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What is selection bias?

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University Course Reader · STEM

Reviewers noted the study's selection bias: every participant had been recruited from a single hospital's waiting room.

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Overview

Selection bias is error caused by how a sample was chosen. When some people or cases were likelier to be included than others, the sample does not represent the wider group, and conclusions from it start out wrong. Survey by phone and you learn what phone-answerers think; recruit volunteers and you study people who volunteer. The sample can be huge and honestly collected and still describe only the people in it.
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Overview

Selection bias is the answer being rigged by who got asked, no rigging required. Online reviews are written by people angry or thrilled enough to type; the satisfied middle is busy living. A poll on an app samples people who use the app. Before any data says anything about the world, it says who was in the room, and most of the time nobody checks who wasn't. 😎

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Detail

Selection bias means your sample was collected in a way that does not represent the population you care about. The classic demonstration is a 1936 US election poll. A magazine collected 2.4 million responses, drawn from telephone directories and car registrations, and predicted the wrong winner, because owning a phone or car in 1936 meant being well-off, and the well-off voted differently. A rival pollster called it correctly with a small fraction of the sample, chosen to mirror the electorate. The lesson still holds: how you select matters more than how many you select, and a bigger sample from a skewed source produces the same wrong answer with more confidence. Selection error enters in several ways. Some people are unreachable by your method, some refuse, some volunteer because they feel strongly, and some drop out along the way; survivorship bias is the same failure on the way out. Studying a specific group is fine while your conclusions stay about that group; the bias appears when a narrow selection speaks for a broader population. The fix is structural: select at random from the population you mean, or state clearly which group your data can describe.
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Detail

Selection bias breaks the one promise data ever makes: that the sample should look like the world it claims to describe. Break it, and the numbers describe the sample and nothing else. Reviews come from the furious and the delighted, so every product looks polarizing. Replies under a post come from whoever cared enough to type, so every opinion looks intense. "9 out of 10 professionals agree" invites the question of which ten got asked. Serious research trips on the same stone, famously by studying whatever cases are convenient, often university students, then publishing conclusions about everyone. And piling on volume fixes none of it, because a million entries collected through the same crooked doorway are the same unrepresentative sample, louder. The bias lives in the collection step, the one step the headline never shows. So ask the boring question: how did these particular cases end up in this particular dataset? The answer usually explains the finding better than the finding does. 😎

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Analogy

Selection bias is fishing with a wide-mesh net and concluding the lake holds only large fish. The net is your sampling method, and the mesh decides what can end up in the boat: everything below a certain size swims straight through and never appears in the catch. The fisherman counts honestly and writes down exactly what the net delivered. The records are accurate; the lake is misrepresented, because the instrument could only gather one kind. Hauling in ten more netfuls will not help; every netful passes the same mesh. The only fix is changing the net, and the first question to ask about any dataset is the same one: what could this net not catch?
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Analogy

Selection bias is judging the whole city from talk-radio callers. The host asks what people think of the new stadium, the phone lines light up, and every caller has a take. By hour's end the city is apparently furious. Except calling a radio station is a hobby for a very specific kind of person: strong opinions, open afternoons, a phone already in hand. The millions who shrugged and changed the station are, by definition, not on the air. The show honestly broadcast every call it received. It just never received the city. 😎
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Formal definition — The same term, explained the usual way

Selection bias is systematic error introduced when the process by which units enter a sample is related to the variables under study, rendering the sample unrepresentative of the target population. Mechanisms include undercoverage of the sampling frame, self-selection of volunteers, non-response, and differential attrition, of which survivorship bias is a special case. Because the error is structural, increasing sample size amplifies precision without reducing the bias; randomized selection, as institutionalized in randomized controlled trials and probability polling, is the principal safeguard.

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