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World desk6 min

How to Avoid Misleading Conclusions from Small or Biased Samples

A large sample is not automatically representative. Check who was included, how responses were gathered, and whether uncertainty and limitations are reported.
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A sample can mislead for two different reasons: it may be too small to estimate a result precisely, or it may leave out—or overrepresent—parts of the population. A larger sample can reduce random sampling error, but it cannot by itself fix biased recruitment, nonresponse, misleading questions, inaccurate answers, or data-processing mistakes. Before trusting a poll or survey, check who it was meant to represent, how people were selected, who did not respond, and whether the conclusion stays within what the study measured.

Start with the population the claim is about

Write down the exact group a study claims to describe: for example, a country’s adults, a city’s households, current customers, or people with a particular condition. Then check whether the headline goes beyond that group. A survey of a company’s customers does not automatically describe everyone who might buy the product; a poll of social-media users does not automatically describe the wider public.

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A sample is useful only in relation to a defined population and a way of selecting people from it. The Australian Bureau of Statistics explains that samples may be random or non-random, and that a small sample may not represent the total population: ABS: Census and sample.

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Separate sample size from sample selection

What size can tell you

With a suitable probability-based design, more observations generally reduce random sampling variability and can make an estimate more precise. But there is no universal minimum number that makes a survey reliable. Adequacy depends on the population, how variable the outcome is, the sampling design, the precision needed, and whether the study needs to report results for subgroups.

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What selection can tell you

Ask what sampling frame was used, who had a chance to be included, how participants were recruited, and whether each person’s chance of selection was known. A self-selected online poll can attract people with unusually strong opinions or particular access to the platform. Adding many more volunteers may make the volunteer group larger without making it representative of people who never had an opportunity to take part.

Weighting can give some respondents more or less influence so that measured characteristics align with population benchmarks. It does not automatically fix missing groups or differences that were not measured. Look for which characteristics were weighted and whether the benchmarks fit both the intended population and the sample. The U.S. Census Bureau’s guidance explains the role of sample design: Statistical Quality Standard A3: Developing and Implementing a Sample Design.

Look beyond the number surveyed

A headline sample size may refer to people contacted, invited, or who started a questionnaire—not necessarily the number who completed it or answered the question behind a particular claim. Check completed responses and the denominator for each reported result. People who cannot be reached or choose not to respond may differ from those who do.

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These are examples of nonsampling error, which can also include inaccurate answers and mistakes in processing or analysis. Such errors may affect a study even when it surveys every member of its defined population. The Office for National Statistics distinguishes sampling variability from these other sources of error in its explanation of survey uncertainty: ONS: Uncertainty and how we measure it for our surveys.

Read the questions, response options, mode, and timing

Question wording can steer answers, while limited response options can prevent people from expressing what they think. The way a survey is administered—such as online, by phone, or in person—and when it is conducted can affect who participates and how they answer.

For a poll or survey, look for the full question wording and answer options, survey mode, field dates, target population, recruitment method, and any weighting. If these details are missing, you may not be able to tell whether a reported percentage is a sound measure of the opinion or behavior in question. AAPOR’s Best Practices for Survey Research calls for transparent reporting of these methodological details and attributes this statement to the American Statistical Association’s What is a Survey?: “The quality of a survey is best judged not by its size, scope, or prominence, but by how much attention is given to [preventing, measuring and] dealing with the many important problems that can arise.”

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Check whether the uncertainty measure fits the design

Look for a standard error, confidence interval, coefficient of variation, or another measure appropriate to the design. Note the confidence level and method used. These measures describe uncertainty from sampling under stated assumptions; they do not erase selection bias, nonresponse, poor measurement, or every other source of error.

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Be especially cautious with a reported margin of error. A conventional margin of error is based on assumptions about how the sample was drawn. AAPOR’s journalist guidance cautions against reporting error margins for non-probability samples as though they were conventional probability-sample margins: A Journalist’s Guide to Understanding Polls & Surveys. A number labeled “margin of error” is not a complete account of a survey’s quality.

Statistical significance also has a limited meaning: it addresses whether an observed result would be surprising under a specified statistical model, not whether the difference is large or important in practice. The U.S. Census Bureau’s Statistical Quality Standard E1: Analyzing Data calls for appropriate measures of statistical uncertainty and notes that a p-value does not tell readers the size of an effect.

Be careful with subgroup findings

A result for a subgroup—such as one age bracket, region, or customer type—uses fewer observations than the full sample and may have substantially greater uncertainty. Before comparing subgroup percentages, check each group’s denominator and uncertainty measure. Do not turn a difference based on a very small group into a firm conclusion, and make clear which subgroup a reported result describes. AAPOR discusses these cautions in its journalist’s guide to polls and surveys.

Compare studies on their methods, not just their headline numbers

What to compare What to check
Target population and coverage Whom each study intends to represent and who could enter its sampling frame.
Selection and recruitment Whether selection was probability-based or relied on volunteers or another non-probability method; how nonresponse was handled.
Measurement Question wording, answer options, survey mode, and timing.
Precision Completed sample size, design effects, the uncertainty measure, and its confidence level.
Subgroup support The number of observations and uncertainty behind each subgroup claim.
Transparency Whether methods and weighting are described well enough for an outside reader to assess them.

These comparisons are more informative than ranking studies by sample size alone. A study can have many respondents yet poor coverage or weak measurement; another can have fewer respondents but a design better suited to its stated population and question.

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Do not turn a descriptive result into a causal claim

A well-designed survey can estimate characteristics or opinions in a population, but a survey result alone may not establish why an outcome occurred. An association or a difference between groups is not automatically evidence that one factor caused another. Match the wording of a conclusion to what the study design can support, and state limitations that materially affect interpretation.

A quick check before trusting or repeating a claim

  1. Define the target: What exact population does the claim describe?
  2. Trace selection: How were people or units sampled and recruited?
  3. Check coverage and response: Who was excluded, unreachable, or nonresponsive?
  4. Inspect measurement: What were the exact questions, answer options, mode, and field dates?
  5. Verify uncertainty: Does the measure fit the design, and is it reported for the relevant subgroup?
  6. Consider remaining errors: Could inaccurate answers, processing, or analysis affect the result?
  7. Limit the conclusion: Does the claim stay within what the population, method, and evidence can establish?

If essential methods are not reported, say that the result cannot be fully evaluated from the available information rather than assuming the missing details.

Example: evaluating a change between two estimates

The ONS gives a historical example of the share of people aged 18 and over in the UK who were current smokers: 20.2% in 2011 and 14.7% in 2018. In its 2019 example, the ONS says a statistical significance test found the difference larger than would be expected if it were caused by random sampling alone. This illustrates why changes between sample estimates should be considered alongside uncertainty. Those figures are historical, not a current estimate of smoking prevalence, and the example is not a universal test of whether a sample is good.

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