1450:
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
1497:
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
1739:
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
1465:
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
1445:
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
580:
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
1649:
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
1551:
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
2103:
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
1496:
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
1449:
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
1426:
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
651:
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
2625:
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
1536:
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
2790:
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
1784:
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
139:
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
1560:
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
1747:
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
1453:
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).
1788:
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
2660:
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
1251:
1595:
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
1488:
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
1921:
853:
1620:
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.
1427:
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.
1732:
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".
3031:
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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1339:
4599:
2088:
2186:
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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1501:
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
187:
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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96:
patients than unvaccinated ones might suggest that the vaccine is ineffective, but such an imbalance is to be expected within a highly vaccinated population.
3625:
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.; SchĂĽnemann, H. (2011). SchĂĽnemann, 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%.
1785:
shown that graphical representations of natural frequencies (e.g., icon arrays, hypothetical outcome plots) help people to make better inferences.
1537:
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
191:
population with the condition, then a test administrator whose experience has been drawn from testing in a high-prevalence population may
3579:
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
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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.
4793:
3555:
3040:
3015:
1441:
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.
1438:
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.
291:
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
75:
2805:
2720:
1686:
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
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4176:
2649:
1597:
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5521:
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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:
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5437:
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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:
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614:
Therefore, the probability that any given driver among the 1 + 49.95 = 50.95 positive test results really is drunk is
584:
Many would estimate the probability that the driver is drunk as high as 95%, but the correct probability is about 2%.
1030:
970:
3056:
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
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4289:
3815:
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1533:
was tried and acquitted in 1995 for the murders of his ex-wife Nicole Brown
Simpson and her friend Ronald Goldman.
1525:
3921:
3278:
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
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4003:
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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:
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1981:(e.g., in scientific experiments). In the latter case it is not possible to infer the posterior probability
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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)}}.}
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2251:
Suss, Richard A. (October 4, 2023). "The Prosecutor's Fallacy Framed as a Sample Space Substitution".
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1776:| sober)—is presented in terms of natural frequencies with respect to a certain reference class (see
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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.
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88:
2594:"Resolution adopted by the Senate (21 October 1998) on the retirement of Professor Sir Roy Meadow"
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2303:"Quantitative literacy - drug testing, cancer screening, and the identification of igneous rocks"
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After the court found that the forensic pathologist who had examined both babies had withheld
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1461:
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,}
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1934:) denotes the number of drivers that are drunk and get a positive breathalyzer result, and
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Frequency tree of 100 000 battered American women showing the prosecutor's fallacy in the
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4688:
2340:"100,000 false positives for every real terrorist: Why anti-terror algorithms don't work"
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3134:
Tversky, A.; Kahneman, D. (1974). "Judgment under Uncertainty: Heuristics and Biases".
2583:
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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17:
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5127:
4859:
4822:
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3208:
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1999:
1617:
by squaring the likelihood of a single such death in all otherwise similar families.
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192:
140:
imputations of guilt or liability that are not analyzable as errors in base rates or
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587:
An explanation for this is as follows: on average, for every 1,000 drivers tested,
577:
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465:, of which only 2% are infected. The expected outcome of 1000 tests on population
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5156:
4218:
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3400:
3333:"Using alternative statistical formats for presenting risks and risk reductions"
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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
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5273:
5185:
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3524:
Kim, Yea-Seul; Walls, Logan A.; Krafft, Peter; Hullman, Jessica (2 May 2019).
3104:
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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
5459:
5243:
5227:
4910:
4424:
3911:
3745:
3547:
3530:
Proceedings of the 2019 CHI Conference on Human Factors in Computing Systems
2260:
2165:
2061:
117:
5389:
3709:
Kleiter, G. D. (1994). "Natural Sampling: Rationality without Base Rates".
3646:
3600:
3510:
3440:
Brase, G. L. (2009). "Pictorial representations in statistical reasoning".
3418:
3366:
3309:
3163:
3112:
2984:
2832:
2747:
2605:
2544:
2417:"Effective Counterterrorism and the Limited Role of Predictive Data Mining"
2311:
At first glance, this seems perverse: the less the students as a whole use
4459:
2920:
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.
2142:
164:
test results than true positives (this means the classifier has a low
3453:
2933:
2652:
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
1645:
Other possibilities (including one homicide and one case of SIDS)
3782:
2645:
2281:
1668:
1581:
602:
999 drivers are not drunk, and among those drivers there are 5%
4463:
3755:
2028: – List of statements that appear to contradict themselves
581:
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.
1333:
Plugging these numbers into Bayes' theorem, one finds that
287:
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
1474:
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
497:
Uninfected and test indicates disease (false positive)
331:
Uninfected and test indicates disease (false positive)
53:
1639:
Two successive deaths in the same family, both by SIDS
858:
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
1342:
1265:
1106:
1033:
973:
920:
867:
727:
668:
620:
3385:"Teaching Bayesian reasoning in less than two hours"
2122:
Organizational Behavior and Human Decision Processes
2057:
Pages displaying wikidata descriptions as a fallback
473:
Infected and test indicates disease (true positive)
5336:
5324:
5183:
5174:
5083:
5058:
5033:
4957:
4909:
4845:
4820:
4792:
4757:
4707:
4661:
4652:
4590:
4556:
4512:
4503:
4412:
4277:
4152:
3789:
3713:. Recent Research in Psychology. pp. 375–388.
2656:"Cot Death or Murder? – Weighing the Probabilities"
2277:
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:Ă— 0.05 = 49 people would receive a false positive
461:Now consider the same test applied to population
350:Ă— 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:
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1842:
1813:
1805:
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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:
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1059:
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1047:
999:
996:
993:
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987:
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937:
934:
931:
928:
887:
884:
881:
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815:
812:
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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:
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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:MĂĽnchausen syndrome by proxy
2628:Joyce, H. (September 2002).
1598:MĂĽnchausen syndrome by proxy
4296:DĂ©formation 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:
18:False positive paradox
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
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:
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3515:
3514:
3504:
3472:
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3465:
3454:10.1002/acp.1460
3437:
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3412:
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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:. Archived from
2810:
2800:
2794:
2793:
2787:
2780:
2772:
2766:
2765:
2763:
2762:
2756:
2750:. Archived from
2725:
2716:
2710:
2709:
2707:
2706:
2695:
2689:
2688:
2683:. Archived from
2670:
2664:
2663:
2643:
2641:
2640:
2635:. plus.maths.org
2634:
2623:
2617:
2616:
2614:
2613:
2600:. No. 428.
2590:
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2078:
2058:
2037:
2016:
1971:natural sampling
1922:
1920:
1919:
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1906:
1898:
1893:
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1877:
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1843:
1829:
1565:Sally Clark case
1414:
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541:
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489:
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438:(true negative)
433:(false negative)
387:
378:
376:
375:
372:
369:
349:
347:
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:
3029:
3025:
3018:
3005:
3004:
3000:
2954:
2953:
2949:
2919:
2918:
2909:
2885:
2877:
2876:
2872:
2859:
2858:
2854:
2845:
2843:
2839:
2808:
2803:
2801:
2797:
2785:
2778:
2774:
2773:
2769:
2760:
2758:
2754:
2723:
2718:
2717:
2713:
2704:
2702:
2697:
2696:
2692:
2672:
2671:
2667:
2653:
2638:
2636:
2632:
2627:
2624:
2620:
2611:
2609:
2592:
2591:
2587:
2582:
2578:
2569:
2565:
2556:
2552:
2498:
2497:
2493:
2448:
2447:
2436:
2427:
2425:
2414:
2413:
2404:
2395:
2393:
2375:Schneier, Bruce
2373:
2372:
2365:
2337:
2336:
2329:
2319:
2300:
2299:
2292:
2273:
2272:
2268:
2250:
2249:
2245:
2233:
2228:
2227:
2223:
2185:
2184:
2180:
2171:
2169:
2164:
2163:
2159:
2115:
2114:
2110:
2097:
2095:
2091:
2084:
2080:
2079:
2075:
2070:
2056:
2035:
2014:
1991:
1946:(drunk ∩
1930:(drunk ∩
1878:
1844:
1802:
1801:
1722:Richard Nisbett
1702:Daniel Kahneman
1684:
1586:historical data
1567:
1554:Gerd Gigerenzer
1528:
1522:
1517:
1511:
1509:Examples in law
1480:
1472:burden of proof
1424:
1380:
1338:
1337:
1261:
1260:
1102:
1101:
1029:
1028:
969:
968:
916:
915:
863:
862:
826:
765:
723:
722:
664:
663:
616:
615:
574:
539:
536:
533:
532:
530:
510:
507:
504:
503:
501:
486:
483:
480:
479:
477:
437:
432:
427:
417:
413:(true positive)
412:
407:
391:
385:
373:
370:
367:
366:
364:
344:
341:
338:
337:
335:
320:
317:
314:
313:
311:
263:
258:
253:
243:
239:(true positive)
238:
233:
217:
211:
206:
201:
156:(also known as
150:
142:Bayes's theorem
120:(e.g., general
112:, is a type of
82:
71:
65:
62:
51:
39:
35:
28:
23:
22:
15:
12:
11:
5:
5540:
5538:
5530:
5529:
5524:
5519:
5514:
5509:
5499:
5498:
5492:
5491:
5489:
5488:
5477:
5474:
5473:
5470:
5469:
5466:
5465:
5463:
5462:
5457:
5452:
5451:
5450:
5440:
5435:
5430:
5425:
5416:
5411:
5404:
5399:
5392:
5386:
5383:
5382:
5380:
5379:
5372:
5367:
5362:
5357:
5356:
5355:
5342:
5340:
5331:
5322:
5321:
5318:
5317:
5315:
5314:
5313:
5312:
5298:
5293:
5288:
5287:
5286:
5277:
5270:
5268:Accomplishment
5259:
5256:
5255:
5253:
5252:
5247:
5240:
5235:
5230:
5225:
5224:
5223:
5216:
5215:
5214:
5197:
5191:
5189:
5178:
5172:
5171:
5168:
5167:
5165:
5164:
5159:
5154:
5149:
5144:
5139:
5134:
5125:
5120:
5115:
5110:
5105:
5100:
5095:
5089:
5087:
5081:
5080:
5078:
5077:
5072:
5064:
5062:
5053:
5052:
5043:
5037:
5035:
5031:
5030:
5028:
5027:
5022:
5020:Slippery slope
5017:
5012:
5007:
5006:
5005:
4995:
4994:
4993:
4986:
4976:
4975:
4974:
4963:
4961:
4955:
4954:
4952:
4951:
4946:
4941:
4939:Slippery slope
4936:
4931:
4926:
4921:
4915:
4913:
4907:
4906:
4904:
4903:
4898:
4893:
4888:
4883:
4874:
4873:
4872:
4867:
4865:Cherry picking
4857:
4851:
4849:
4843:
4842:
4840:
4839:
4834:
4828:
4826:
4818:
4817:
4815:
4814:
4809:
4804:
4798:
4796:
4790:
4789:
4787:
4786:
4781:
4776:
4775:
4774:
4763:
4761:
4755:
4754:
4752:
4751:
4746:
4733:
4732:
4731:
4721:
4711:
4709:
4705:
4704:
4702:
4701:
4696:
4691:
4686:
4681:
4676:
4671:
4665:
4663:
4656:
4650:
4649:
4646:
4645:
4643:
4642:
4637:
4632:
4627:
4622:
4617:
4612:
4607:
4602:
4596:
4594:
4588:
4587:
4585:
4584:
4579:
4574:
4569:
4563:
4561:
4554:
4553:
4551:
4550:
4545:
4540:
4535:
4530:
4525:
4519:
4517:
4507:
4501:
4500:
4489:
4487:
4486:
4479:
4472:
4464:
4455:
4454:
4452:
4451:
4446:
4439:
4436:
4435:
4433:
4432:
4427:
4422:
4416:
4414:
4413:Bias reduction
4410:
4409:
4407:
4406:
4401:
4396:
4391:
4389:Political bias
4386:
4381:
4380:
4379:
4374:
4369:
4364:
4359:
4354:
4349:
4344:
4334:
4329:
4324:
4319:
4317:Infrastructure
4314:
4309:
4304:
4299:
4292:
4287:
4281:
4279:
4275:
4274:
4272:
4271:
4266:
4261:
4256:
4251:
4246:
4241:
4236:
4234:Self-selection
4231:
4226:
4221:
4216:
4211:
4206:
4201:
4196:
4191:
4186:
4185:
4184:
4174:
4169:
4164:
4158:
4156:
4150:
4149:
4147:
4146:
4141:
4136:
4131:
4126:
4121:
4116:
4111:
4106:
4101:
4096:
4091:
4086:
4081:
4076:
4071:
4069:Pro-innovation
4066:
4061:
4056:
4054:Overton window
4051:
4046:
4041:
4036:
4031:
4026:
4021:
4016:
4011:
4006:
4001:
3996:
3991:
3986:
3981:
3976:
3971:
3966:
3961:
3956:
3951:
3946:
3941:
3936:
3935:
3934:
3924:
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:
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4214:Participation
4212:
4210:
4207:
4205:
4202:
4200:
4197:
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4192:
4190:
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4183:
4182:Psychological
4180:
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3949:Fading affect
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3042:0-470-99007-4
3038:
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3019:
3017:0-521-62749-4
3013:
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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:
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2662:
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2647:
2631:
2622:
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2608:on 2016-04-16
2607:
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2455:
2451:
2450:Sageman, Marc
2445:
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2258:
2254:
2253:OSF Preprints
2247:
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2239:
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2222:
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2209:
2205:
2201:
2197:
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2042:
2039:
2033:
2030:
2027:
2024:
2021:
2018:
2012:
2009:
2007:
2004:
2001:
2000:Data dredging
1998:
1996:
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1988:
1986:
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1980:
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1557:
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1547:
1542:
1538:
1534:
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1531:O. J. Simpson
1527:
1519:
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1500:
1494:
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1483:
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1272:
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1257:
1217:
1193:
1190:
1184:
1181:
1155:
1131:
1128:
1122:
1119:
1113:
1107:
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1092:
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1006:
983:
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947:
921:
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900:
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868:
861:
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827:
799:
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728:
721:
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695:
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669:
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658:
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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:
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454:
451:
448:
445:
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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:
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241:
236:
231:
230:
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223:
220:
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214:
208:
203:
198:
196:
194:
190:
186:
181:
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171:
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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) Ă—
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
4167:Forecast
4079:Response
4039:Optimism
4034:Omission
4029:Normalcy
3999:In-group
3994:Implicit
3907:Cultural
3811:Affinity
3647:12044739
3601:11124351
3566:57761146
3511:11934777
3462:18817707
3427:11147078
3419:11561916
3367:21412897
3318:33050943
3310:11188724
3265:16281385
3217:18631755
3193:: 1–73.
3164:17835457
3121:31741077
3113:17963533
3078:53343238
3064:: 1–17.
2985:17835457
2942:17786757
2881:(1980).
2833:15367318
2748:15367318
2598:Reporter
2545:27398389
2313:steroids
2089:Archived
1989:See also
1979:a priori
1666:a priori
1633:a priori
1629:a priori
1624:a priori
1400:0.019627
1318:0.05095.
636:0.019627
395:Infected
374:30 + 400
339:100 – 40
221:Infected
199:Examples
94:COVID-19
5305:Novelty
5280:Poverty
5142:Loyalty
5108:Novelty
5085:Emotion
5034:Appeals
5003:Inverse
4983:Cum hoc
4972:Furtive
4490:Common
4444:General
4442:Lists:
4377:Ukraine
4302:Funding
4064:Present
4049:Outcome
3954:Framing
3655:9595672
3609:8588451
3502:1122766
3358:6464912
3280:Science
3144:Bibcode
3136:Science
2965:Bibcode
2957:Science
2661:likely.
2536:4934658
2515:Bibcode
2208:1393631
1793:(drunk|
1712:called
1662:Salford
1392:0.05095
543:
540:20 + 49
531:
514:
505:100 – 2
502:
500:1000 Ă—
490:
478:
476:1000 Ă—
377:
365:
348:
336:
334:1000 Ă—
324:
312:
310:1000 Ă—
178:overall
114:fallacy
5390:Cliché
5325:Other
5296:Nature
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