SAT-61: Selection Bias and Generalizing Results
Spot selection bias, judge when results generalize, and decide which population a conclusion applies to.
SAT-61: Selection Bias and Generalizing Results
Description: SAT-60 said good conclusions need random samples. This lesson studies what goes wrong when they aren't: selection bias. You'll learn to spot a biased sample and to state exactly which population (if any) a result can be generalized to.
What is selection bias?
Selection bias happens when the way the sample is chosen makes some members of the population more likely to be included than others. The sample then no longer looks like the population, so its results are distorted. (Oʻzbekcha: tanlov xatosi — namunani tanlash usuli baʼzi aʼzolarni koʻproq kiritsa yuzaga keladi.)
Common sources of bias
- Convenience sampling: surveying whoever is easiest to reach (e.g. only your friends).
- Voluntary response: only people who feel strongly reply (online polls, call-ins).
- Undercoverage: part of the population is left out entirely (e.g. phone survey misses people without phones).
(Oʻzbekcha: qulaylik namunasi, ixtiyoriy javob va qamrab olinmaganlik — bularning hammasi noxolislik keltiradi.)
Generalizing — match the conclusion to the sample
You can generalize results only to the population that was randomly sampled. If the sample came from a narrower group, the conclusion applies only to that narrower group — not to everyone. (Oʻzbekcha: xulosa faqat tasodifiy tanlangan guruhga tegishli boʻladi.)
Worked Example 1 — name the bias
To find the favorite sport of a whole city, a reporter interviews people leaving a football stadium. What's wrong?
- People at a stadium already like football, so they're over-represented — this is selection bias (convenience/undercoverage). The result will overstate football's popularity.
Worked Example 2 — who can we generalize to?
A study randomly samples students at one university and finds they sleep 6.5 hours on average. To whom does this apply?
- The random sample came only from that university, so the conclusion generalizes to students at that university — not to all university students everywhere.
(Oʻzbekcha: namuna faqat bitta universitetdan olingani uchun xulosa faqat oʻsha universitet talabalariga tegishli.)
Worked Example 3 — fix the design
A magazine mails a survey and only readers who care enough mail it back. Why is this biased, and how to fix it?
- Voluntary response: strong-opinion readers reply more, so it's biased.
- Fix: take a random sample of the target population and actively collect responses from all of them.
Two-question checklist: (1) Was the sample random? (2) From which population? Your conclusion can only reach that population. (Oʻzbekcha: namuna tasodifiymi va qaysi guruhdan — xulosa faqat oʻsha guruhga boradi.)
Predicting the direction of the bias
The SAT often wants more than "it's biased" — it wants to know which way the result is wrong. To predict this, ask who is over-represented and who is missing. A satisfaction survey answered mainly by happy customers will overstate satisfaction. A stadium poll will overstate love of that sport. A phone survey that misses people without phones will understate whatever those missing people believe. If you can name who got left out, you can usually name the direction of the error — and that is exactly the wording the correct answer choice uses. (Oʻzbekcha: kim ortiqcha, kim tushib qolganini aniqlang — shunda xato qaysi tomonga ekanini bilasiz.)
Practice 1
An online store emails a satisfaction survey; only happy customers tend to respond. Name the bias and its effect.
Show answer
Voluntary-response (selection) bias. It overstates satisfaction, because unhappy customers are under-represented among the responders.
Practice 2
Researchers randomly sample registered voters in one state about a national law. Can they generalize to the whole country?
Show answer
No. The random sample was only from that one state, so the conclusion applies to that state's registered voters — not the entire nation.
Key words — Kalit soʻzlar
- Selection bias — tanlov xatosi (noxolislik)
- Biased sample — noxolis namuna
- Convenience sampling — qulaylik namunasi
- Voluntary response — ixtiyoriy javob
- Undercoverage — qamrab olinmaganlik
- Generalize — umumlashtirish
- Representative — ifodalovchi (vakil)
- Over-represented — ortiqcha ifodalangan
- Target population — maqsadli guruh
Summary
- Selection bias = the sampling method over- or under-includes certain members.
- Watch for convenience samples, voluntary response, and undercoverage.
- Generalize a result only to the population that was randomly sampled.