Base rate fallacy - Knowledge

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that the inhabitant is a non-terrorist given the bell rings) are unrelated quantities; one does not necessarily equal—or even be close to—the other. To show this, consider what happens if an identical alarm system were set up in a second city with no terrorists at all. As in the first city, the alarm sounds for 1 out of every 100 non-terrorist inhabitants detected, but unlike in the first city, the alarm never sounds for a terrorist. Therefore, 100% of all occasions of the alarm sounding are for non-terrorists, but a false negative rate cannot even be calculated. The 'number of non-terrorists per 100 bells' in that city is 100, yet P(T | B) = 0%. There is zero chance that a terrorist has been detected given the ringing of the bell.

168:). For example, if a facial recognition camera can identify wanted criminals 99% accurately, but analyzes 10,000 people a day, the high accuracy is outweighed by the number of tests, and the program's list of criminals will likely have far more false positives than true. The probability of a positive test result is determined not only by the accuracy of the test but also by the characteristics of the sampled population. When the prevalence, the proportion of those who have a given condition, is lower than the test's 89: 1541: 1493:(that is, prior to the blood test) that he is a random innocent person. Assume, for instance, that 1000 people live in the town where the crime occurred. This means that 100 people live there who have the perpetrator's blood type, of whom only one is the true perpetrator; therefore, the true probability that the defendant is guilty – based only on the fact that his blood type matches that of the killer – is only 1%, far less than the 90% argued by the prosecutor. 124:) in favor of the individuating information (i.e., information pertaining only to a specific case). For example, if someone hears that a friend is very shy and quiet, they might think the friend is more likely to be a librarian than a salesperson, even though there are far more salespeople than librarians overall - hence making it more likely that their friend is actually a salesperson. Base rate neglect is a specific form of the more general 1966:(drunk). Importantly, although this equation is formally equivalent to Bayes' rule, it is not psychologically equivalent. Using natural frequencies simplifies the inference because the required mathematical operation can be performed on natural numbers, instead of normalized fractions (i.e., probabilities), because it makes the high number of false positives more transparent, and because natural frequencies exhibit a "nested-set structure". 1752: 1 out of 1000 drivers are driving drunk. The breathalyzers never fail to detect a truly drunk person. For 50 out of the 999 drivers who are not drunk the breathalyzer falsely displays drunkenness. Suppose the policemen then stop a driver at random, and force them to take a breathalyzer test. It indicates that they are drunk. No other information is known about them. Estimate the probability the driver is really drunk. 5482: 1693:(GPAs) of hypothetical students. When given relevant statistics about GPA distribution, students tended to ignore them if given descriptive information about the particular student even if the new descriptive information was obviously of little or no relevance to school performance. This finding has been used to argue that interviews are an unnecessary part of the 36: 1466:

of accuracy required to make these models viable is likely unachievable. Foremost, the low base rate of terrorism also means there is a lack of data with which to make an accurate algorithm. Further, in the context of detecting terrorism false negatives are highly undesirable and thus must be minimised as much as possible; however, this requires

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safely disregard the possibility that this defendant is innocent, correct?" The claim assumes that the probability that evidence is found on an innocent man is the same as the probability that a man is innocent given that evidence was found on him, which is not true. Whilst the former is usually small (10% in the previous example) due to good

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There is considerable debate in psychology on the conditions under which people do or do not appreciate base rate information. Researchers in the heuristics-and-biases program have stressed empirical findings showing that people tend to ignore base rates and make inferences that violate certain norms

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and predictive algorithms to identify terrorists cannot feasibly work due to the false positive paradox. Estimates of the number of false positives for each accurate result vary from over ten thousand to one billion; consequently, investigating each lead would be cost- and time-prohibitive. The level

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Suppose now that an inhabitant triggers the alarm. Someone making the base rate fallacy would infer that there is a 99% probability that the detected person is a terrorist. Although the inference seems to make sense, it is actually bad reasoning, and a calculation below will show that the probability

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displaying false drunkenness in 5% of the cases in which the driver is sober. However, the breathalyzers never fail to detect a truly drunk person. One in a thousand drivers is driving drunk. Suppose the police officers then stop a driver at random to administer a breathalyzer test. It indicates that

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It is unclear whether an estimate of the probability for the second possibility was ever proposed during the trial, or whether the comparison of the first two probabilities was understood to be the key estimate to make in the statistical analysis assessing the prosecution's case against the case for

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In the same trial, the prosecution presented evidence that Simpson had been violent toward his wife. The defense argued that there was only one woman murdered for every 2500 women who were subjected to spousal abuse, and that any history of Simpson being violent toward his wife was irrelevant to the

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If the exposure to COVID-19 stays the same, as more individuals are vaccinated, more cases, hospitalizations, and deaths will be in vaccinated individuals, as they will continue to make up more and more of the population. For example, if 100% of the population was vaccinated, 100% of cases would be

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The prosecutor's fallacy involves assuming that the prior probability of a random match is equal to the probability that the defendant is innocent. When using it, a prosecutor questioning an expert witness may ask: "The odds of finding this evidence on an innocent man are so small that the jury can

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The fallacy arises from confusing the natures of two different failure rates. The 'number of non-bells per 100 terrorists' (P(¬B | T), or the probability that the bell fails to ring given the inhabitant is a terrorist) and the 'number of non-terrorists per 100 bells' (P(¬T | B), or the probability

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In a city of 1 million inhabitants, let there be 100 terrorists and 999,900 non-terrorists. To simplify the example, it is assumed that all people present in the city are inhabitants. Thus, the base rate probability of a randomly selected inhabitant of the city being a terrorist is 0.0001, and the

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The validity of this result does, however, hinge on the validity of the initial assumption that the police officer stopped the driver truly at random, and not because of bad driving. If that or another non-arbitrary reason for stopping the driver was present, then the calculation also involves the

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The population-wide probability of a SIDS fatality was about 1 in 1,303; Meadow generated his 1-in-73 million estimate from the lesser probability of SIDS death in the Clark household, which had lower risk factors (e.g. non-smoking). In this sub-population he estimated the probability of a single

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Crime scene blood matched Simpson's with characteristics shared by 1 in 400 people. However, the defense argued that the number of people from Los Angeles matching the sample could fill a football stadium and that the figure of 1 in 400 was useless. It would have been incorrect, and an example of

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Society does not tolerate doctors making serious clinical errors because it is widely understood that such errors could mean the difference between life and death. The case of R v. Sally Clark is one example of a medical expert witness making a serious statistical error, one which may have had a

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recommend using this kind of format for communicating health statistics. Teaching people to translate these kinds of Bayesian reasoning problems into natural frequency formats is more effective than merely teaching them to plug probabilities (or percentages) into Bayes' theorem. It has also been

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when applied to the results of statistical tests (such as DNA tests) in the context of law proceedings. These terms were introduced by William C. Thompson and Edward Schumann in 1987, although it has been argued that their definition of the prosecutor's fallacy extends to many additional invalid

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killed (by someone). Gigerenzer writes "the chances that a batterer actually murdered his partner, given that she has been killed, is about 8 in 9 or approximately 90%". While most cases of spousal abuse do not end in murder, most cases of murder where there is a history of spousal abuse were

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Consider again Example 2 from above. The required inference is to estimate the (posterior) probability that a (randomly picked) driver is drunk, given that the breathalyzer test is positive. Formally, this probability can be calculated using Bayes' theorem, as shown above. However, there are

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Imagine that the first city's entire population of one million people pass in front of the camera. About 99 of the 100 terrorists will trigger the alarm—and so will about 9,999 of the 999,900 non-terrorists. Therefore, about 10,098 people will trigger the alarm, among which about 99 will be

1744:. The conclusion drawn from this line of research was that human probabilistic thinking is fundamentally flawed and error-prone. Other researchers have emphasized the link between cognitive processes and information formats, arguing that such conclusions are not generally warranted. 1985:(drunk | positive test) from comparing the number of drivers who are drunk and test positive compared to the total number of people who get a positive breathalyzer result, because base rate information is not preserved and must be explicitly re-introduced using Bayes' theorem. 1457:

The base rate fallacy is so misleading in this example because there are many more non-terrorists than terrorists, and the number of false positives (non-terrorists scanned as terrorists) is so much larger than the true positives (terrorists scanned as terrorists).

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One important reason why natural frequency formats are helpful is that this information format facilitates the required inference because it simplifies the necessary calculations. This can be seen when using an alternative way of computing the required probability

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it is patently unfair to use the characteristics which basically make her a good, clean-living, mother as factors which count against her. Yes, we can agree that such factors make a natural death less likely – but those same characteristics also make murder less

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Meadow acknowledged that 1-in-73 million is not an impossibility, but argued that such accidents would happen "once every hundred years" and that, in a country of 15 million 2-child families, it is vastly more likely that the double-deaths are due to

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However, this conclusion is only close to correct if the defendant was selected as the main suspect based on robust evidence discovered prior to the blood test and unrelated to it. Otherwise, the reasoning presented is flawed, as it overlooks the high

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The 1-in-73 million figure greatly underestimated the chance of two successive accidents, but even if that assessment were accurate, the court seems to have missed the fact that the 1-in-73 million number meant nothing on its own. As an

1413: 2648:, excluding those factors that increased risk (especially that both children were boys) and (more importantly) because reductions in SIDS risk factors will proportionately reduce murder risk factors, so that the relative frequencies of 1780:). Empirical studies show that people's inferences correspond more closely to Bayes' rule when information is presented this way, helping to overcome base-rate neglect in laypeople and experts. As a consequence, organizations like the 1716:. They argued that many judgments relating to likelihood, or to cause and effect, are based on how representative one thing is of another, or of a category. Kahneman considers base rate neglect to be a specific form of 1600:

than to such a rare accident. However, there is good reason to suppose that the likelihood of a death from SIDS in a family is significantly greater if a previous child has already died in these circumstances, (a

1328: 1664:) attempted to accurately compare the chances of these two possible explanations; he concluded that successive accidents are between 4.5 and 9 times more likely than are successive murders, so that the 1482:

A crime is committed. Forensic analysis determines that the perpetrator has a certain blood type shared by 10% of the population. A suspect is arrested, and found to have that same blood type.

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base rate probability of that same inhabitant being a non-terrorist is 0.9999. In an attempt to catch the terrorists, the city installs an alarm system with a surveillance camera and automatic

1080: 1023: 1942:) denotes the total number of cases with a positive breathalyzer result. The equivalence of this equation to the above one follows from the axioms of probability theory, according to which 1454:

terrorists. The probability that a person triggering the alarm actually is a terrorist is only about 99 in 10,098, which is less than 1% and very, very far below the initial guess of 99%.

964: 911: 1103: 709: 529:, only 20 of the 69 total people with a positive test result are actually infected. So, the probability of actually being infected after one is told that one is infected is only 29% ( 646: 2286:

MESSAGE: False positive tests are more probable than true positive tests when the overall population has a low prevalence of the disease. This is called the false-positive paradox.

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are instances of the base rate fallacy: people do not use the "consensus information" (the "base rate") about how others behaved in similar situations and instead prefer simpler

1803: 1556:, the correct probability requires additional context: Simpson's wife had not only been subjected to domestic violence, but rather subjected to domestic violence (by Simpson) 724: 4371: 3185:

Cosmides, Leda; John Tooby (1996). "Are humans good intuitive statisticians after all? Rethinking some conclusions of the literature on judgment under uncertainty".

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Nisbett, Richard E.; E. Borgida; R. Crandall; H. Reed (1976). "Popular induction: Information is not always informative". In J. S. Carroll & J. W. Payne (ed.).

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Thompson, W.C.; Schumann, E.L. (1987). "Interpretation of Statistical Evidence in Criminal Trials: The Prosecutor's Fallacy and the Defense Attorney's Fallacy".

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procedures, the latter (99% in that example) does not directly relate to it and will often be much higher, since, in fact, it depends on the likely quite high

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after having dealt with positive results drawn from a high-prevalence population. If the false positive rate of the test is higher than the proportion of the

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patients than unvaccinated ones might suggest that the vaccine is ineffective, but such an imbalance is to be expected within a highly vaccinated population.

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Hoffrage, U.; Gigerenzer, G.; Krauss, S.; Martignon, L. (2002). "Representation facilitates reasoning: What natural frequencies are and what they are not".

1572:, a British woman, was accused in 1998 of having killed her first child at 11 weeks of age and then her second child at 8 weeks of age. The prosecution had 3331:

Akl, E. A.; Oxman, A. D.; Herrin, J.; Vist, G. E.; Terrenato, I.; Sperati, F.; Costiniuk, C.; Blank, D.; Schünemann, H. (2011). Schünemann, Holger (ed.).

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A prosecutor might charge the suspect with the crime on that basis alone, and claim at trial that the probability that the defendant is guilty is 90%.

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shown that graphical representations of natural frequencies (e.g., icon arrays, hypothetical outcome plots) help people to make better inferences.

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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.

4376: 2230: 659:. The goal is to find the probability that the driver is drunk given that the breathalyzer indicated they are drunk, which can be represented as 57: 44: 3726: 4982: 1631:

probabilities of the alternatives. Given that two deaths had occurred, one of the following explanations must be true, and all of them are

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population with the condition, then a test administrator whose experience has been drawn from testing in a high-prevalence population may

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Girotto, V.; Gonzalez, M. (2001). "Solving probabilistic and statistical problems: A matter of information structure and question form".

2775: 1973:, which preserves base rate information (e.g., number of drunken drivers when taking a random sample of drivers). This is different from 1262: 4639: 4481: 2802:

The uncertainty in this range is mainly driven by uncertainty in the likelihood of killing a second child, having killed a first, see:

2416: 2674: 1588: – Meadow estimated it from single-SIDS death data, and the assumption that the probability of such deaths should be 195:

that a positive test result usually indicates a positive subject, when in fact a false positive is far more likely to have occurred.

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The false positive rate: If the camera scans a non-terrorist, a bell will not ring 99% of the time, but it will ring 1% of the time.

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The false negative rate: If the camera scans a terrorist, a bell will ring 99% of the time, and it will fail to ring 1% of the time.

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of 1,000 persons, of which 40% are infected. The test has a false positive rate of 5% (0.05) and a false negative rate of zero. The

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In experiments, people have been found to prefer individuating information over general information when the former is available.

3773: 2005: 1470:, increasing false positives. It is also questionable whether the use of such models by law enforcement would meet the requisite 1969:

Not every frequency format facilitates Bayesian reasoning. Natural frequencies refer to frequency information that results from

4366: 4176: 2649: 1597: 5526: 5521: 4295: 2644:. Professor Ray Hill questioned even this first step (1/8,500 vs 1/1,300) in two ways: firstly, on the grounds that it was 1748:

different ways of presenting the relevant information. Consider the following, formally equivalent variant of the problem:

5401: 4609: 4181: 3835: 1729: 3830: 5506: 5437: 5413: 5002: 2231:"Ambiguity, the Certainty Illusion, and Gigerenzer's Natural Frequency Approach to Reasoning with Inverse Probabilities" 1713: 2081: 1580:, a professor and consultant paediatrician, testify that the probability of two children in the same family dying from 5516: 5014: 4758: 3953: 2655: 2593: 1467: 1428: 614:

Therefore, the probability that any given driver among the 1 + 49.95 = 50.95 positive test results really is drunk is

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Many would estimate the probability that the driver is drunk as high as 95%, but the correct probability is about 2%.

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Koehler, J. J. (2010). "The base rate fallacy reconsidered: Descriptive, normative, and methodological challenges".

2315:, the more likely a student identified as a user will be a non-user. This has been called the False Positive Paradox 5024: 4289: 3815: 1545: 1533:

was tried and acquitted in 1995 for the murders of his ex-wife Nicole Brown Simpson and her friend Ronald Goldman.

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Hoffrage, U.; Lindsey, S.; Hertwig, R.; Gigerenzer, G. (2000). "Medicine: Communicating Statistical Information".

1246:{\displaystyle p(D)=p(D\mid \mathrm {drunk} )\,p(\mathrm {drunk} )+p(D\mid \mathrm {sober} )\,p(\mathrm {sober} )} 5511: 5432: 4989: 4885: 4419: 4143: 3943: 3233:

Gigerenzer, G.; Hoffrage, U. (1995). "How to improve Bayesian reasoning without instruction: Frequency formats".

1733: 1654: 3670:"Overcoming difficulties in Bayesian reasoning: A reply to Lewis and Keren (1999) and Mellers and McGraw (1999)" 917: 864: 556:, a result that had usually correctly indicated infection is now usually a false positive. The confusion of the 5427: 5267: 4735: 4571: 4527: 4448: 4443: 4356: 4238: 4003: 3983: 3879: 2237: 2019: 1606: 1094: 665: 3006:

Kahneman, Daniel (2000). "Evaluation by moments, past and future". In Daniel Kahneman and Amos Tversky (ed.).

2055: – cognitive phenomenon where organisms use data to make generalizations and predictions about the world 617: 5447: 5262: 4778: 4474: 1981:(e.g., in scientific experiments). In the latter case it is not possible to infer the posterior probability 1777: 184: 2302: 5369: 5359: 5309: 5283: 5059: 4933: 4900: 4801: 4783: 4683: 4532: 4514: 4429: 4113: 4093: 3874: 3852: 3242: 3194: 1916:{\displaystyle p(\mathrm {drunk} \mid D)={\frac {N(\mathrm {drunk} \cap D)}{N(D)}}={\frac {1}{51}}=0.0196} 1781: 1602: 3091:

Barbey, A. K.; Sloman, S. A. (2007). "Base-rate respect: From ecological rationality to dual processes".

848:{\displaystyle p(\mathrm {drunk} \mid D)={\frac {p(D\mid \mathrm {drunk} )\,p(\mathrm {drunk} )}{p(D)}}.} 5407: 5395: 5375: 5364: 5279: 5092: 5068: 4890: 4846: 4698: 4624: 4537: 4208: 4123: 4098: 4043: 1661: 1471: 557: 2251:

Suss, Richard A. (October 4, 2023). "The Prosecutor's Fallacy Framed as a Sample Space Substitution".

5422: 5326: 5290: 5205: 5161: 4997: 4928: 4718: 4547: 4522: 4161: 4013: 3889: 3766: 3143: 2964: 2882: 2514: 2052: 2046: 2031: 1994: 1776:| sober)—is presented in terms of natural frequencies with respect to a certain reference class (see 1675: 183:

It is especially counter-intuitive when interpreting a positive result in a test on a low-prevalence

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process because interviewers are unable to pick successful candidates better than basic statistics.

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Tversky, Amos; Kahneman, Daniel (1974-09-27). "Judgment under uncertainty: Heuristics and biases".

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trial. However, the reasoning behind the defense's calculation was fallacious. According to author

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probability of a drunk driver driving competently and a non-drunk driver driving (in-)competently.

169: 88: 2594:"Resolution adopted by the Senate (21 October 1998) on the retirement of Professor Sir Roy Meadow" 1540: 5485: 5418: 5232: 5117: 5102: 5049: 5009: 4958: 4895: 4854: 4831: 4811: 4714: 4558: 4542: 4467: 4213: 4198: 3958: 3948: 3931: 3650: 3604: 3561: 3533: 3457: 3422: 3313: 3260: 3212: 3167: 3116: 3073: 2988: 2937: 2684: 2481: 2303:"Quantitative literacy - drug testing, cancer screening, and the identification of igneous rocks" 2211: 2203: 2040: 2010: 1725: 1610: 141: 3525: 2782: 5304: 5141: 5131: 5107: 5084: 5040: 4966: 4918: 4836: 4678: 4673: 4495: 4326: 4263: 4248: 4171: 4153: 4088: 3884: 3800: 3722: 3642: 3596: 3551: 3506: 3414: 3362: 3305: 3159: 3108: 3036: 3011: 2980: 2828: 2743: 2540: 2473: 2386: 2147: 2025: 1741: 1717: 1694: 1674:

After the court found that the forensic pathologist who had examined both babies had withheld

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Multiple practitioners have argued that as the base rate of terrorism is extremely low, using

1408:{\displaystyle p(\mathrm {drunk} \mid D)={\frac {1.00\times 0.001}{0.05095}}\approx 0.019627,} 656: 561: 125: 2526: 2339: 5454: 5295: 5194: 5136: 5074: 4869: 4748: 4743: 4728: 4693: 4653: 4581: 4576: 4393: 4253: 4193: 4118: 4103: 3963: 3916: 3825: 3820: 3805: 3714: 3689: 3681: 3634: 3588: 3543: 3496: 3488: 3449: 3404: 3396: 3352: 3344: 3295: 3287: 3252: 3204: 3151: 3100: 3065: 2972: 2929: 2897: 2820: 2735: 2530: 2522: 2465: 2351: 2256: 2195: 2137: 2129: 1934:) denotes the number of drivers that are drunk and get a positive breathalyzer result, and 5175: 5151: 4971: 4943: 4923: 4771: 4739: 4723: 4361: 4351: 4128: 4108: 4023: 3926: 3901: 3896: 3869: 3847: 3759: 3694: 3409: 3300: 2878: 2860: 1721: 1701: 1553: 1544:

Frequency tree of 100 000 battered American women showing the prosecutor's fallacy in the

5211: 4688: 2340:"100,000 false positives for every real terrorist: Why anti-terror algorithms don't work" 3147: 2968: 2836: 2751: 2518: 5112: 5097: 5019: 4938: 4864: 4504: 4403: 4398: 4388: 4311: 4228: 4188: 4138: 4083: 4073: 4058: 4053: 4018: 3973: 3938: 3842: 3791: 3501: 3476: 3357: 3332: 3134:

Tversky, A.; Kahneman, D. (1974). "Judgment under Uncertainty: Heuristics and Biases".

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Gigerenzer, G., Reckoning with Risk: Learning to Live with Uncertainty, Penguin, (2003)

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is about 1 in 73 million. That was much less frequent than the actual rate measured in

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means that the breathalyzer indicates that the driver is drunk. Using Bayes's theorem,

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by squaring the likelihood of a single such death in all otherwise similar families.

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imputations of guilt or liability that are not analyzable as errors in base rates or

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An explanation for this is as follows: on average, for every 1,000 drivers tested,

577: 3291: 3155: 2976: 2469: 465:, of which only 2% are infected. The expected outcome of 1000 tests on population 3718: 2117: 17: 5442: 5219: 5156: 4218: 3988: 3978: 3968: 3864: 3685: 3400: 3333:"Using alternative statistical formats for presenting risks and risk reductions" 3256: 2629: 2453: 2133: 1609:) making some families more susceptible to SIDS and the error an outcome of the 1569: 1462: 1093:) for Bayes' theorem, which can be computed from the preceding values using the 5352: 5346: 5273: 5185: 4336: 4331: 4306: 3524:

Kim, Yea-Seul; Walls, Logan A.; Krafft, Peter; Hullman, Jessica (2 May 2019).

3104: 3069: 2275: 1577: 1502: 121: 3492: 2477: 2390: 2151: 2022: – Systematic patterns of deviation from norm or rationality in judgment 655:

More formally, the same probability of roughly 0.02 can be established using

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Proceedings of the 2019 CHI Conference on Human Factors in Computing Systems

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Kleiter, G. D. (1994). "Natural Sampling: Rationality without Base Rates".

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Brase, G. L. (2009). "Pictorial representations in statistical reasoning".

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At first glance, this seems perverse: the less the students as a whole use

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Kahneman, Daniel; Amos Tversky (1973). "On the psychology of prediction".

2776:"Royal Statistical Society concerned by issues raised in Sally Clark case" 2356: 591:

1 driver is drunk, and it is 100% certain that for that driver there is a

5337: 4383: 4268: 2312: 1623: 1613:. The likelihood of two SIDS deaths in the same family cannot be soundly 93: 3711:

Contributions to Mathematical Psychology, Psychometrics, and Methodology

4491: 2207: 2199: 1678:, a higher court later quashed Clark's conviction, on 29 January 2003. 565: 113: 3035:. Vol. 2. John Wiley & Sons, Incorporated. pp. 227–236. 2559:

Interpreting evidence: Evaluating forensic evidence in the courtroom.

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test results than true positives (this means the classifier has a low

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and SIDS will remain in the same ratio as in the general population:

2806:"Multiple sudden infant deaths – coincidence or beyond coincidence?" 2721:"Multiple sudden infant deaths – coincidence or beyond coincidence?" 2082:"COVID-19 Cases, Hospitalizations, and Deaths by Vaccination Status" 27:

Error in thinking which involves under-valuing base rate information

3538: 3477:"Explaining risks: Turning numerical data into meaningful pictures" 1323:{\displaystyle p(D)=(1.00\times 0.001)+(0.05\times 0.999)=0.05095.} 1539: 363:, a person receiving a positive test could be over 93% confident ( 172:, even tests that have a very low risk of giving a false positive 87: 1653:

Clark was convicted in 1999, resulting in a press release by the

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Other possibilities (including one homicide and one case of SIDS)

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999 drivers are not drunk, and among those drivers there are 5%

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the driver is drunk. No other information is known about them.

29: 3526:"A Bayesian Cognition Approach to Improve Data Visualization" 3384: 2118:"Seeing is believing: Priors, trust, and base rate neglect" 1671:

of Clark's guilt were between 4.5 to 1 and 9 to 1 against.

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Plugging these numbers into Bayes' theorem, one finds that

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Imagine running an infectious disease test on a population

160:). This paradox describes situations where there are more 3669: 3378: 3376: 2861:"R v Clark. [2003] EWCA Crim 1020 (11 April 2003)" 2499:

Fenton, Norman; Neil, Martin; Berger, Daniel (June 2016).

545:) for a test that otherwise appears to be "95% accurate". 3751: 3228: 3226: 1689:

In some experiments, students were asked to estimate the

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given that over 99% of results would be false positives.

2454:"The Implication of Terrorism's Extremely Low Base Rate" 2036:

Pages displaying short descriptions of redirect targets

2015:

Pages displaying short descriptions of redirect targets

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Uninfected and test indicates disease (false positive)

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Uninfected and test indicates disease (false positive)

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Two successive deaths in the same family, both by SIDS

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The following information is known in this scenario:

2675:"Gene find casts doubt on double 'cot death' murders" 2087:. Washington State Department of Health. 2023-01-18. 1806: 1627:

probability, it should have been weighed against the

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Organizational Behavior and Human Decision Processes

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Pages displaying wikidata descriptions as a fallback

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Infected and test indicates disease (true positive)

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Probability and Statistics in Aerospace Engineering

2049: – Error in statistical reasoning with groups 1915: 1446:of a terrorist is actually near 1%, not near 99%. 1407: 1322: 1245: 1074: 1017: 958: 905: 847: 703: 640: 568:after receiving a health-threatening test result. 1756:In this case, the relevant numerical information— 1505:of the defendant being a random innocent person. 1468:increasing sensitivity at the cost of specificity 516:× 0.05 = 49 people would receive a false positive 461:Now consider the same test applied to population 350:× 0.05 = 30 people would receive a false positive 2883:"The base-rate fallacy in probability judgments" 1708:attempted to explain this finding in terms of a 3620: 3618: 2506:Annual Review of Statistics and Its Application 2274:Rheinfurth, M. H.; Howell, L. W. (March 1998). 2229:Fountain, John; Gunby, Philip (February 2010). 1075:{\displaystyle p(D\mid \mathrm {sober} )=0.05.} 1018:{\displaystyle p(D\mid \mathrm {drunk} )=1.00,} 521:The remaining 931 tests are correctly negative. 355:The remaining 570 tests are correctly negative. 4600:Affirmative conclusion from a negative premise 2116:Welsh, Matthew B.; Navarro, Daniel J. (2012). 2034: – Evidence relying on personal testimony 1660:In 2002, Ray Hill (a mathematics professor at 4605:Negative conclusion from affirmative premises 4475: 3767: 1605:to SIDS is likely to invalidate that assumed 576:Imagine that a group of police officers have 8: 2557:Robertson, B., & Vignaux, G. A. (1995). 3475:Edwards, A.; Elwyn, G.; Mulley, A. (2002). 3389:Journal of Experimental Psychology: General 3337:The Cochrane Database of Systematic Reviews 1085:As can be seen from the formula, one needs 564:of receiving a false positive is a natural 152:An example of the base rate fallacy is the 5333: 5180: 5055: 4658: 4509: 4482: 4468: 4460: 4430:Heuristics in judgment and decision-making 3774: 3760: 3752: 2791:profound effect on the outcome of the case 2673:Sweeney, John; Law, Bill (July 15, 2001). 1478:Example 4: biological testing of a suspect 1434:The software has two failure rates of 1%: 959:{\displaystyle p(\mathrm {sober} )=0.999,} 906:{\displaystyle p(\mathrm {drunk} )=0.001,} 606:positive test results, so there are 49.95 386: 326:= 400 people would receive a true positive 212: 3693: 3537: 3500: 3408: 3356: 3299: 3246: 3198: 2534: 2355: 2338:Munk, Timme Bisgaard (1 September 2017). 2141: 1897: 1851: 1842: 1813: 1805: 1378: 1349: 1341: 1264: 1223: 1216: 1196: 1161: 1154: 1134: 1105: 1046: 1032: 986: 972: 927: 919: 874: 866: 805: 798: 778: 763: 734: 726: 704:{\displaystyle p(\mathrm {drunk} \mid D)} 675: 667: 624: 619: 492:= 20 people would receive a true positive 379:) that it correctly indicates infection. 176:will give more false than true positives 76:Learn how and when to remove this message 2527:10.1146/annurev-statistics-041715-033428 2296: 2294: 2166:"Logical Fallacy: The Base Rate Fallacy" 1642:Double homicide (the prosecution's case) 2415:Jonas, Jeff; Harper, Jim (2006-12-11). 2324:. New York: Harper Collins. p. 49. 2073: 641:{\displaystyle 1/50.95\approx 0.019627} 3383:Sedlmeier, P.; Gigerenzer, G. (2001). 2915: 2913: 2911: 552:might find it a paradox that in group 3668:Gigerenzer, G.; Hoffrage, U. (1999). 2813:Paediatric and Perinatal Epidemiology 2728:Paediatric and Perinatal Epidemiology 2574:CRC Press Taylor & Francis Group. 2444: 2442: 2440: 2438: 2410: 2408: 2406: 2369: 2367: 303:Infected and test indicates disease ( 92:A hospital receiving more vaccinated 7: 2333: 2331: 1740:of probabilistic reasoning, such as 1418:which is the precision of the test. 595:positive test result, so there is 1 2379:"Why Data Mining Won't Stop Terror" 2013: – Method of logical reasoning 1422:Example 3: Terrorist identification 116:in which people tend to ignore the 3099:(3): 241–254, discussion 255–297. 2604:. 30 November 1998. Archived from 1864: 1861: 1858: 1855: 1852: 1826: 1823: 1820: 1817: 1814: 1362: 1359: 1356: 1353: 1350: 1236: 1233: 1230: 1227: 1224: 1209: 1206: 1203: 1200: 1197: 1174: 1171: 1168: 1165: 1162: 1147: 1144: 1141: 1138: 1135: 1059: 1056: 1053: 1050: 1047: 999: 996: 993: 990: 987: 940: 937: 934: 931: 928: 887: 884: 881: 878: 875: 818: 815: 812: 809: 806: 791: 788: 785: 782: 779: 747: 744: 741: 738: 735: 688: 685: 682: 679: 676: 548:A tester with experience of group 25: 2781:. 23 October 2001. Archived from 2572:Criminal Investigative Failures. 2043: – Situation in epidemiology 295:of the 1,000 tests on population 5481: 5480: 2825:10.1111/j.1365-3016.2004.00560.x 2740:10.1111/j.1365-3016.2004.00560.x 2561:Chichester: John Wiley and Sons. 2458:Terrorism and Political Violence 1977:, in which base rates are fixed 1657:which pointed out the mistakes. 34: 2322:The cartoon guide to statistics 2307:Journal of Geoscience Education 2094:from the original on 2023-01-26 2002: – Misuse of data analysis 4978:Correlation implies causation 3695:11858/00-001M-0000-0025-9CB4-8 3410:11858/00-001M-0000-0025-9504-E 3349:10.1002/14651858.CD006776.pub2 3301:11858/00-001M-0000-0025-9B18-3 2320:Gonick, L.; Smith, W. (1993). 1888: 1882: 1874: 1848: 1836: 1810: 1372: 1346: 1311: 1299: 1293: 1281: 1275: 1269: 1240: 1220: 1213: 1187: 1178: 1158: 1151: 1125: 1116: 1110: 1063: 1037: 1003: 977: 944: 924: 891: 871: 836: 830: 822: 802: 795: 769: 757: 731: 698: 672: 1: 3639:10.1016/S0010-0277(02)00050-1 3593:10.1016/S0010-0277(00)00133-5 3292:10.1126/science.290.5500.2261 3156:10.1126/science.185.4157.1124 3093:Behavioral and Brain Sciences 3058:Behavioral and Brain Sciences 3033:Cognition and social behavior 2977:10.1126/science.185.4157.1124 2470:10.1080/09546553.2021.1880226 2006:Evidence under Bayes' theorem 1730:fundamental attribution error 3719:10.1007/978-1-4612-4308-3_27 3442:Applied Cognitive Psychology 3209:10.1016/0010-0277(95)00664-8 2902:10.1016/0001-6918(80)90046-3 2650:Münchausen syndrome by proxy 2628:Joyce, H. (September 2002). 1598:Münchausen syndrome by proxy 4296:Déformation professionnelle 3686:10.1037/0033-295X.106.2.425 3401:10.1037/0096-3445.130.3.380 3257:10.1037/0033-295X.102.4.684 2134:10.1016/j.obhdp.2012.04.001 1429:facial recognition software 5543: 5402:I'm entitled to my opinion 4290:Basking in reflected glory 3008:Choices, Values and Frames 2700:"Convicted on Statistics?" 2626:death at 1 in 8,500. See: 2301:Vacher, H. L. (May 2003). 1734:dispositional attributions 1710:simple rule or "heuristic" 1546:O. J. Simpson murder trial 1526:O. J. Simpson murder trial 1523: 1512: 209:High-prevalence population 137:defense attorney's fallacy 5476: 5385: 5258: 4438: 4420:Cognitive bias mitigation 3105:10.1017/S0140525X07001653 3070:10.1017/S0140525X00041157 2630:"Beyond reasonable doubt" 1655:Royal Statistical Society 1561:committed by the spouse. 383:Low-prevalence population 5428:Motte-and-bailey fallacy 4528:Affirming the consequent 4004:Illusion of transparency 3493:10.1136/bmj.324.7341.827 2238:University of Canterbury 2104:among vaccinated people. 2020:List of cognitive biases 1607:statistical independence 1095:law of total probability 572:Example 2: Drunk drivers 193:conclude from experience 48:may need to be rewritten 5448:Two wrongs make a right 4779:Denying the correlative 3548:10.1145/3290605.3300912 2570:Rossmo, D. Kim (2009). 1778:reference class problem 5433:Psychologist's fallacy 5370:Argument to moderation 5360:Argument from anecdote 5310:Chronological snobbery 4934:Quoting out of context 4901:Overwhelming exception 4784:Suppressed correlative 4684:Quoting out of context 4559:quantificational logic 4533:Denying the antecedent 2188:Law and Human Behavior 1917: 1782:Cochrane Collaboration 1682:Findings in psychology 1635:extremely improbable: 1603:genetic predisposition 1548: 1409: 1324: 1247: 1076: 1019: 960: 907: 849: 705: 642: 560:of infection with the 154:false positive paradox 148:False positive paradox 131:It is also called the 97: 5527:Statistical paradoxes 5522:Probability fallacies 5396:The Four Great Errors 5376:Argumentum ad populum 5365:Argument from silence 5069:Argumentum ad baculum 4847:Faulty generalization 4538:Argument from fallacy 4372:Arab–Israeli conflict 4099:Social influence bias 4044:Out-group homogeneity 3746:The Base Rate Fallacy 2357:10.5210/fm.v22i9.7126 2261:10.31219/osf.io/cs248 1918: 1724:has argued that some 1543: 1410: 1325: 1248: 1077: 1020: 961: 908: 850: 706: 643: 610:positive test results 558:posterior probability 174:in an individual case 91: 5414:Invincible ignorance 5220:Reductio ad Stalinum 5206:Reductio ad Hitlerum 5162:Wisdom of repugnance 4929:Moving the goalposts 4794:Illicit transference 4719:Begging the question 4640:Undistributed middle 4548:Mathematical fallacy 4523:Affirming a disjunct 4014:Mere-exposure effect 3944:Extrinsic incentives 3890:Selective perception 3674:Psychological Review 3235:Psychological Review 2922:Psychological Review 2053:Intuitive statistics 2032:Misleading vividness 1995:Precision and recall 1804: 1726:attributional biases 1691:grade point averages 1676:exculpatory evidence 1340: 1263: 1104: 1031: 971: 918: 865: 725: 666: 618: 599:positive test result 133:prosecutor's fallacy 5507:Relevance fallacies 5147:Parade of horribles 5123:In-group favoritism 4949:Syntactic ambiguity 4592:Syllogistic fallacy 4515:propositional logic 4239:Social desirability 4134:von Restorff effect 4009:Mean world syndrome 3984:Hostile attribution 3286:(5500): 2261–2262. 3148:1974Sci...185.1124T 3142:(4157): 1124–1131. 2969:1974Sci...185.1124T 2963:(4157): 1124–1131. 2788:on 24 August 2011. 2602:University of Leeds 2519:2016AnRSA...3...51F 2501:"Bayes and the Law" 1975:systematic sampling 1520:O. J. Simpson trial 170:false positive rate 5517:Behavioral finance 5233:Poisoning the well 5050:Proof by assertion 5025:Texas sharpshooter 4959:Questionable cause 4896:Slothful induction 4855:Anecdotal evidence 4715:Circular reasoning 4610:Exclusive premises 4572:Illicit conversion 4154:Statistical biases 3932:Curse of knowledge 2698:Vincent Scheurer. 2654:Hill, Ray (2002). 2200:10.1007/BF01044641 2168:. Fallacyfiles.org 2041:Prevention paradox 2011:Inductive argument 1913: 1714:representativeness 1695:college admissions 1611:ecological fallacy 1549: 1405: 1320: 1243: 1072: 1015: 956: 903: 845: 701: 638: 359:So, in population 204:Example 1: Disease 98: 5494: 5493: 5472: 5471: 5468: 5467: 5408:Ignoratio elenchi 5320: 5319: 5170: 5169: 5132:Not invented here 4837:Converse accident 4759:Correlative-based 4736:Compound question 4679:False attribution 4674:False equivalence 4648: 4647: 4457: 4456: 4094:Social comparison 3875:Choice-supportive 3748:The Fallacy Files 3728:978-0-387-94169-1 3532:. pp. 1–14. 3487:(7341): 827–830. 2890:Acta Psychologica 2804:Hill, R. (2004). 2719:Hill, R. (2004). 2047:Simpson's paradox 2026:List of paradoxes 1905: 1892: 1718:extension neglect 1592:between infants. 1515:People v. Collins 1499:forensic evidence 1491:prior probability 1394: 840: 562:prior probability 459: 458: 418:(false positive) 285: 284: 244:(false positive) 126:extension neglect 106:base rate neglect 102:base rate fallacy 86: 85: 78: 58:lead layout guide 18:Base-rate fallacy 16:(Redirected from 5534: 5512:Cognitive biases 5484: 5483: 5455:Special pleading 5334: 5195:Appeal to motive 5181: 5157:Stirring symbols 5137:Island mentality 5075:Wishful thinking 5056: 4772:Perfect solution 4749:No true Scotsman 4744:Complex question 4729:Leading question 4708:Question-begging 4694:No true Scotsman 4659: 4582:Quantifier shift 4577:Proof by example 4510: 4484: 4477: 4470: 4461: 4254:Systematic error 4209:Omitted-variable 4124:Trait ascription 3964:Frog pond effect 3792:Cognitive biases 3776: 3769: 3762: 3753: 3733: 3732: 3706: 3700: 3699: 3697: 3665: 3659: 3658: 3622: 3613: 3612: 3576: 3570: 3569: 3541: 3521: 3515: 3514: 3504: 3472: 3466: 3465: 3454:10.1002/acp.1460 3437: 3431: 3430: 3412: 3380: 3371: 3370: 3360: 3328: 3322: 3321: 3303: 3275: 3269: 3268: 3250: 3230: 3221: 3220: 3202: 3182: 3176: 3175: 3131: 3125: 3124: 3088: 3082: 3081: 3053: 3047: 3046: 3028: 3022: 3021: 3003: 2997: 2996: 2952: 2946: 2945: 2934:10.1037/h0034747 2917: 2906: 2905: 2887: 2879:Bar-Hillel, Maya 2875: 2869: 2868: 2857: 2851: 2850: 2848: 2847: 2841: 2835:. 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346: 343: 340: 325: 323: 322: 319: 316: 293:expected outcome 264:(true negative) 259:(false negative) 213: 158:accuracy paradox 81: 74: 70: 67: 61: 54:improve the lead 38: 37: 30: 21: 5542: 5541: 5537: 5536: 5535: 5533: 5532: 5531: 5497: 5496: 5495: 5490: 5464: 5438:Rationalization 5381: 5328: 5316: 5254: 5176:Genetic fallacy 5166: 5079: 5054: 5029: 4953: 4944:Sorites paradox 4924:False precision 4905: 4886:Double counting 4841: 4816: 4788: 4753: 4740:Loaded question 4724:Loaded language 4703: 4644: 4586: 4552: 4499: 4488: 4458: 4453: 4434: 4408: 4273: 4148: 4129:Turkey illusion 3897:Compassion fade 3794: 3785: 3780: 3742: 3737: 3736: 3729: 3708: 3707: 3703: 3667: 3666: 3662: 3624: 3623: 3616: 3578: 3577: 3573: 3558: 3523: 3522: 3518: 3474: 3473: 3469: 3439: 3438: 3434: 3382: 3381: 3374: 3343:(3): CD006776. 3330: 3329: 3325: 3277: 3276: 3272: 3248:10.1.1.128.3201 3232: 3231: 3224: 3200:10.1.1.131.8290 3184: 3183: 3179: 3133: 3132: 3128: 3090: 3089: 3085: 3055: 3054: 3050: 3043: 3030: 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3922:Dunning–Kruger 3919: 3914: 3909: 3904: 3899: 3894: 3893: 3892: 3882: 3877: 3872: 3867: 3862: 3861: 3860: 3850: 3845: 3840: 3839: 3838: 3836:Correspondence 3833: 3831:Actor–observer 3823: 3818: 3813: 3808: 3803: 3797: 3795: 3790: 3787: 3786: 3781: 3779: 3778: 3771: 3764: 3756: 3750: 3749: 3741: 3740:External links 3738: 3735: 3734: 3727: 3701: 3660: 3633:(3): 343–352. 3614: 3587:(3): 247–276. 3571: 3556: 3516: 3467: 3448:(3): 369–381. 3432: 3395:(3): 380–400. 3372: 3323: 3270: 3222: 3177: 3126: 3083: 3048: 3041: 3023: 3016: 2998: 2947: 2928:(4): 237–251. 2907: 2896:(3): 211–233. 2870: 2865:www.bailii.org 2852: 2819:(5): 322–323. 2795: 2767: 2711: 2690: 2687:on 2012-07-11. 2665: 2618: 2585: 2576: 2563: 2550: 2491: 2464:(2): 302–311. 2452:(2021-02-17). 2434: 2422:CATO Institute 2402: 2363: 2327: 2290: 2284:. p. 16. 2266: 2243: 2221: 2178: 2157: 2108: 2072: 2071: 2069: 2066: 2065: 2064: 2059: 2050: 2044: 2038: 2029: 2023: 2017: 2008: 2003: 1997: 1990: 1987: 1924: 1923: 1912: 1909: 1904: 1901: 1896: 1890: 1887: 1884: 1881: 1876: 1873: 1870: 1866: 1863: 1860: 1857: 1854: 1850: 1847: 1841: 1838: 1835: 1832: 1828: 1825: 1822: 1819: 1816: 1812: 1809: 1754: 1753: 1742:Bayes' theorem 1700:Psychologists 1683: 1680: 1647: 1646: 1643: 1640: 1574:expert witness 1566: 1563: 1559: 1521: 1518: 1510: 1507: 1479: 1476: 1443: 1442: 1439: 1423: 1420: 1416: 1415: 1404: 1401: 1398: 1393: 1389: 1386: 1383: 1377: 1374: 1371: 1368: 1364: 1361: 1358: 1355: 1352: 1348: 1345: 1331: 1330: 1319: 1316: 1313: 1310: 1307: 1304: 1301: 1298: 1295: 1292: 1289: 1286: 1283: 1280: 1277: 1274: 1271: 1268: 1254: 1253: 1242: 1238: 1235: 1232: 1229: 1226: 1222: 1219: 1215: 1211: 1208: 1205: 1202: 1199: 1195: 1192: 1189: 1186: 1183: 1180: 1176: 1173: 1170: 1167: 1164: 1160: 1157: 1153: 1149: 1146: 1143: 1140: 1137: 1133: 1130: 1127: 1124: 1121: 1118: 1115: 1112: 1109: 1083: 1082: 1071: 1068: 1065: 1061: 1058: 1055: 1052: 1049: 1045: 1042: 1039: 1036: 1026: 1014: 1011: 1008: 1005: 1001: 998: 995: 992: 989: 985: 982: 979: 976: 966: 955: 952: 949: 946: 942: 939: 936: 933: 930: 926: 923: 913: 902: 899: 896: 893: 889: 886: 883: 880: 877: 873: 870: 856: 855: 844: 838: 835: 832: 829: 824: 820: 817: 814: 811: 808: 804: 801: 797: 793: 790: 787: 784: 781: 777: 774: 771: 768: 762: 759: 756: 753: 749: 746: 743: 740: 737: 733: 730: 712: 711: 700: 697: 694: 690: 687: 684: 681: 678: 674: 671: 657:Bayes' theorem 637: 634: 631: 627: 623: 612: 611: 600: 573: 570: 525:In population 523: 522: 519: 518: 517: 495: 494: 493: 457: 456: 453: 450: 447: 443: 442: 439: 434: 429: 423: 422: 419: 414: 409: 403: 402: 399: 396: 393: 384: 381: 357: 356: 353: 352: 351: 329: 328: 327: 283: 282: 279: 276: 273: 269: 268: 265: 260: 255: 249: 248: 245: 240: 235: 229: 228: 225: 222: 219: 210: 207: 205: 202: 200: 197: 162:false positive 149: 146: 110:base rate bias 104:, also called 84: 83: 43:The article's 42: 40: 33: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 5539: 5528: 5525: 5523: 5520: 5518: 5515: 5513: 5510: 5508: 5505: 5504: 5502: 5487: 5479: 5478: 5475: 5461: 5458: 5456: 5453: 5449: 5446: 5445: 5444: 5441: 5439: 5436: 5434: 5431: 5429: 5426: 5424: 5420: 5417: 5415: 5412: 5410: 5409: 5405: 5403: 5400: 5398: 5397: 5393: 5391: 5388: 5387: 5384: 5378: 5377: 5373: 5371: 5368: 5366: 5363: 5361: 5358: 5354: 5351: 5350: 5349: 5348: 5344: 5343: 5341: 5339: 5335: 5332: 5330: 5323: 5311: 5308: 5307: 5306: 5302: 5299: 5297: 5294: 5292: 5289: 5285: 5281: 5278: 5276: 5275: 5271: 5269: 5266: 5265: 5264: 5261: 5260: 5257: 5251: 5248: 5246: 5245: 5241: 5239: 5236: 5234: 5231: 5229: 5226: 5222: 5221: 5217: 5213: 5210: 5209: 5208: 5207: 5203: 5202: 5201: 5198: 5196: 5193: 5192: 5190: 5188: 5187: 5182: 5179: 5177: 5173: 5163: 5160: 5158: 5155: 5153: 5150: 5148: 5145: 5143: 5140: 5138: 5135: 5133: 5129: 5128:Invented here 5126: 5124: 5121: 5119: 5116: 5114: 5111: 5109: 5106: 5104: 5101: 5099: 5096: 5094: 5091: 5090: 5088: 5086: 5082: 5076: 5073: 5071: 5070: 5066: 5065: 5063: 5061: 5057: 5051: 5047: 5044: 5042: 5039: 5038: 5036: 5032: 5026: 5023: 5021: 5018: 5016: 5013: 5011: 5008: 5004: 5001: 5000: 4999: 4996: 4992: 4991: 4987: 4985: 4984: 4980: 4979: 4977: 4973: 4970: 4969: 4968: 4965: 4964: 4962: 4960: 4956: 4950: 4947: 4945: 4942: 4940: 4937: 4935: 4932: 4930: 4927: 4925: 4922: 4920: 4917: 4916: 4914: 4912: 4908: 4902: 4899: 4897: 4894: 4892: 4891:False analogy 4889: 4887: 4884: 4882: 4878: 4875: 4871: 4868: 4866: 4863: 4862: 4861: 4860:Sampling bias 4858: 4856: 4853: 4852: 4850: 4848: 4844: 4838: 4835: 4833: 4830: 4829: 4827: 4825: 4824: 4823:Secundum quid 4819: 4813: 4810: 4808: 4805: 4803: 4800: 4799: 4797: 4795: 4791: 4785: 4782: 4780: 4777: 4773: 4770: 4769: 4768: 4767:False dilemma 4765: 4764: 4762: 4760: 4756: 4750: 4747: 4745: 4741: 4737: 4734: 4730: 4727: 4726: 4725: 4722: 4720: 4716: 4713: 4712: 4710: 4706: 4700: 4697: 4695: 4692: 4690: 4687: 4685: 4682: 4680: 4677: 4675: 4672: 4670: 4667: 4666: 4664: 4660: 4657: 4655: 4651: 4641: 4638: 4636: 4635:Illicit minor 4633: 4631: 4630:Illicit major 4628: 4626: 4623: 4621: 4618: 4616: 4613: 4611: 4608: 4606: 4603: 4601: 4598: 4597: 4595: 4593: 4589: 4583: 4580: 4578: 4575: 4573: 4570: 4568: 4565: 4564: 4562: 4560: 4555: 4549: 4546: 4544: 4541: 4539: 4536: 4534: 4531: 4529: 4526: 4524: 4521: 4520: 4518: 4516: 4511: 4508: 4506: 4502: 4497: 4493: 4485: 4480: 4478: 4473: 4471: 4466: 4465: 4462: 4450: 4447: 4445: 4441: 4440: 4437: 4431: 4428: 4426: 4423: 4421: 4418: 4417: 4415: 4411: 4405: 4402: 4400: 4397: 4395: 4392: 4390: 4387: 4385: 4382: 4378: 4375: 4373: 4370: 4368: 4367:United States 4365: 4363: 4360: 4358: 4355: 4353: 4350: 4348: 4345: 4343: 4342:False balance 4340: 4339: 4338: 4335: 4333: 4330: 4328: 4325: 4323: 4320: 4318: 4315: 4313: 4310: 4308: 4305: 4303: 4300: 4298: 4297: 4293: 4291: 4288: 4286: 4283: 4282: 4280: 4276: 4270: 4267: 4265: 4262: 4260: 4257: 4255: 4252: 4250: 4247: 4245: 4242: 4240: 4237: 4235: 4232: 4230: 4227: 4225: 4222: 4220: 4217: 4215: 4214:Participation 4212: 4210: 4207: 4205: 4202: 4200: 4197: 4195: 4192: 4190: 4187: 4183: 4182:Psychological 4180: 4179: 4178: 4175: 4173: 4170: 4168: 4165: 4163: 4160: 4159: 4157: 4155: 4151: 4145: 4142: 4140: 4137: 4135: 4132: 4130: 4127: 4125: 4122: 4120: 4117: 4115: 4112: 4110: 4107: 4105: 4102: 4100: 4097: 4095: 4092: 4090: 4087: 4085: 4082: 4080: 4077: 4075: 4072: 4070: 4067: 4065: 4062: 4060: 4057: 4055: 4052: 4050: 4047: 4045: 4042: 4040: 4037: 4035: 4032: 4030: 4027: 4025: 4022: 4020: 4017: 4015: 4012: 4010: 4007: 4005: 4002: 4000: 3997: 3995: 3992: 3990: 3987: 3985: 3982: 3980: 3977: 3975: 3972: 3970: 3967: 3965: 3962: 3960: 3957: 3955: 3952: 3950: 3949:Fading affect 3947: 3945: 3942: 3940: 3937: 3933: 3930: 3929: 3928: 3925: 3923: 3920: 3918: 3915: 3913: 3910: 3908: 3905: 3903: 3900: 3898: 3895: 3891: 3888: 3887: 3886: 3883: 3881: 3878: 3876: 3873: 3871: 3868: 3866: 3863: 3859: 3856: 3855: 3854: 3851: 3849: 3846: 3844: 3841: 3837: 3834: 3832: 3829: 3828: 3827: 3824: 3822: 3819: 3817: 3814: 3812: 3809: 3807: 3804: 3802: 3799: 3798: 3796: 3793: 3788: 3784: 3777: 3772: 3770: 3765: 3763: 3758: 3757: 3754: 3747: 3744: 3743: 3739: 3730: 3724: 3720: 3716: 3712: 3705: 3702: 3696: 3691: 3687: 3683: 3679: 3675: 3671: 3664: 3661: 3656: 3652: 3648: 3644: 3640: 3636: 3632: 3628: 3621: 3619: 3615: 3610: 3606: 3602: 3598: 3594: 3590: 3586: 3582: 3575: 3572: 3567: 3563: 3559: 3557:9781450359702 3553: 3549: 3545: 3540: 3535: 3531: 3527: 3520: 3517: 3512: 3508: 3503: 3498: 3494: 3490: 3486: 3482: 3478: 3471: 3468: 3463: 3459: 3455: 3451: 3447: 3443: 3436: 3433: 3428: 3424: 3420: 3416: 3411: 3406: 3402: 3398: 3394: 3390: 3386: 3379: 3377: 3373: 3368: 3364: 3359: 3354: 3350: 3346: 3342: 3338: 3334: 3327: 3324: 3319: 3315: 3311: 3307: 3302: 3297: 3293: 3289: 3285: 3281: 3274: 3271: 3266: 3262: 3258: 3254: 3249: 3244: 3240: 3236: 3229: 3227: 3223: 3218: 3214: 3210: 3206: 3201: 3196: 3192: 3188: 3181: 3178: 3173: 3169: 3165: 3161: 3157: 3153: 3149: 3145: 3141: 3137: 3130: 3127: 3122: 3118: 3114: 3110: 3106: 3102: 3098: 3094: 3087: 3084: 3079: 3075: 3071: 3067: 3063: 3059: 3052: 3049: 3044: 3042:0-470-99007-4 3038: 3034: 3027: 3024: 3019: 3017:0-521-62749-4 3013: 3009: 3002: 2999: 2994: 2990: 2986: 2982: 2978: 2974: 2970: 2966: 2962: 2958: 2951: 2948: 2943: 2939: 2935: 2931: 2927: 2923: 2916: 2914: 2912: 2908: 2903: 2899: 2895: 2891: 2884: 2880: 2874: 2871: 2866: 2862: 2856: 2853: 2842:on 2012-08-30 2838: 2834: 2830: 2826: 2822: 2818: 2814: 2807: 2799: 2796: 2792: 2784: 2777: 2771: 2768: 2757:on 2012-08-30 2753: 2749: 2745: 2741: 2737: 2733: 2729: 2722: 2715: 2712: 2701: 2694: 2691: 2686: 2682: 2681: 2676: 2669: 2666: 2662: 2657: 2651: 2647: 2631: 2622: 2619: 2608:on 2016-04-16 2607: 2603: 2599: 2595: 2589: 2586: 2580: 2577: 2573: 2567: 2564: 2560: 2554: 2551: 2546: 2542: 2537: 2532: 2528: 2524: 2520: 2516: 2512: 2508: 2507: 2502: 2495: 2492: 2487: 2483: 2479: 2475: 2471: 2467: 2463: 2459: 2455: 2451: 2450:Sageman, Marc 2445: 2443: 2441: 2439: 2435: 2424: 2423: 2418: 2411: 2409: 2407: 2403: 2392: 2388: 2384: 2380: 2376: 2370: 2368: 2364: 2358: 2353: 2349: 2345: 2341: 2334: 2332: 2328: 2323: 2316: 2314: 2308: 2304: 2297: 2295: 2291: 2287: 2283: 2279: 2278: 2270: 2267: 2262: 2258: 2254: 2253:OSF Preprints 2247: 2244: 2239: 2232: 2225: 2222: 2217: 2213: 2209: 2205: 2201: 2197: 2193: 2189: 2182: 2179: 2167: 2161: 2158: 2153: 2149: 2144: 2139: 2135: 2131: 2127: 2123: 2119: 2112: 2109: 2105: 2090: 2083: 2077: 2074: 2067: 2063: 2060: 2054: 2051: 2048: 2045: 2042: 2039: 2033: 2030: 2027: 2024: 2021: 2018: 2012: 2009: 2007: 2004: 2001: 2000:Data dredging 1998: 1996: 1993: 1992: 1988: 1986: 1984: 1980: 1976: 1972: 1967: 1965: 1961: 1957: 1953: 1949: 1945: 1941: 1937: 1933: 1929: 1910: 1907: 1902: 1899: 1894: 1885: 1879: 1871: 1868: 1845: 1839: 1833: 1830: 1807: 1800: 1799: 1798: 1796: 1792: 1786: 1783: 1779: 1775: 1771: 1767: 1763: 1759: 1751: 1750: 1749: 1745: 1743: 1737: 1735: 1731: 1727: 1723: 1719: 1715: 1711: 1707: 1703: 1698: 1696: 1692: 1687: 1681: 1679: 1677: 1672: 1670: 1667: 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J. Simpson 1527: 1519: 1516: 1508: 1506: 1504: 1500: 1494: 1492: 1486: 1483: 1477: 1475: 1473: 1469: 1464: 1459: 1455: 1451: 1447: 1440: 1437: 1436: 1435: 1432: 1430: 1421: 1419: 1402: 1399: 1396: 1391: 1387: 1384: 1381: 1375: 1369: 1366: 1343: 1336: 1335: 1334: 1317: 1314: 1308: 1305: 1302: 1296: 1290: 1287: 1284: 1278: 1272: 1266: 1259: 1258: 1257: 1217: 1193: 1190: 1184: 1181: 1155: 1131: 1128: 1122: 1119: 1113: 1107: 1100: 1099: 1098: 1096: 1092: 1088: 1069: 1066: 1043: 1040: 1034: 1027: 1012: 1009: 1006: 983: 980: 974: 967: 953: 950: 947: 921: 914: 900: 897: 894: 868: 861: 860: 859: 842: 833: 827: 799: 775: 772: 766: 760: 754: 751: 728: 721: 720: 719: 717: 695: 692: 669: 662: 661: 660: 658: 653: 649: 635: 632: 629: 625: 621: 609: 605: 601: 598: 594: 590: 589: 588: 585: 582: 579: 578:breathalyzers 571: 569: 567: 563: 559: 555: 551: 546: 528: 520: 499: 498: 496: 475: 474: 472: 471: 470: 468: 464: 454: 451: 448: 445: 444: 440: 435: 430: 425: 424: 420: 415: 410: 405: 404: 400: 397: 394: 389: 388: 382: 380: 362: 354: 333: 332: 330: 309: 308: 306: 305:true positive 302: 301: 300: 298: 294: 290: 280: 277: 274: 271: 270: 266: 261: 256: 251: 250: 246: 241: 236: 231: 230: 226: 223: 220: 215: 214: 208: 203: 198: 196: 194: 190: 186: 181: 179: 175: 171: 167: 163: 159: 155: 147: 145: 143: 138: 134: 129: 127: 123: 119: 115: 111: 107: 103: 95: 90: 80: 77: 69: 59: 56:and read the 55: 49: 46: 41: 32: 31: 19: 5423:Naturalistic 5406: 5394: 5374: 5345: 5329:of relevance 5272: 5250:Whataboutism 5242: 5218: 5212:Godwin's law 5204: 5184: 5067: 5060:Consequences 5041:Law/Legality 5015:Single cause 4988: 4981: 4876: 4821: 4689:Loki's Wager 4669:Equivocation 4662:Equivocation 4327:In education 4294: 4278:Other biases 4264:Verification 4249:Survivorship 4199:Non-response 4172:Healthy user 4114:Substitution 4089:Self-serving 3885:Confirmation 3853:Availability 3801:Acquiescence 3710: 3704: 3677: 3673: 3663: 3630: 3626: 3584: 3580: 3574: 3529: 3519: 3484: 3480: 3470: 3445: 3441: 3435: 3392: 3388: 3340: 3336: 3326: 3283: 3279: 3273: 3238: 3234: 3190: 3186: 3180: 3139: 3135: 3129: 3096: 3092: 3086: 3061: 3057: 3051: 3032: 3026: 3007: 3001: 2960: 2956: 2950: 2925: 2921: 2893: 2889: 2873: 2864: 2855: 2844:. Retrieved 2837:the original 2816: 2812: 2798: 2789: 2783:the original 2770: 2759:. Retrieved 2752:the original 2731: 2727: 2714: 2703:. Retrieved 2693: 2685:the original 2680:The Observer 2678: 2668: 2659: 2637:. Retrieved 2621: 2610:. Retrieved 2606:the original 2597: 2588: 2579: 2571: 2566: 2558: 2553: 2513:(1): 51–77. 2510: 2504: 2494: 2461: 2457: 2426:. Retrieved 2420: 2394:. Retrieved 2382: 2347: 2344:First Monday 2343: 2321: 2310: 2306: 2285: 2276: 2269: 2252: 2246: 2240:. p. 6. 2224: 2191: 2187: 2181: 2170:. Retrieved 2160: 2125: 2121: 2111: 2102: 2096:. Retrieved 2076: 1982: 1978: 1974: 1970: 1968: 1963: 1959: 1955: 1951: 1947: 1943: 1939: 1935: 1931: 1927: 1925: 1794: 1790: 1787: 1773: 1769: 1765: 1761: 1757: 1755: 1746: 1738: 1706:Amos Tversky 1699: 1688: 1685: 1673: 1665: 1659: 1652: 1648: 1632: 1628: 1622: 1619: 1594: 1590:uncorrelated 1568: 1550: 1535: 1529: 1495: 1487: 1484: 1481: 1460: 1456: 1452: 1448: 1444: 1433: 1425: 1417: 1332: 1256:which gives 1255: 1090: 1086: 1084: 857: 715: 713: 654: 650: 613: 607: 603: 596: 592: 586: 583: 575: 553: 549: 547: 526: 524: 466: 462: 460: 360: 358: 296: 288: 286: 188: 182: 177: 173: 157: 153: 151: 136: 132: 130: 109: 105: 101: 99: 72: 63: 52:Please help 47: 45:lead section 5443:Red herring 5200:Association 4881:Conjunction 4802:Composition 4699:Reification 4615:Existential 4567:Existential 4394:Publication 4347:Vietnam War 4194:Length time 4177:Information 4119:Time-saving 3979:Horn effect 3969:Halo effect 3917:Distinction 3826:Attribution 3821:Attentional 2128:(1): 1–14. 1962:| drunk) × 1650:innocence. 1570:Sally Clark 1463:data mining 5501:Categories 5419:Moralistic 5353:Sealioning 5347:Ad nauseam 5274:Ipse dixit 5186:Ad hominem 5010:Regression 4812:Ecological 4625:Four terms 4543:Masked man 4357:South Asia 4332:Liking gap 4144:In animals 4109:Status quo 4024:Negativity 3927:Egocentric 3902:Congruence 3880:Commitment 3870:Blind spot 3858:Mean world 3848:Automation 3680:(2): 425. 3539:1901.02949 3241:(4): 684. 2846:2010-06-13 2761:2010-06-13 2734:(5): 321. 2705:2010-05-21 2639:2010-06-12 2612:2015-10-17 2428:2022-08-30 2396:2022-08-30 2318:- Citing: 2194:(3): 167. 2172:2013-06-15 2143:2440/41190 2098:2023-02-14 2068:References 1768:| drunk), 1578:Roy Meadow 1524:See also: 1513:See also: 1503:prior odds 469:would be: 398:Uninfected 299:would be: 224:Uninfected 185:population 122:prevalence 5460:Straw man 5338:Arguments 5327:fallacies 5301:Tradition 5291:Etymology 5263:Authority 5244:Tu quoque 5228:Bulverism 4998:Gambler's 4967:Animistic 4911:Ambiguity 4877:Base rate 4620:Necessity 4492:fallacies 4425:Debiasing 4404:White hat 4399:Reporting 4312:Inductive 4229:Selection 4189:Lead time 4162:Estimator 4139:Zero-risk 4104:Spotlight 4084:Restraint 4074:Proximity 4059:Precision 4019:Narrative 3974:Hindsight 3959:Frequency 3939:Emotional 3912:Declinism 3843:Authority 3816:Anchoring 3806:Ambiguity 3627:Cognition 3581:Cognition 3243:CiteSeerX 3195:CiteSeerX 3187:Cognition 3172:143452957 2993:143452957 2486:232341781 2478:0954-6553 2391:1059-1028 2216:147472915 2152:0749-5978 2062:R v Adams 1869:∩ 1831:∣ 1760:(drunk), 1728:like the 1615:estimated 1397:≈ 1385:× 1367:∣ 1306:× 1288:× 1194:∣ 1132:∣ 1044:∣ 984:∣ 776:∣ 752:∣ 693:∣ 633:≈ 428:negative 408:positive 392:of people 254:negative 234:positive 218:of people 166:precision 118:base rate 66:July 2023 5486:Category 5118:Ridicule 5103:Flattery 5093:Children 4990:Post hoc 4870:McNamara 4832:Accident 4807:Division 4654:Informal 4322:Inherent 4285:Academic 4259:Systemic 4244:Spectrum 4224:Sampling 4204:Observer 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