A completely randomized design is an experimental design in which every experimental unit is assigned to a treatment group purely by chance, with no grouping or blocking beforehand, so that differences among units get spread roughly evenly across all treatments.
A completely randomized design (CRD) is the simplest experimental design in AP Stats. You take all your experimental units, throw them into one big pool, and use a chance process (like a random number generator) to assign each unit to a treatment. No sorting, no pairing, no blocking. Just pure random assignment.
The whole point is that randomization tends to balance out everything you can't control, like differences in age, ability, or metabolism, across the treatment groups. So if the groups end up with different results, you can attribute that difference to the treatments rather than to some lurking variable. The tradeoff is that CRD relies entirely on chance to do that balancing. If your units vary a lot on something related to the response (say, students with very different abilities in a teaching-method experiment), that variability stays in your data as noise, which makes real treatment effects harder to detect.
CRD lives in Topic 3.6 (Selecting an Experimental Design) in Unit 3: Collecting Data, supporting learning objective 3.6.A, which asks you to explain why a particular experimental design is appropriate. The CED's essential knowledge is blunt about this. Every design has advantages and disadvantages depending on the question of interest, the resources available, and the nature of the experimental units. CRD is your baseline. It's easy to run and works great when units are fairly similar or when you have no good blocking variable. The exam almost never asks you to just define CRD. It asks you to choose between CRD, randomized block design, and matched pairs, and then defend your choice. Knowing when CRD is the wrong answer is just as valuable as knowing what it is.
Keep studying AP Statistics Unit 3
Randomization (Unit 3)
Randomization is the engine inside a CRD. Random assignment is what lets you make cause-and-effect conclusions from an experiment, because it spreads lurking variables roughly evenly across treatment groups. A CRD is just randomization with no extra structure added.
Treatment Group and Control Group (Unit 3)
In a CRD, the treatment groups (and any control group) are created entirely by chance. When an FRQ asks you to describe a CRD, the answer is basically a recipe for randomly splitting units into these groups, often using a random number generator.
Power of a Test (Units 6-7)
This is the payoff for choosing the right design. A CRD with highly variable units leaves a lot of noise in the data, which lowers your power to detect a real treatment effect. Blocking removes that variability, which is why 'increases power' is a classic justification for rejecting CRD on the exam.
Cluster Sampling (Unit 3)
These get mixed up because both involve random selection of groups, but they live in different worlds. Cluster sampling is about how you collect data from a population (a survey method). CRD is about how you assign treatments in an experiment. Sampling answers 'who do we study?' while experimental design answers 'who gets which treatment?'
Topic 3.6 questions almost always present a scenario and make you pick or justify a design. Multiple-choice stems describe a researcher with limited time, money, or space, plus experimental units that vary in some obvious way (student ability, starting weight, soil quality), and ask which design is most appropriate. CRD is the right answer when units are similar or no useful blocking variable exists; it's the wrong answer when there's a known source of variability you could block on. On the free-response side, the 2022 FRQ used 36 pairs of identical twins to test an acne drug, a setup practically begging you to recognize that matched pairs beats CRD because twins control for genetic variability. The 2024 FRQ about four car models and gas mileage similarly tested whether you could describe and justify an appropriate design. When you describe a CRD in an FRQ, be concrete. Name the chance mechanism (random number generator, slips of paper), say how many units go to each treatment, and explain what randomization accomplishes.
Both designs use random assignment, so the names blur together. The difference is what happens before the randomization. In a CRD, you randomize everyone in one big pool. In a randomized block design, you first sort units into blocks of similar units (by initial weight, ability level, soil region), then randomize to treatments within each block. Blocking removes a known source of variability from the comparison; CRD just hopes randomization spreads it evenly. Quick test: if the problem mentions an obvious variable that affects the response, the exam probably wants blocking, not CRD.
A completely randomized design assigns all experimental units to treatments purely by chance, with no blocking or pairing first.
Random assignment is what allows cause-and-effect conclusions, because it balances lurking variables across treatment groups on average.
CRD is the best choice when experimental units are fairly similar or when there is no clear variable to block on.
When units vary widely on something related to the response, a randomized block design beats CRD because it removes that variability and makes treatment effects easier to detect.
On FRQs, describing a CRD means naming a specific chance mechanism, stating how units are split among treatments, and explaining what the randomization accomplishes.
Don't confuse CRD with cluster sampling; CRD assigns treatments in an experiment, while cluster sampling selects participants for a survey.
It's an experimental design where every experimental unit is assigned to a treatment group entirely by chance, with no blocking or pairing beforehand. It's the baseline design in Topic 3.6 of Unit 3.
No. The CED says each design has advantages and disadvantages depending on the question, resources, and the experimental units. If units vary widely on something tied to the response, like initial weight in a diet study, a randomized block design usually detects treatment effects better.
In a CRD, all units are randomized in one pool. In a block design, you first group similar units into blocks (by ability, weight, soil region), then randomize within each block. Blocking removes a known source of variability that a CRD leaves in as noise.
No, and mixing these up costs points. Random sampling is how you select participants from a population (it supports generalizing results). Random assignment in a CRD is how you give out treatments (it supports cause-and-effect conclusions).
Name a concrete chance mechanism, like numbering all 60 students and using a random number generator to assign the first 20 selected to method A, the next 20 to method B, and the rest to method C. Then state that randomization balances variables like student ability across groups. The 2024 FRQ on car mileage rewarded exactly this kind of specific, justified description.
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