Random Sampling versus Random Assignment

12.5: Random Sampling versus Random Assignment. Original editorial SAT preparation with three worked examples, ten flashcards, and thirty practice questions. Educator-review draft.

Lesson 5 of 63 parts Practice Flashcards

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Sampling purpose

Objective: Connect random selection to population inference.

Prerequisite skills: observational versus experimental designs. Random sampling concerns which population members enter the study. It reduces systematic inclusion differences and supports generalizing sample results to the sampled population, subject to nonresponse and measurement limitations. Common error: claiming random selection by itself proves causation. Restrictions and interpretation: Random sampling supports generalization; random assignment supports causal treatment comparison; neither substitutes for the other.

Formulas

random sample → population generalization

Worked examples

Try itA random sample of 330 adults is asked about existing diet habits and health. What does random sampling chiefly support?Show answer

Random selection supports population inference because the sample comes from the target population through a chance method. Existing diets were not assigned, so causal effects are not established. Therefore the requested answer is Generalization to the population from which the sample was drawn.

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Sampling purpose

Objective: Connect random selection to population inference.

Formulas

random sample → population generalization

Worked examples

Try itA random sample of 330 adults is asked about existing diet habits and health. What does random sampling chiefly support?Show answer

Assignment purpose

Objective: Connect randomized treatment allocation to causal evidence.

Random assignment concerns which treatment an enrolled participant receives. It tends to balance both measured and unmeasured preexisting factors across groups, enabling a causal treatment contrast when the experiment is properly conducted. Common error: assuming treatment randomization makes a convenience sample nationally representative. Restrictions and interpretation: Random sampling supports generalization; random assignment supports causal treatment comparison; neither substitutes for the other.

Formulas

random assignment → causal treatment comparison

Worked examples

Try itA convenience sample of 104 volunteers is randomly assigned to two training programs. Which conclusion is most appropriate?Show answer

Random assignment supports the causal treatment contrast. The convenience recruitment limits generalizing that result to a broader population; it does not erase the treatment randomization. Therefore the requested answer is A causal program comparison may be supported for the study participants, but broad population generalization is limited.

Both design features

Objective: Evaluate a study that uses random sampling and random assignment.

When a representative random sample is enrolled and then randomly assigned to treatments, the study can support both causal comparison and generalization to the sampled target population, subject to its execution and measurement quality. Common error: using only one of the two design features to claim both kinds of inference. Restrictions and interpretation: Random sampling supports generalization; random assignment supports causal treatment comparison; neither substitutes for the other. Desmos and method choice: Use Desmos for arithmetic or a graph/table check when that reduces work. Enter parentheses explicitly and verify the requested quantity and units. Use the algebraic steps shown here for an exact result; a rounded graph display is not proof of exact equality.

Formulas

random sampling + random assignment → potential generalization and causation

Worked examples

Try itA random sample of 246 district students is randomly assigned to tutoring methods A and B. Assuming a well-conducted study, which inference is best supported?Show answer

Random sampling connects participants to district students; random assignment supports a causal comparison between the methods. The target remains the district population, not every person worldwide. Therefore the requested answer is A causal method comparison that can be generalized to the district’s student population.

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