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Sampling bias

Sampling bias is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Sampling bias rather than just read about it. In short: In statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. It results in a biased sample of a population (or non-human factors) in which all individuals, or instances, were not equally likely to have been selected.

Sampling bias — main illustration
Sampling bias — illustration

Key takeaways

  • Sampling bias belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Sampling bias to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Sampling bias from memory before moving on to harder problems.

Reference excerpt

In statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. It results in a biased sample of a population (or non-human factors) in which all individuals, or instances, were not equally likely to have been selected. If this is not accounted for, results can be erroneously attributed to the phenomenon under study rather than to the method of sampling. Medical sources sometimes refer to sampling bias as ascertainment bias. Ascertainment bias has basically the same definition, but is still sometimes classified as a separate type of bias.

Distinction from selection bias Sampling bias is usually classified as a subtype of selection bias, sometimes specifically termed sample selection bias, but some classify it as a separate type of bias. A distinction, albeit not universally accepted, of sampling bias is that it undermines the external validity of a test (the ability of its results to be generalized to the entire population), while selection bias mainly addresses internal validity for differences or similarities found in the sample at hand. In this sense, errors occurring in the process of gathering the sample or cohort cause sampling bias, while errors in any process thereafter cause selection bias. However, selection bias and sampling bias are often used synonymously.

Types Selection from a specific real area. For example, a survey of high school students to measure teenage use of illegal drugs will be a biased sample because it does not include home-schooled students or dropouts. A sample is also biased if certain members are underrepresented or overrepresented relative to others in the population. For example, a "man on the street" interview which selects people who walk by a certain location is going to have an overrepresentation of healthy individuals who are more likely to be out of the home than individuals with a chronic illness. This may be an extreme form of biased sampling, because certain members of the population are totally excluded from the sample (that is, they have zero probability of being selected). Self-selection bias (see also Non-response bias), which is possible whenever the group of people being studied has any form of control over whether to participate (as current standards of human-subject research ethics require for many real-time and some longitudinal forms of study). Participants' decision to participate may be correlated with traits that affect the study, making the participants a non-representative sample. For example, people who have strong opinions or substantial knowledge may be more willing to spend time answering a survey than those who do not. Another example is online and phone-in polls, which are biased samples because the respondents are self-selected. Those individuals who are highly motivated to respond, typically individuals who have strong opinions, are overrepresented, and individuals that are indifferent or apathetic are less likely to respond. This often leads to a polarization of responses with extreme perspectives being given a disproportionate weight in the summary. As a result, these types of polls are regarded as unscientific. Exclusion bias results from exclusion of particular groups from the sample, e.g. exclusion of subjects who have recently migrated into the study area (this may occur when newcomers are not available in a register used to identify the source population). Excluding subjects who move out of the study area during follow-up is rather equivalent of dropout or nonresponse, a selection bias in that it rather affects the internal validity of the study. Healthy user bias, when the study population is likely healthier than the general population. For example, someone in poor health is unlikely to have a job as manual laborer, so if a study is conducted on manual laborers, the health of the general population will likely be overestimated. Berkson's fallacy, when the study population is selected from a hospital and so is less healthy than the general population. This can result in a spurious negative correlation between diseases: a hospital patient without diabetes is more likely to have another given disease such as cholecystitis, since they must have had some reason to enter the hospital in the first place. Overmatching, matching for an apparent confounder that actually is a result of the exposure. The control group becomes more similar to the cases in regard to exposure than does the general population. Survivorship bias, in which only "surviving" subjects are selected, ignoring those that fell out of view. For example, using the record of current companies as an indicator of business climate or economy ignores the businesses that failed and no longer exist. Malmquist bias, an effect in observational astronomy which leads to the preferential detection of intrinsically bright objects.

Spotlight fallacy, the uncritical assumption that all members or cases of a certain class or type are like those that receive the most attention or coverage in the media.

Symptom-based sampling The study of medical conditions begins with anecdotal reports. By their nature, such reports only include those referred for diagnosis and treatment. A child who can't function in school is more likely to be diagnosed with dyslexia than a child who struggles but passes. A child examined for one condition is more likely to be tested for and diagnosed with other conditions, skewing comorbidity statistics. As certain diagnoses become associated with behavior problems or intellectual disability, parents try to prevent their children from being stigmatized with those diagnoses, introducing further bias. Studies carefully selected from whole populations are showing that many conditions are much more common and usually much milder than formerly believed.

… excerpt ends here. Continue reading the full article.

Illustrations

Sampling bias: An example of a biased sample in a hypothetical population survey, which asks if participants like responding to surveys, thus selecting for the individuals who were most likely to respond in the first place
An example of a biased sample in a hypothetical population survey, which asks if participants like responding to surveys, thus selecting for the individuals who were most likely to respond in the first place
Sampling bias: Simple pedigree example of sampling bias, showing the pedigrees of all the possible families with two children when the parents are carriers (Aa)
Simple pedigree example of sampling bias, showing the pedigrees of all the possible families with two children when the parents are carriers (Aa)
Sampling bias: Example of biased sample: as of June 2008 55% of web browsers (Internet Explorer) in use did not pass the Acid2 test. Due to the nature of the test, the sample consisted mostly of web developers.[16]
Example of biased sample: as of June 2008 55% of web browsers (Internet Explorer) in use did not pass the Acid2 test. Due to the nature of the test, the sample consisted mostly of web developers.[16]

Worked examples

Example 1 — a first encounter with Sampling bias

Start with the simplest possible case. Write down what Sampling bias claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Sampling bias before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Sampling bias ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Sampling bias

In research
Sampling bias appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Sampling bias in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Sampling bias is common in secondary-school and first-year university syllabi. It links to neighbouring topics Experimental bias, Misuse of statistics, Sampling (statistics), so understanding it makes those chapters shorter.
In everyday life
Look for Sampling bias outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Sampling bias in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Sampling bias means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Sampling bias out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Sampling bias in simple terms?

In statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. It results in a biased sample of a population (or non-human factors) in which all individuals, or instances, were…

Why does Sampling bias matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Sampling bias?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Sampling bias.

Tags

  • Experimental bias
  • Misuse of statistics
  • Sampling (statistics)

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