---
title: "Completely Randomized Experiment — AP Stats Definition"
description: "A completely randomized experiment assigns all units to treatments by chance alone, no blocking. The Unit 3 design AP Stats asks you to justify or improve."
canonical: "https://fiveable.me/ap-stats/key-terms/completely-randomized-experiment"
type: "key-term"
subject: "AP Statistics"
unit: "Unit 3"
---

# Completely Randomized Experiment — AP Stats Definition

## Definition

A completely randomized experiment is an experimental design in which all experimental units are assigned to treatments purely by chance, with no blocking or grouping beforehand. In AP Stats Unit 3, it's the baseline design that random assignment alone is expected to balance out confounding variables.

## What It Is

A completely randomized experiment is the simplest experimental design in [AP Stats](/ap-stats "fv-autolink"). You take all of your experimental units (people, plants, driveways, whatever you're testing on), throw them into one big pool, and use [chance](/ap-stats/unit-3 "fv-autolink") alone to assign each one to a treatment group. No sorting by age, no pairing up similar units, no blocking. Just random assignment.

The whole bet behind this design is that randomness will spread out lurking [variables](/ap-stats/unit-1/language-variation-variables/study-guide/nKpeaxi1H3Ht9aFhTHKt "fv-autolink") roughly evenly across the treatment groups. If sunny plots, older subjects, or sandy soil end up scattered across both groups instead of piling up in one, then any difference you see in the response can be attributed to the treatments rather than to those other variables. The CED frames this under choosing a design wisely. Every design has trade-offs depending on the question, the resources, and the nature of the units (EK under AP Stats 3.6.A), and the trade-off here is simplicity in exchange for trusting randomization to handle everything.

## Why It Matters

This term lives in [Topic 3.6](/ap-stats/unit-3/interpreting-p-values/study-guide/b0FEXf5MDjyQtz4Skz70 "fv-autolink") (Selecting an Experimental Design) in Unit 3: Collecting Data, supporting learning objective AP Stats 3.6.A, which asks you to explain why a particular experimental design is appropriate. That word *explain* is the point. The exam rarely just asks you to name a [completely randomized design](/ap-stats/key-terms/completely-randomized-design "fv-autolink"). It asks whether it's the right choice for a given scenario, or whether a known source of variability (like sunlight exposure across crop plots) means a blocked design would be better. Completely randomized experiments are also your reference point for the biggest idea in Unit 3, which is that random assignment is what lets you make cause-and-effect conclusions. If you can't explain why this design works and when it falls short, you can't fully answer design questions on the exam.

## Connections

### [Completely Randomized Design (Unit 3)](/ap-stats/key-terms/completely-randomized-design)

These are two names for the same idea. 'Design' is the blueprint, and '[experiment](/ap-stats/key-terms/experiment "fv-autolink")' is that blueprint actually carried out. AP questions use the terms interchangeably, so treat them as one concept.

### [Random Number Generator (Unit 3)](/ap-stats/key-terms/random-number-generator)

This is the tool that makes the design real. When an FRQ asks you to describe how you'd carry out a completely randomized experiment, you describe a concrete random process, like numbering the units and using a [random number generator](/ap-stats/key-terms/random-number-generator "fv-autolink") to pick which ones get each treatment.

### [Randomized Block Design (Unit 3)](/ap-stats/key-terms/randomized-block-design)

[Blocking](/ap-stats/key-terms/blocking "fv-autolink") is the upgrade you reach for when a completely randomized experiment isn't enough. If you already know a variable (like sunlight or soil type) affects the response, you group similar units into blocks first and randomize within each block, instead of hoping chance balances it out.

## On the AP Exam

Expect this term in design-evaluation questions. The 2023 FRQ Q2 used exactly this setup, where a developer testing whether fibers in concrete reduce driveway cracking needed treatments assigned to driveways by chance. On FRQs like that, you have to describe the random assignment process step by step (number the units, use a random number generator, assign the first half selected to one treatment) and explain what the randomization accomplishes. Multiple-choice questions often probe the design's weakness. One Fiveable practice question describes a researcher worried that sunlight exposure wasn't evenly split between two treatment groups in a completely randomized crop experiment, then asks which graphical display would investigate that concern. The takeaway is the same either way. Know how to execute the design, know what it's supposed to balance, and know when a known nuisance variable means blocking would have been smarter.

## Completely randomized experiment vs Randomized block design

A completely randomized experiment randomizes all units in one pool and trusts chance to balance lurking variables. A randomized block design first sorts units into blocks of similar units (by sun exposure, age, etc.) and then randomizes within each block. Use blocking when you already know a variable affects the response; use a completely randomized design when you don't have a known variable to control for or when blocking isn't practical.

## Key Takeaways

- A completely randomized experiment assigns every experimental unit to a treatment by chance alone, with no blocking or grouping beforehand.
- The purpose of the random assignment is to spread lurking and confounding variables roughly evenly across treatment groups, so differences in the response can be attributed to the treatments.
- On FRQs, you have to describe the randomization concretely, for example by numbering the units and using a random number generator to assign them to treatments.
- Under AP Stats 3.6.A, you should be able to argue when this design is appropriate and when a known source of variability makes a blocked design the better choice.
- Random assignment is what justifies cause-and-effect conclusions, which is the single biggest payoff of any well-run experiment in Unit 3.

## FAQs

### What is a completely randomized experiment in AP Stats?

It's an experimental design where all experimental units are assigned to treatment groups purely by chance, with no blocking or pre-sorting. It's covered in Topic 3.6 of Unit 3 and is the baseline design every other design gets compared to.

### Does a completely randomized experiment guarantee the groups are balanced?

No. Random assignment makes groups balanced on average, but in any single experiment a variable like sunlight exposure can still end up unevenly split by bad luck. That's exactly why exam questions ask how you'd check for imbalance, or whether blocking on a known variable would have been smarter.

### What's the difference between a completely randomized experiment and a randomized block design?

In a completely randomized experiment, all units go into one pool and chance handles everything. In a randomized block design, you first group similar units into blocks based on a variable you know matters, then randomize treatments within each block to reduce that variable's effect.

### Is a completely randomized design the same as a completely randomized experiment?

Yes, for AP purposes they're the same thing. 'Design' refers to the plan and 'experiment' refers to the plan being carried out, and the exam uses both phrasings.

### How do you describe a completely randomized experiment on an FRQ?

Name a specific chance process. For example, number the units 1 through n, use a random number generator to select half of them for treatment A, and assign the rest to treatment B. The 2023 FRQ Q2 about fibers in concrete driveways rewarded exactly this kind of concrete, repeatable description.

## Related Study Guides

- [Legacy AP Statistics Topic: Selecting an Experimental Design](/ap-stats/unit-3/selecting-an-experimental-design/study-guide/v0yhDrgjwaxeCkjNXNC1)

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