Insensitivity to sample size is a

cognitive bias A cognitive bias is a systematic pattern of deviation from norm or rationality in judgment. Individuals create their own "subjective reality" from their perception of the input. An individual's construction of reality, not the objective input, m ...

that occurs when people judge the probability of obtaining a

sample statistic A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypo ...

without respect to the

sample size Sample size determination is the act of choosing the number of observations or Replication (statistics), replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make stat ...

. For example, in one study subjects assigned the same probability to the likelihood of obtaining a mean height of above six feet 83 cmin samples of 10, 100, and 1,000 men. In other words, variation is more likely in smaller samples, but people may not expect this. In another example,

Amos Tversky Amos Nathan Tversky ( he, עמוס טברסקי; March 16, 1937 – June 2, 1996) was an Israeli cognitive and mathematical psychologist and a key figure in the discovery of systematic human cognitive bias and handling of risk. Much of his ...

and

Daniel Kahneman Daniel Kahneman (; he, דניאל כהנמן; born March 5, 1934) is an Israeli-American psychologist and economist notable for his work on the psychology of judgment and decision-making, as well as behavioral economics, for which he was award ...

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). Relative neglect of sample size were obtained in a different study of statistically sophisticated psychologists. Tversky and Kahneman explained these results as being caused by the

representativeness heuristic The representativeness heuristic is used when making judgments about the probability of an event under uncertainty. It is one of a group of heuristics (simple rules governing judgment or decision-making) proposed by psychologists Amos Tversky and D ...

, according to 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 The clustering illusion is the tendency to erroneously consider the inevitable "streaks" or "clusters" arising in small samples from random distributions to be non-random. The illusion is caused by a human tendency to underpredict the amount of v ...

, in which people under-expect streaks or runs in small samples. Insensitivity to sample size is a subtype of

extension neglect __NOTOC__ Extension neglect is a type of cognitive bias which occurs when the sample size is ignored when its determination is relevant. For instance, when reading an article about a scientific study, extension neglect occurs when the reader igno ...

. To illustrate this point,

Howard Wainer Howard Wainer (born 1943) is an American statistician, past principal research scientist at the Educational Testing Service, adjunct professor of statistics at the Wharton School of the University of Pennsylvania, and author, known for his contri ...

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.{{Cite journal, issn = 0031-7217, volume = 88, issue = 4, pages = 300–303, last1 = Wainer, first1 = Howard, last2 = Zwerling, first2 = Harris L., title = Evidence That Smaller Schools Do Not Improve Student Achievement, journal = The Phi Delta Kappan, date = 2006, jstor = 20442243, doi = 10.1177/003172170608800411

References

Cognitive biases