Algebra 2
Statistics and probability
Sample surveys, experiments, observational studies
20 practice questions
0 video lessons
Theory + worked examples
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.
The three study types.
What conclusions each supports.
The key distinction:
\[\text{random assignment}\Rightarrow\text{causation};\quad \text{observation}\Rightarrow\text{association}\]
Random assignment is what separates experiments from observation.
How to classify a study
- Was a treatment applied? If yes, it's an experiment.
- If only observed/asked, it's observational or a survey.
- Check for random assignment (experiments) vs random sampling (surveys).
- 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.
Example 2 — Observational study
Researchers record diets and health without intervening. Which type?
Solution
No treatment is applied, so it is observational.
Example 3 — Causation
Which study type can establish causation?
Solution
Only a randomized experiment can, because random assignment controls other factors.
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).
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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