Sampling Bias

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Sampling Bias: meaning, method and solved example (AP Statistics) – Maths PDF

In short: Sampling bias is a flaw in how individuals are selected that makes some members of the population systematically more likely to be chosen, so the results lean away from the truth.

AP StatisticsStatisticsAP Statistics Unit 1

What is Sampling Bias?

Sampling bias means the way a sample was gathered favors some answers over others. The error leans in a consistent direction, so it does not cancel out and it does not shrink when more people are surveyed.

Common sources are voluntary response (people choose to reply, so strong opinions dominate), convenience sampling (easy-to-reach people only), undercoverage (some groups never had a chance to be selected) and nonresponse (chosen people who do not answer differ from those who do). Random selection is the main defense, because it removes the judgment that tilts the sample.

How to spot it

  • A poll invites listeners, readers or website visitors to call, click or write in.
  • The sample comes from whoever was nearby, such as shoppers at one mall or students in one hallway.
  • The list used to pick people leaves out a group, like households without landline phones.
  • A report gives an impressive sample size but says nothing about how people were chosen.

The method

  1. Identify the population and the exact way individuals came into the sample.
  2. Ask which kind of people could never be chosen, or would be much more likely to respond.
  3. Name the type of sampling bias (voluntary response, convenience, undercoverage or nonresponse) and say which direction the results probably lean.
  4. Recommend a fix: select from a complete list with a random method and follow up with nonrespondents.
PopulationRandom sample: matches the populationBiased sample: amber group nearly missing60%40%60%40%90%10%
The biased method gives the amber group only 10 percent of the sample when it is 40 percent of the population.

Sampling Bias: solved example

Problem

A local radio show asks listeners to call in about a proposed bike lane downtown. Of 312 callers, 81% oppose the lane. Can the station conclude that about 81% of all residents are against it?

Solution

No. The callers volunteered, and people with strong feelings, often negative, are the most likely to phone in. People without a radio, or without a strong opinion, are missing. This is voluntary response bias, and it probably overstates opposition.

The sample of 312 is large, but size does not repair bias. A random sample of residents drawn from the voter rolls, with follow-up calls to nonrespondents, would give a trustworthy estimate.

Try it

Question 1

To learn how often students work out, a high school junior surveys 40 people she meets outside the weight room. Name the bias.

Show the answer

Convenience sampling, which also causes undercoverage: students who never visit the weight room cannot appear, so workout rates are probably overstated.

Question 2

Will surveying 5,000 volunteers instead of 500 remove the bias in a voluntary-response poll?

Show the answer

No. A bigger sample picked by the same flawed method repeats the same lean; the estimate just becomes more precisely wrong.

Sampling Bias vs. Margin of Error

The margin of error describes chance variation from sample to sample, and it shrinks as the sample grows. Sampling bias is a systematic tilt caused by the selection method; the margin of error does not cover it, and a bigger sample cannot cure it.

Margin of Error

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