AP® Statistics · Unit 1 · Topic 1.10
Generalizing from a Sample
You can only generalize a sample's results to the specific population it was randomly drawn from, never to a broader group it didn't represent, no matter how large the sample is.
A poll of 1,000 randomly chosen people can speak for a country because those 1,000 were selected in a way that gives every member of the country a known chance of being included. A poll of your friends can't, because your friends were never a random slice of anyone but your friends. The sample's reach is set entirely by how it was selected, not by how many people are in it.
To decide which population a result generalizes to, ask one question: what group was this sample actually drawn from? Trace the sampling method back to its source. A random sample of 400 shoppers at one mall was drawn from that mall's shoppers, so the result describes that mall's shoppers. It says nothing reliable about shoppers nationwide, because shoppers elsewhere never had a chance to be chosen.
This is why a huge sample can't rescue bad selection. Size controls how precise an estimate is for the group actually sampled, but it does nothing to fix who got left out. A thousand biased responses are still biased; they're just biased with more decimal places of confidence. Volunteer samples show this clearly: people who choose to respond to an online ad often differ systematically from the general population in motivation, interest, or opportunity, so even 500 volunteers only generalize to 'people like these volunteers,' not everyone. This idea connects directly to how samples get chosen in the first place, since random selection is what earns the right to generalize at all.
Key terms
- Population
- The entire group a researcher wants to draw conclusions about.
- Sample
- The subset of the population actually measured or surveyed.
- Generalize
- To extend a conclusion from the sample to describe the broader population it came from.
- Self-selection
- When individuals choose on their own to be part of a sample, often making them unrepresentative.
- Sampling bias
- A systematic tendency for a sample to differ from the population due to how it was selected.
Watch it explained
- How it worksWalk me through deciding which population a sample result is allowed to describe.
- Common mistakeWhy isn't a huge sample enough to fix a badly chosen one?
- Worked exampleFind the population you can generalize to from a survey of 400 shoppers at one mall.
- Going furtherWhat happens to your conclusion when the sample was made entirely of volunteers?
Check yourself
End of topic.