Key takeaway: Sampling bias occurs when the method of choosing a sample systematically favors some members of the population over others, so results consistently miss the true population value in one direction.
Grade 12 – AP StatisticsAP Statistics Unit 1Statistics and Data
Definition of Sampling Bias
Sampling bias is a flaw in how individuals are selected, not an accident of chance. If the selection method leaves out certain people or invites certain people more strongly, the sample cannot represent the population, and the estimate lands off target again and again.
Common sources are undercoverage (some groups never get a chance), voluntary response (only people with strong opinions reply) and nonresponse (chosen people cannot be reached or refuse). Random selection is the main protection.
Formula and notation
Bias is the gap between what the method estimates on average and the truth. For a statistic \(\hat{p}\) estimating a proportion \(p\):
\[ \text{bias}=\text{(average of }\hat{p}\text{ over many samples)}-p. \]
An unbiased method has zero bias. Sampling variability remains, but it shrinks as the sample grows.
Key facts
- Bias comes from the selection method, so enlarging a biased sample does not repair it.
- Voluntary response samples, such as call-in polls, over-represent people with strong feelings.
- Undercoverage happens when the sampling frame leaves out part of the population.
- Random selection from a complete list is the standard cure for sampling bias.
Sampling Bias example
A radio station asks listeners to call about new bike lanes. Of 900 callers, 639 are opposed. A random sample of 400 residents finds 156 opposed. Compare the results and explain.
-
Call-in share: \(\frac{639}{900}=0.71\), or 71%.
-
Random-sample share: \(\frac{156}{400}=0.39\), or 39%.
-
Callers chose themselves, and people angry about the lanes are most motivated to phone in.
The call-in poll shows sampling bias (voluntary response), so the random sample’s 39% is the more trustworthy estimate.
Common mistake
Watch out
A student argues that the 900-caller poll beats the 400-person sample because 900 is a bigger number.
Why it is wrong
Size reduces random error only. A biased method keeps missing the truth in the same direction however many people respond, so 9,000 callers would still overstate opposition. Judge a poll first by how the sample was chosen, then by its size, to avoid sampling bias.
Related terms and lessons
Browse the glossary: A–Z list · AP Statistics vocabulary · Statistics and Data