science

Insensitivity to sample size

Insensitivity to sample size is a science 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 Insensitivity to sample size rather than just read about it. In short: Insensitivity to sample size is a cognitive bias where people estimate the probability of obtaining a sample statistic without considering the sample size. For example, in one study, subjects assigned the same probability to the likelihood of obtaining a mean height of above six feet [183 cm] in samples of 10, 100, and 1,000 men.

Key takeaways

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

Reference excerpt

Insensitivity to sample size is a cognitive bias where people estimate the probability of obtaining a sample statistic without considering the sample size. For example, in one study, subjects assigned the same probability to the likelihood of obtaining a mean height of above six feet [183 cm] in samples of 10, 100, and 1,000 men. In fact, variability is more likely in smaller samples, the law of small numbers, but people generally do not understand this. In another example, Amos Tversky and Daniel Kahneman asked subjects

A certain town is served by two hospitals. In the larger hospital about 45 babies are born each day, and in the smaller hospital about 15 babies are born each day. As you know, about 50% of all babies are boys. However, the exact percentage varies from day to day. Sometimes it may be higher than 50%, sometimes lower. For a period of 1 year, each hospital recorded the days on which more than 60% of the babies born were boys. Which hospital do you think recorded more such days?

The larger hospital The smaller hospital About the same (that is, within 5% of each other)

56% of subjects chose option 3, and 22% of subjects respectively chose options 1 or 2. However, according to sampling theory the larger hospital is much more likely to report a sex ratio close to 50% on a given day than the smaller hospital which requires that the correct answer to the question is the smaller hospital (see the law of large numbers). Even in a survey of psychologists with statistical training, most failed to consider sample size in their analyses. Tversky and Kahneman explained these results as examples of the representativeness heuristic: which people intuitively judge samples as having similar properties to their population, without taking other considerations into effect. A related bias is the clustering illusion, in which people under-expect streaks or runs in small samples. Insensitivity to sample size is a subtype of extension neglect. To illustrate this point, Howard Wainer and Harris L. Zwerling demonstrated that kidney cancer rates are lowest in counties that are mostly rural, sparsely populated, and located in traditionally Republican states in the Midwest, the South, and the West, but that they are also highest in counties that are mostly rural, sparsely populated, and located in traditionally Republican states in the Midwest, the South, and the West. While various environmental and economic reasons could be advanced for these facts, Wainer and Zwerlig argue that this is an artifact of sample size. Because of the small sample size, the incidence of a certain kind of cancer in small rural counties is more likely to be further from the mean, in one direction or another, than the incidence of the same kind of cancer in much more heavily populated urban counties.

References

Worked examples

Example 1 — a first encounter with Insensitivity to sample size

Start with the simplest possible case. Write down what Insensitivity to sample size claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 Insensitivity to sample size 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 Insensitivity to sample size 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 Insensitivity to sample size

In research: Insensitivity to sample size appears in science 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 Insensitivity to sample size 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: Insensitivity to sample size is common in secondary-school and first-year university syllabi. It links to neighbouring topics Cognitive biases, so understanding it makes those chapters shorter.
In everyday life: Look for Insensitivity to sample size 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.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Insensitivity to sample size in 20 minutes

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

Frequently asked questions

What is Insensitivity to sample size in simple terms?

Why does Insensitivity to sample size matter?

Because it connects several science 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 Insensitivity to sample size?

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 Insensitivity to sample size.