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Algebra 2 Statistics and probability

Sample surveys, experiments, observational studies

20 practice questions 0 video lessons Theory + worked examples

Surveys, Experiments, and Observational Studies

California Algebra 2 • Standard S-IC.3 • Statistics & Probability

Surveys, Experiments, and Observational Studies is a topic in Statistics & Probability in the California Common Core State Standards. It is aligned to Standard S-IC.3, which requires students to recognize the purposes of and differences among sample surveys, experiments, and observational studies.

Surveys estimate a population value, observational studies watch without intervening, and experiments apply a treatment.

California Algebra 2 › Statistics & Probability › Surveys, Experiments, and Observational Studies  —  Standard S-IC.3

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Theory

Three kinds of statistical study differ in how data are collected:

  • Survey: ask questions of a sample to estimate a population value.
  • Observational study: record data without applying a treatment.
  • Experiment: impose a treatment and compare groups.
Only a randomized experiment can establish causation; observational studies show association.
Three study types Three study types Three study types survey: ask a sample (observational) observational: watch, no treatment experiment: apply a treatment
The three study types.
What each shows What each shows What each shows experiment (random assignment) → causation observational study → association only survey → estimate a population value
What conclusions each supports.

The key distinction:

\[\text{random assignment}\Rightarrow\text{causation};\quad \text{observation}\Rightarrow\text{association}\]
random assignment supports causation; observation supports association only
Random assignment is what separates experiments from observation.

How to classify a study

  1. Was a treatment applied? If yes, it's an experiment.
  2. If only observed/asked, it's observational or a survey.
  3. Check for random assignment (experiments) vs random sampling (surveys).
  4. Match the conclusion: causation vs association.
Example 1 — Identify the type
Researchers give one group a new drug and another a placebo. Which type?
Solution

A treatment is imposed, so it is an experiment.

an experiment, because a treatment is applied
Example 2 — Observational study
Researchers record diets and health without intervening. Which type?
Solution

No treatment is applied, so it is observational.

an observational study
Example 3 — Causation
Which study type can establish causation?
Solution

Only a randomized experiment can, because random assignment controls other factors.

a randomized experiment can establish causation
Example 4 — Sampling vs assignment
What is the difference between random sampling and random assignment?
Solution

Random sampling chooses who is studied (for surveys); random assignment sorts subjects into groups (for experiments).

sampling chooses who is studied; assignment sorts them into groups

Common pitfalls

Observational studies can't prove causation — only association.
Random sampling \(\neq\) random assignment.
A survey is observational — it applies no treatment.

Frequently asked questions

What is an experiment?

A study that applies a treatment and compares groups.

What is an observational study?

One that records data without applying a treatment.

Which study can show causation?

A randomized experiment.

What does an observational study show?

Association, not causation.

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