39-Easy-11. Design or critique a study in a commuter route study for randomized experiments, emphasizing single and double blinding.
Worked solution and validity check
Worked solution P39-Easy-11. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Easy 12: Blocking
Question P39-Easy-12. Design or critique a study in a public-parks visitor survey for randomized experiments, emphasizing blocking.
Worked solution and validity check
Worked solution P39-Easy-12. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Easy 13: Matched pairs
Question P39-Easy-13. Design or critique a study in a website response-time study for randomized experiments, emphasizing matched pairs.
Worked solution and validity check
Worked solution P39-Easy-13. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Easy 14: Replication
Question P39-Easy-14. Design or critique a study in a public-parks visitor survey for randomized experiments, emphasizing replication.
Worked solution and validity check
Worked solution P39-Easy-14. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Easy 15: Completely randomized design
Question P39-Easy-15. Design or critique a study in a reading-speed investigation for randomized experiments, emphasizing completely randomized design.
Worked solution and validity check
Worked solution P39-Easy-15. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Easy 16: Worked designs
Question P39-Easy-16. Design or critique a study in a package-delivery sample for randomized experiments, emphasizing worked designs.
Worked solution and validity check
Worked solution P39-Easy-16. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Easy 17: Random assignment
Question P39-Easy-17. Design or critique a study in a water-filtration experiment for randomized experiments, emphasizing random assignment.
Worked solution and validity check
Worked solution P39-Easy-17. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Easy 18: Control group
Question P39-Easy-18. Design or critique a study in a greenhouse germination experiment for randomized experiments, emphasizing control group.
Worked solution and validity check
Worked solution P39-Easy-18. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Easy 19: Placebo
Question P39-Easy-19. Design or critique a study in a website response-time study for randomized experiments, emphasizing placebo.
Worked solution and validity check
Worked solution P39-Easy-19. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough Practice
Tough 1: Control group
Question P39-Tough-1. Design or critique a study in a battery-life laboratory trial for randomized experiments, emphasizing control group.
Worked solution and validity check
Worked solution P39-Tough-1. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough 2: Placebo
Question P39-Tough-2. Design or critique a study in a seedling-growth comparison for randomized experiments, emphasizing placebo.
Worked solution and validity check
Worked solution P39-Tough-2. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough 3: Single and double blinding
Question P39-Tough-3. Design or critique a study in a manufacturing fill-volume check for randomized experiments, emphasizing single and double blinding.
Worked solution and validity check
Worked solution P39-Tough-3. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough 4: Blocking
Question P39-Tough-4. Design or critique a study in a school library checkout study for randomized experiments, emphasizing blocking.
Worked solution and validity check
Worked solution P39-Tough-4. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough 5: Matched pairs
Question P39-Tough-5. Design or critique a study in an online-course completion sample for randomized experiments, emphasizing matched pairs.
Worked solution and validity check
Worked solution P39-Tough-5. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough 6: Replication
Question P39-Tough-6. Design or critique a study in a quality-control inspection for randomized experiments, emphasizing replication.
Worked solution and validity check
Worked solution P39-Tough-6. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough 7: Completely randomized design
Question P39-Tough-7. Design or critique a study in a water-filtration experiment for randomized experiments, emphasizing completely randomized design.
Worked solution and validity check
Worked solution P39-Tough-7. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough 8: Worked designs
Question P39-Tough-8. Design or critique a study in a school library checkout study for randomized experiments, emphasizing worked designs.
Worked solution and validity check
Worked solution P39-Tough-8. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough 9: Random assignment
Question P39-Tough-9. Design or critique a study in a quality-control inspection for randomized experiments, emphasizing random assignment.
Worked solution and validity check
Worked solution P39-Tough-9. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough 10: Control group
Question P39-Tough-10. Design or critique a study in a water-filtration experiment for randomized experiments, emphasizing control group.
Worked solution and validity check
Worked solution P39-Tough-10. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough 11: Placebo
Question P39-Tough-11. Design or critique a study in an online-course completion sample for randomized experiments, emphasizing placebo.
Worked solution and validity check
Worked solution P39-Tough-11. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough 12: Single and double blinding
Question P39-Tough-12. Design or critique a study in a reading-speed investigation for randomized experiments, emphasizing single and double blinding.
Worked solution and validity check
Worked solution P39-Tough-12. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough 13: Blocking
Question P39-Tough-13. Design or critique a study in a battery-life laboratory trial for randomized experiments, emphasizing blocking.
Worked solution and validity check
Worked solution P39-Tough-13. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough 14: Matched pairs
Question P39-Tough-14. Design or critique a study in an online-course completion sample for randomized experiments, emphasizing matched pairs.
Worked solution and validity check
Worked solution P39-Tough-14. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough 15: Replication
Question P39-Tough-15. Design or critique a study in a recycling-behavior survey for randomized experiments, emphasizing replication.
Worked solution and validity check
Worked solution P39-Tough-15. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough 16: Completely randomized design
Question P39-Tough-16. Design or critique a study in a seedling-growth comparison for randomized experiments, emphasizing completely randomized design.
Worked solution and validity check
Worked solution P39-Tough-16. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough 17: Worked designs
Question P39-Tough-17. Design or critique a study in a classroom memory study for randomized experiments, emphasizing worked designs.
Worked solution and validity check
Worked solution P39-Tough-17. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough 18: Random assignment
Question P39-Tough-18. Design or critique a study in a greenhouse germination experiment for randomized experiments, emphasizing random assignment.
Worked solution and validity check
Worked solution P39-Tough-18. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Tough 19: Control group
Question P39-Tough-19. Design or critique a study in a website response-time study for randomized experiments, emphasizing control group.
Worked solution and validity check
Worked solution P39-Tough-19. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest Practice
Toughest 1: Matched pairs
Question P39-Toughest-1. Design or critique a study in an online-course completion sample for randomized experiments, emphasizing matched pairs.
Worked solution and validity check
Worked solution P39-Toughest-1. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest 2: Replication
Question P39-Toughest-2. Design or critique a study in a city bus arrival investigation for randomized experiments, emphasizing replication.
Worked solution and validity check
Worked solution P39-Toughest-2. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest 3: Completely randomized design
Question P39-Toughest-3. Design or critique a study in an online-course completion sample for randomized experiments, emphasizing completely randomized design.
Worked solution and validity check
Worked solution P39-Toughest-3. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest 4: Worked designs
Question P39-Toughest-4. Design or critique a study in a reading-speed investigation for randomized experiments, emphasizing worked designs.
Worked solution and validity check
Worked solution P39-Toughest-4. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest 5: Random assignment
Question P39-Toughest-5. Design or critique a study in a school library checkout study for randomized experiments, emphasizing random assignment.
Worked solution and validity check
Worked solution P39-Toughest-5. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest 6: Control group
Question P39-Toughest-6. Design or critique a study in a water-filtration experiment for randomized experiments, emphasizing control group.
Worked solution and validity check
Worked solution P39-Toughest-6. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest 7: Placebo
Question P39-Toughest-7. Design or critique a study in a website response-time study for randomized experiments, emphasizing placebo.
Worked solution and validity check
Worked solution P39-Toughest-7. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest 8: Single and double blinding
Question P39-Toughest-8. Design or critique a study in a classroom memory study for randomized experiments, emphasizing single and double blinding.
Worked solution and validity check
Worked solution P39-Toughest-8. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest 9: Blocking
Question P39-Toughest-9. Design or critique a study in a school library checkout study for randomized experiments, emphasizing blocking.
Worked solution and validity check
Worked solution P39-Toughest-9. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest 10: Matched pairs
Question P39-Toughest-10. Design or critique a study in a water-filtration experiment for randomized experiments, emphasizing matched pairs.
Worked solution and validity check
Worked solution P39-Toughest-10. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest 11: Replication
Question P39-Toughest-11. Design or critique a study in a quality-control inspection for randomized experiments, emphasizing replication.
Worked solution and validity check
Worked solution P39-Toughest-11. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest 12: Completely randomized design
Question P39-Toughest-12. Design or critique a study in a city bus arrival investigation for randomized experiments, emphasizing completely randomized design.
Worked solution and validity check
Worked solution P39-Toughest-12. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest 13: Worked designs
Question P39-Toughest-13. Design or critique a study in a battery-life laboratory trial for randomized experiments, emphasizing worked designs.
Worked solution and validity check
Worked solution P39-Toughest-13. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest 14: Random assignment
Question P39-Toughest-14. Design or critique a study in a recycling-behavior survey for randomized experiments, emphasizing random assignment.
Worked solution and validity check
Worked solution P39-Toughest-14. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest 15: Control group
Question P39-Toughest-15. Design or critique a study in a public-parks visitor survey for randomized experiments, emphasizing control group.
Worked solution and validity check
Worked solution P39-Toughest-15. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest 16: Placebo
Question P39-Toughest-16. Design or critique a study in a greenhouse germination experiment for randomized experiments, emphasizing placebo.
Worked solution and validity check
Worked solution P39-Toughest-16. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest 17: Single and double blinding
Question P39-Toughest-17. Design or critique a study in a seedling-growth comparison for randomized experiments, emphasizing single and double blinding.
Worked solution and validity check
Worked solution P39-Toughest-17. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest 18: Blocking
Question P39-Toughest-18. Design or critique a study in a greenhouse germination experiment for randomized experiments, emphasizing blocking.
Worked solution and validity check
Worked solution P39-Toughest-18. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
Toughest 19: Matched pairs
Question P39-Toughest-19. Design or critique a study in a campus dining survey for randomized experiments, emphasizing matched pairs.
Worked solution and validity check
Worked solution P39-Toughest-19. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.
AP Response and Publication Checklist
| Audit point | Required evidence for randomized experiment |
|---|---|
| Scope | Random assignment supports causation; random sampling supports population generalization. |
| Method or source | Random assignment supports a causal comparison by balancing lurking variables in the long run, while random sampling separately controls how far results can be generalized. |
| Calculation | With 120 units and four treatments, equal random assignment gives units per treatment before attrition. |
| Interpretation | Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. |
| Validity | Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. |
| Correction | A large observational comparison is not automatically an experiment, because sample size does not replace random assignment. |
Frequently Asked Questions
How does random assignment work in randomized experiment?
Answer for randomized experiment and Random assignment. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. The required validity evidence is: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible.
How does control group work in randomized experiment?
Answer for randomized experiment and Control group. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. The required validity evidence is: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible.
How does placebo work in randomized experiment?
Answer for randomized experiment and Placebo. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. The required validity evidence is: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible.
How does single and double blinding work in randomized experiment?
Answer for randomized experiment and Single and double blinding. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. The required validity evidence is: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible.
How does blocking work in randomized experiment?
Answer for randomized experiment and Blocking. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. The required validity evidence is: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible.
How does matched pairs work in randomized experiment?
Answer for randomized experiment and Matched pairs. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. The required validity evidence is: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible.
How does replication in experimental design connect to Randomized Experiment?
replication in experimental design within randomized experiment. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. For Random assignment, the controlling scope is: Random assignment supports causation; random sampling supports population generalization.
How does matched pairs experimental design connect to Randomized Experiment?
matched pairs experimental design within randomized experiment. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. For Control group, the controlling scope is: Random assignment supports causation; random sampling supports population generalization.
How does blocking in experimental design connect to Randomized Experiment?
blocking in experimental design within randomized experiment. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. For Placebo, the controlling scope is: Random assignment supports causation; random sampling supports population generalization.
How does blocking experimental design connect to Randomized Experiment?
blocking experimental design within randomized experiment. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. For Single and double blinding, the controlling scope is: Random assignment supports causation; random sampling supports population generalization.
How does randomised experimental design connect to Randomized Experiment?
randomised experimental design within randomized experiment. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. For Blocking, the controlling scope is: Random assignment supports causation; random sampling supports population generalization.
How does randomized experimental design connect to Randomized Experiment?
randomized experimental design within randomized experiment. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. For Matched pairs, the controlling scope is: Random assignment supports causation; random sampling supports population generalization.
How does replication experimental design connect to Randomized Experiment?
replication experimental design within randomized experiment. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. For Replication, the controlling scope is: Random assignment supports causation; random sampling supports population generalization.
How does blind experimental design connect to Randomized Experiment?
blind experimental design within randomized experiment. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. For Completely randomized design, the controlling scope is: Random assignment supports causation; random sampling supports population generalization.
Sources
Administrative and curricular statements in Randomized Experiments: Control Groups, Blinding, Blocking, and Matched Pairs were checked on July 18, 2026. The linked College Board pages control any later policy change; all instructional datasets in original questions are explicitly constructed rather than attributed to a real study.
Randomized Experiment Conclusion
Random assignment supports a causal comparison by balancing lurking variables in the long run, while random sampling separately controls how far results can be generalized. Mastery of randomized experiment therefore requires the exact evidence, mathematics, interpretation, and scope developed in this guide, while preserving this boundary: Random assignment supports causation; random sampling supports population generalization.
