Can a small sample represent a large population?

A well-designed sample can support useful estimates; method and uncertainty matter more than the population-to-sample ratio alone.

Does a narrow interval prove a poll is accurate?

No. Bias can remain outside the sampling calculation.

Are online polls always nonprobability polls?

No. Online is a collection mode; recruitment can follow different sampling designs.

AI Glossary / Statistics and probability / Intermediate

Opinion poll

Definition

An opinion poll is a survey designed to measure people's views, preferences, or intentions on specified questions. Pollsters collect responses from a sample and may use them to estimate opinions in a defined population. The credibility of those estimates depends on sampling, measurement, participation, weighting, and analysis, rather than simply on the number of responses collected.

What it means

A poll is a snapshot of answers obtained under particular conditions and during a particular period. It may concern a product proposal, public service, social issue, or voting intention. What people say now is not automatically what they will do later.
The target population must be clear. Results for customers, all adults, registered voters, and likely voters answer different questions. A poll of visitors who voluntarily click a website link describes a different selection process from a sample recruited through a probability design.

How it works

Define the population and the question to be measured. Specify eligibility, timing, and the sampling frame. Probability sampling uses a selection mechanism with known probabilities; nonprobability approaches rely on additional assumptions and adjustment methods to support broader inference.
Write clear, neutral questions and appropriate answer options. Question order, wording, interview mode, and whether alternatives are prompted can influence responses. Preserve the exact wording when reporting results or comparing them over time.
Collect responses and assess participation, coverage, and data quality. A low response rate is not by itself a numerical estimate of nonresponse bias, but differences between respondents and nonrespondents can matter. Large samples do not automatically remove such differences.
Weighting can adjust for selection probabilities and align measured characteristics with credible population information. It can also increase sampling variance and cannot guarantee correction for unmeasured differences associated with opinion.
Estimate uncertainty using methods consistent with the design and analysis. A conventional margin of sampling error describes sampling variability under specified assumptions; it does not include every source of poll error. Model-based intervals for nonprobability samples require their own assumptions and should not be presented as ordinary probability-sample margins without explanation.
Report who conducted and funded the poll, field dates, sample size, target population, recruitment method, question wording, weighting, and uncertainty method. Evaluate subgroup results separately because their effective sample sizes are usually smaller than the overall sample.

Three practical examples

Customer research: estimate support for a proposed service feature among a defined customer population.
Community planning: measure residents' preferences for alternative opening hours using a documented survey design.
AI adoption research: ask workers about expected benefits and concerns, distinguishing reported attitudes from observed adoption behavior.

Think of it this way

Think of taking a photograph through a particular lens at a particular moment. The image can be informative, but framing, lighting, and who appears in the picture affect what it shows. A sharper image of an unrepresentative scene does not automatically become a picture of the whole population.

Worked example

Suppose a fictional simple random sample of 1,000 people from a much larger population produces 540 responses favoring a proposal. Assume complete response and a binary outcome for this calculation.
The estimated proportion is 540/1,000 = 0.54. Ignoring the negligible finite-population correction, the estimated standard error is the square root of [0.54 times 0.46 divided by 1,000], approximately 0.01576.
A normal-approximation 95% interval uses a margin of 1.96 times that standard error, approximately 0.03089. The interval is therefore about 50.91% to 57.09%.
If a different probability design had a design effect of 1.5 for this estimate, its standard error would be multiplied by the square root of 1.5. The corresponding margin would be about 3.78 percentage points, rather than 3.09.
These calculations address sampling variation under the stated assumptions. They do not account for leading wording, coverage gaps, dishonest answers, or later changes in opinion. They also cannot be transferred unchanged to an unrestricted online vote.

Illustrative case study

Fictional case: Elm Transit polls residents about an AI-assisted journey planner. A social-media vote attracts many enthusiastic users, while a separately recruited survey includes residents who rarely use the app.
The research team reports the recruitment methods separately and checks whether both questions used the same description of the proposal. Managers use the findings to understand different audiences rather than treating the larger click-in poll as automatically more representative. A follow-up pilot measures actual use, which the opinion questions alone did not establish.

Common misconceptions and mistakes

A poll is not a census, an election result, or a guaranteed forecast. Voting intentions can change, and turnout is a separate source of uncertainty in election polling.
Do not apply the full-sample margin of error to every subgroup or to a difference between two estimates without the appropriate calculation. Estimates from the same respondents can be correlated.
A margin of error is expressed in percentage points for a percentage estimate. It is not a percentage of the reported percentage.
Weighting does not make every sample representative, and averaging several polls does not eliminate errors they share. AI-generated synthetic responses should not be presented as measured human opinion.

Business use

Businesses can use opinion polls to inform product priorities, communications, and service planning when the target population and question match the decision. Keep reported intentions separate from purchasing or usage behavior. Compare studies only after examining their populations, dates, wording, and methods. Treat unexpected results as a reason to investigate, rather than choosing whichever poll supports an existing preference.

Check your understanding

Why did the example's margin increase with design effect?

Answer: The assumed design increased the estimator's sampling variance relative to simple random sampling.

Why publish exact wording?

Answer: Readers need to know which opinion was actually measured and whether comparisons use equivalent questions.

Related terms

Survey
Design effect
probability sample
nonprobability sample
weighting
margin of error
nonresponse bias
likely-voter model

Learn next

compare two poll reports by population, recruitment, wording, field dates, weighting, and uncertainty before comparing their headline percentages.

Sources

Sources: AAPOR, Disclosure Standards: https://aapor.org/standards-and-ethics/disclosure-standards/ . Pew Research Center, Understanding the margin of error in election polls: https://www.pewresearch.org/short-reads/2016/09/08/understanding-the-margin-of-error-in-election-polls/ . Primary methodological pages were opened. The numerical poll and case study are invented illustrations, not current opinion findings.

Previous: Operator precedence Next: Opportunistic reasoning