Random Sampling vs. Random Assignment in AP Statistics

Random sampling decides who enters a study. Random assignment decides which treatment each participant receives. Random sampling supports generalizing results to the population sampled. Random assignment supports cause-and-effect conclusions from a well-conducted experiment. A study can use either process, both, or neither.

The College Board AP Statistics course framework distinguishes these roles when explaining the conclusions a study can support. The scenarios below are original Kibo examples, not official AP questions.

Look for two separate decisions

1. Selection: How did people get into the study? Identify the population, then the process used to choose the sample.
2. Assignment: Once people were included, how were treatments allocated? Look for a chance process assigning the conditions being compared.

For example, a simple random sample gives every possible sample of the specified size the same chance of selection. Choosing volunteers who answer an announcement does not do that. OpenStax’s sampling guide explains this definition and how selection and nonresponse can introduce bias.

In an experiment, a treatment is a condition imposed on a participant; the response is the outcome measured. Random assignment reduces systematic differences between treatment groups, making competing explanations less likely. It does not guarantee identical groups. See OpenStax’s introduction to experimental design for the treatment and response terminology.

Four study designs: what can each establish?

Imagine a school with $800$ enrolled students. Its library has two shelf maps: a text-only map and a map with icons. In each scenario, the response is the time needed to find the same book. Before reading each explanation, identify selection, assignment, and the allowable scope of the conclusion.

A random sample with no random assignment

The librarian takes a simple random sample of $80$ students from the complete enrollment roster. All selected students participate. Each uses whichever map they normally prefer, and the librarian records their search time.

Selection is random; assignment is absent. With sound measurement and analysis, the sample can describe the relationship between map preference and search time among this school’s students. It cannot establish that choosing one map causes a faster search.

Perhaps frequent library users favor the icon map and already know the shelves. Library experience could help explain both their choice and their speed. Randomly selecting the participants does not remove that explanation.

Random assignment with a volunteer sample

An announcement recruits $80$ volunteers. The librarian randomly chooses $40$ of those volunteers to receive the icon map; the remaining $40$ receive the text-only map. Everyone follows the same instructions and searches individually under comparable conditions.

Selection is voluntary; assignment is random. An appropriately analyzed difference could support a causal conclusion about map type for these participants under the study conditions. Random assignment alone does not justify extending the result to every student at the school.

For instance, the volunteers might be unusually interested in library activities. Applying a result to people similar to the volunteers requires considering that similarity; it does not turn them into a random sample of the whole school.

Both random sampling and random assignment

The librarian takes a simple random sample of $80$ students from the complete roster, and all participate. Within this sample, a second random draw assigns $40$ students to the icon map and the other $40$ to the text-only map. Instructions, the target book, and testing conditions are held consistent.

Both processes are random. A well-conducted study with appropriate analysis could support a causal conclusion about map type and generalize it to this school’s enrolled students. The roster does not represent all students in other schools.

The sample contains $80$ students; dividing them evenly gives $80\div2=40$ per treatment. The first draw chooses participants from the school. The second draw allocates maps among those participants. These are different jobs, even though both use chance.

Neither random sampling nor random assignment

The librarian invites students already visiting the library to participate. Those who agree choose their own map, then complete the search.

Neither process is random. The results can describe the participating students, but the design provides no random-sampling basis for generalizing to the entire school and no random-assignment basis for a causal claim.

A faster average with one map could reflect who volunteered, who chose that map, or other differences. Recording more volunteers would not repair those design limitations by itself.

A permitted conclusion still needs evidence

Randomization tells you what kind of inference the design can support. It does not tell you that a treatment worked. You still need the results and an analysis that accounts for chance variation.

Suppose the randomized map study reports mean search times of $54$ seconds with the text-only map and $48$ seconds with the icon map. The observed difference is $54-48=6$ seconds. Those means alone do not establish statistical significance; you would need more information about the data and an appropriate inference procedure.

A reusable answer template

Write one sentence about the population and one about cause and effect. Fill the brackets with details from the study:

• “Because participants were [selection method], generalizing the findings to [named population] is [supported by the sampling design / not justified by the selection method].”
• “Because treatments were [assignment method], an appropriately analyzed difference [could support / would not by itself support] a causal conclusion about [treatment] and [response].”

For the volunteer experiment: “The volunteer recruitment does not justify generalizing to all students at the school. Random assignment of map type could support a causal conclusion about map type and search time for the participants under the study conditions, if the results provide sufficient evidence.”

Common mistakes to catch

• Treating any use of “random” as enough. Name the specific action: selecting participants or assigning treatments.
• Assuming random assignment makes volunteers representative. Assignment changes the groups within the study, not the recruitment process.
• Ignoring missing responses. If selected students decline and differ from those who participate, nonresponse can undermine population conclusions.
• Claiming a cause from a raw difference. Check both the design and the statistical evidence before writing a causal conclusion.

If you mixed up the decisions, record the exact phrase you overlooked and rewrite your conclusion. The Kibo error-log template can organize that correction and a later recheck.

Try a free AP Statistics practice question with Kibo to continue working on introductory statistics.

Prepared with AI assistance. The four original designs were checked against the cited principles, and arithmetic was checked separately; no human review is claimed. Sources checked October 9, 2026. AP is a registered trademark of the College Board, which is not affiliated with or endorsing this guide.