What is sampling bias in statistics?
Sampling bias happens when the way a sample is chosen makes some members of the population more likely to be picked than others, so the sample does not represent the population. Its results lean the same wrong way every time. Surveying only gym-goers about exercise, or counting only volunteers who reply, are classic examples.
Sampling Bias in a picture
Formal definition and notation
A sampling method is biased when it systematically favors certain outcomes or individuals, so that its statistics tend to over- or underestimate the population parameter. Common sources are convenience sampling (choosing whoever is easy to reach), voluntary response (only people who choose to answer), and undercoverage (part of the population cannot be selected). Random selection removes this kind of bias; increasing the sample size does not.
| Symbol | Read it as | Meaning |
|---|---|---|
| p̂ | p hat | a sample proportion; under bias it is consistently too high or too low |
| p | p | the true population proportion being estimated |
Key facts
- Bias is about how the sample was chosen, not just bad luck. Repeating a biased method gives the same wrong lean.
- Convenience samples (people nearby) and voluntary-response samples (people who choose to answer) are the most common sources.
- Undercoverage leaves groups out, such as an online-only survey that misses people without internet.
- A bigger biased sample is still biased: it gives a more confident wrong answer.
- The cure is random selection from the whole population, such as drawing names from a full list.
- Biased question wording and people refusing to answer cause related biases (response and nonresponse bias).
Sampling Bias examples, step by step
Example 1: A convenience sample
To estimate how many adults in a city exercise every day, Jo asks 50 people leaving a gym. 45 say they exercise daily. What percent is that, and why is it biased?
- 4550 = 0.9 = 90%.
- People leaving a gym exercise more than typical adults, so they are more likely to say yes.
- The method favors one group, so 90% almost surely overestimates the city rate.
Answer: The sample says 90%, but it is biased upward because only gym-goers were asked.
Example 2: A voluntary-response poll
A city website asks readers to vote on a new parking rule. Of 1,200 votes, 840 are against it. What percent are against it, and can you conclude that 70% of the city’s 80,000 residents oppose the rule?
- 8401200 = 0.7 = 70%.
- The voters chose to answer, and people who feel strongly, often against a change, are more likely to respond.
- So 70% describes the volunteers, not the city.
Answer: 70% of the votes are against, but this voluntary-response sample cannot show that 70% of residents oppose the rule.
Example 3: Compare with a random sample
The city then calls a random sample of 200 residents chosen from the full address list, and 62 oppose the rule. Compare this estimate with the website poll of 70%.
- Random sample: 62200 = 0.31 = 31%.
- Difference: 70 − 31 = 39 percentage points.
- Every resident had the same chance to be picked, so 31% is the more trustworthy estimate.
Answer: The random sample gives 31%, 39 percentage points lower than the biased website poll.
Common mistakes
More data from the same lopsided method repeats the same lean.
Even perfect random samples miss by a little, in either direction.
People choose whom to ask in ways that are not random, like picking friendly-looking people.
Not to be confused with
Sampling variability is the chance difference between random samples, like 30%, 50% and 40% from the same population. It averages out. Bias pushes every result the same way.
Response bias comes from the answers, not the selection: a leading question such as “Don’t you agree the park is too dirty?” pushes people toward yes even in a random sample.
Quick check: 3 questions
Which method is most likely to give a biased sample of a town’s opinion on a new dog park?
Answer: B. Pet store customers are more likely to own dogs and favor a dog park, so the method leans one way. The other three choose people at random from the whole town.Show answer and explanation
A biased survey of 10,000 people is repeated with 50,000 people chosen the same way. What happens to the bias?
Answer: C. Bias comes from how people are chosen, so the same method gives the same lean no matter how many people are included. Only random selection removes it.Show answer and explanation
A biased poll says 90% of students like the new schedule. A random sample later finds 54%. By how many percentage points did the biased poll overestimate?
Answer: A. 90 − 54 = 36 percentage points. 54 is the random-sample result, 144 adds, and 40 is the gap between 90% and 50%.Show answer and explanation
Sampling Bias: frequently asked questions
What are the main types of sampling bias?
Convenience sampling picks whoever is easiest to reach, like friends or people at a mall. Voluntary response lets people choose to answer, so strong opinions dominate. Undercoverage leaves part of the population out, like an online survey that misses people without internet. Each one makes some members more likely to be included than others.
How do you avoid sampling bias?
Choose the sample at random from a list of the whole population, so every member has the same chance to be picked, and follow up with people who do not answer. Use neutral wording in questions to avoid response bias too. A random sample can still be off by chance, but it does not lean one way.
Practice and tools
Sources
- OpenStax, Introductory Statistics 2e, 1.2 Data, Sampling, and Variation in Data and Sampling
- Common Core State Standards, Grade 7 Statistics and Probability (7.SP.A.1)
- Common Core State Standards, High School Statistics and Probability, Making Inferences and Justifying Conclusions (HSS-IC.B.3)
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 7.SP.A.1, CCSS HSS-IC.B.3
Cite this entry
Effortless Math Team. “Sampling Bias.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/sampling-bias/
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