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Insensitivity to sample size is a cognitive bias that occurs when people judge the probability of obtaining a sample statistic without respect to 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.
Hasty generalization (fallacy of insufficient statistics, fallacy of insufficient sample, fallacy of the lonely fact, hasty induction, secundum quid, converse accident, jumping to conclusions) – basing a broad conclusion on a small or unrepresentative sample. [55]
Law of small numbers; Unrepresentative sample; Secundum quid; When referring to a generalization made from a single example, the terms fallacy of the lonely fact, [8] or the fallacy of proof by example, might be used. [9] When evidence is intentionally excluded to bias the result, the fallacy of exclusion—a form of selection bias—is said to ...
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] A classic example of a biased sample and the misleading results it produced occurred in 1936.
Poisson distribution, the use of that name for this distribution originated in the book The Law of Small Numbers; Hasty generalization, a logical fallacy also known as the law of small numbers The tendency for an initial segment of data to show some bias that drops out later, one example in number theory being Kummer's conjecture on cubic Gauss ...
In others, it is purposeful and for the gain of the perpetrator. When the statistical reason involved is false or misapplied, this constitutes a statistical fallacy. The consequences of such misinterpretations can be quite severe. For example, in medical science, correcting a falsehood may take decades and cost lives. Misuses can be easy to ...
A good example of this is a study showed that when making food choices for the coming week, 74% of participants chose fruit, whereas when the food choice was for the current day, 70% chose chocolate. Insensitivity to sample size, the tendency to under-expect variation in small samples.
[14] [15] It would have been incorrect, and an example of prosecutor's fallacy, to rely solely on the "1 in 400" figure to deduce that a given person matching the sample would be likely to be the culprit. Frequency tree of 100 000 battered American women showing the base rate fallacy made by the defense in the O. J. Simpson murder trial