Bias in sampling

About this lesson

Algebra II › Statistical inference

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Bias in sampling

Warm-up

Three quick questions from earlier lessons.

Discover

A TV show asks viewers to text in their opinion; 50,000 do. Is that a better sample than 1,000 randomly chosen adults?

  1. No, the random 1,000 is better
  2. Yes, it is 50 times bigger

Key idea

Bias is a systematic error from how data are collected.

Voluntary response: people choose to respond. Convenience sampling: easy-to-reach individuals. Undercoverage: part of the population cannot be chosen. Nonresponse: chosen people do not answer. Response bias: wording or setting distorts answers. A larger sample does not reduce bias.

Worked example

A survey by phone at 2 p.m. on weekdays.

Working adults are rarely reached
Who is home?
Undercoverage
They cannot be in the sample.
The bias does not shrink with more calls
The estimate leans towards people at home.

Your turn, guided

Your turn: of 1,200 people chosen, 300 answered. The response rate as a fraction:

14\tfrac{1}{4}
300 ÷ 1,200: a high risk of nonresponse bias.

Practice ★

  1. A news website asks readers to vote online; 4824 vote and 80% favor a new law. What is the main problem?
    1. Voluntary response bias: people with strong opinions choose to respond
    2. The sample is too small
    3. None: 4824 responses are representative
  1. A survey of 115 adults is done by calling landline numbers. What kind of bias is most likely?
    1. Undercoverage: people without landlines cannot be chosen
    2. Response bias from the wording
    3. None, if the numbers are chosen at random

Watch out!

Practice ★★

  1. A biased survey of 238 people is repeated with 10 times as many people, chosen the same way. What happens to the bias?
    1. It stays: a larger sample reduces random variability, not bias
    2. It disappears
    3. It becomes 10 times smaller
  2. A biased survey of 402 people is repeated with 10 times as many people, chosen the same way. What happens to the bias?
    1. It stays: a larger sample reduces random variability, not bias
    2. It disappears
    3. It becomes 10 times smaller

Exit ticket

Three questions to check you have got it.

  1. A news website asks readers to vote online; 4824 vote and 80% favor a new law. What is the main problem?
    1. Voluntary response bias: people with strong opinions choose to respond
    2. The sample is too small
    3. None: 4824 responses are representative
  2. A news website asks readers to vote online; 1714 vote and 80% favor a new law. What is the main problem?
    1. Voluntary response bias: people with strong opinions choose to respond
    2. The sample is too small
    3. None: 1714 responses are representative
  3. A news website asks readers to vote online; 3716 vote and 80% favor a new law. What is the main problem?
    1. Voluntary response bias: people with strong opinions choose to respond
    2. The sample is too small
    3. None: 3716 responses are representative

Summary card

Bias

Voluntary response, convenience, undercoverage, nonresponse, response bias.

Watch out: a bigger biased sample is still biased.

End of the lesson

Next lesson: Comparing two groups: two proportions and paired data Back to the chapter

Answers: Bias in sampling

A

  1. Voluntary response bias: people with strong opinions choose to respond

B

  1. Undercoverage: people without landlines cannot be chosen

C

  1. It stays: a larger sample reduces random variability, not bias
  2. It stays: a larger sample reduces random variability, not bias

D

  1. Voluntary response bias: people with strong opinions choose to respond
  2. Voluntary response bias: people with strong opinions choose to respond
  3. Voluntary response bias: people with strong opinions choose to respond

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