Survivorship bias

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Survivorship bias or survival bias is the logical error of concentrating on entities that passed a selection process while overlooking those that did not. This can lead to incorrect conclusions because of incomplete data.

Contents

A popular visual representation of survivorship bias. This demonstrative diagram shows where WW2-era planes were hit but could still return home. Hits are disproportionally present in areas not vital for returning home safely, therefore exhibiting survivorship bias. Survivorship-bias.svg
A popular visual representation of survivorship bias. This demonstrative diagram shows where WW2-era planes were hit but could still return home. Hits are disproportionally present in areas not vital for returning home safely, therefore exhibiting survivorship bias.

Survivorship bias is a form of selection bias that can lead to overly optimistic beliefs because multiple failures are overlooked, such as when companies that no longer exist are excluded from analyses of financial performance. It can also lead to the false belief that the successes in a group have some special property, rather than just coincidence as in correlation "proves" causality.

Another kind of survivorship bias would involve thinking that an incident happened in a particular way because the only people who were involved in the incident who can speak about it are those who survived it. Even if one knew that some people are dead, they would not have their voice to add to the conversation, making it biased.

As a general experimental flaw

The parapsychology researcher Joseph Banks Rhine believed he had identified the few individuals from hundreds of potential subjects who had powers of extra-sensory perception (ESP). His calculations were based on the improbability of these few subjects guessing the Zener cards shown to a partner by chance. [1] A major criticism that surfaced against his calculations was the possibility of unconscious survivorship bias in subject selections. He was accused of failing to take into account the large effective size of his sample (all the people he rejected as not being "strong telepaths" because they failed at an earlier testing stage). Had he done this he might have seen that, from the large sample, one or two individuals would probably achieve purely by chance the track record of success he had found.

Writing about the Rhine case in Fads and Fallacies in the Name of Science , Martin Gardner explained that he did not think the experimenters had made such obvious mistakes out of statistical naivety, but as a result of subtly disregarding some poor subjects. He said that, without trickery of any kind, there would always be some people who had improbable success, if a large enough sample were taken. To illustrate this, he speculates about what would happen if one hundred professors of psychology read Rhine's work and decided to make their own tests; he said that survivor bias would winnow out the typically failed experiments, but encourage the lucky successes to continue testing. He thought that the common null hypothesis (of no result) would not be reported, but "[e]ventually, one experimenter remains whose subject has made high scores for six or seven successive sessions. Neither experimenter nor subject is aware of the other ninety-nine projects, and so both have a strong delusion that ESP is operating." He concludes "The experimenter writes an enthusiastic paper, sends it to Rhine who publishes it in his magazine, and the readers are greatly impressed." [2]

If sufficiently many scientists study a phenomenon, some will find statistically significant results by chance, and these are the experiments submitted for publication. Additionally, papers showing positive results may be more appealing to editors. [3] This problem is known as positive results bias, a type of publication bias. To combat this, some editors now call for the submission of "negative" scientific findings, where "nothing happened". [4]

Survivorship bias is one of the research issues brought up in the provocative 2005 paper "Why Most Published Research Findings Are False", which shows that a large number of published medical research papers contain results that cannot be replicated. [3]

One famous example of immortal time bias was discovered in a study by Redelmeier and Singh in the Annals of Internal Medicine that reported that Academy Award-winning actors and actresses lived almost four years longer than their less successful peers. [5] The statistical method used to derive this statistically significant difference, however, gave winners an unfair advantage, because it credited an Academy Award winner's years of life before winning toward survival subsequent to winning. When the data was reanalyzed using methods that avoided this "immortal time" bias, the survival advantage was closer to one year and was not statistically significant. [6]

Examples

Business, finance, and economics

In finance, survivorship bias is the tendency for failed companies to be excluded from performance studies because they no longer exist. It often causes the results of studies to skew higher because only companies that were successful enough to survive until the end of the period are included. For example, a mutual fund company's selection of funds today will include only those that are successful now. Many losing funds are closed and merged into other funds to hide poor performance. In theory, 70% of extant funds could truthfully claim to have performance in the first quartile of their peers, if the peer group includes funds that have closed. [7]

In 1996, Elton, Gruber, and Blake showed that survivorship bias is larger in the small-fund sector than in large mutual funds (presumably because small funds have a high probability of folding). [8] They estimate the size of the bias across the U.S. mutual fund industry as 0.9% per annum, where the bias is defined and measured as:

"Bias is defined as average α for surviving funds minus average α for all funds"

(Where α is the risk-adjusted return over the S&P 500. This is the standard measure of mutual fund out-performance).

Additionally, in quantitative backtesting of market performance or other characteristics, survivorship bias is the use of a current index membership set rather than using the actual constituent changes over time. Consider a backtest to 1990 to find the average performance (total return) of S&P 500 members who have paid dividends within the previous year. To use the current 500 members only and create a historical equity line of the total return of the companies that met the criteria would be adding survivorship bias to the results. S&P maintains an index of healthy companies, removing companies that no longer meet their criteria as a representative of the large-cap U.S. stock market. Companies that had healthy growth on their way to inclusion in the S&P 500 would be counted as if they were in the index during that growth period, which they were not. Instead there may have been another company in the index that was losing market capitalization and was destined for the S&P 600 Small-cap Index that was later removed and would not be counted in the results. Using the actual membership of the index and applying entry and exit dates to gain the appropriate return during inclusion in the index would allow for a bias-free output.

Framed quotes of successful CEOs in a public library Vizag Public Library-AB 10.jpg
Framed quotes of successful CEOs in a public library

Michael Shermer in Scientific American [9] and Larry Smith of the University of Waterloo [10] have described how advice about commercial success distorts perceptions of it by ignoring all of the businesses and college dropouts that failed. [11] Journalist and author David McRaney observes that the "advice business is a monopoly run by survivors. When something becomes a non-survivor, it is either completely eliminated, or whatever voice it has is muted to zero". [12] Alec Liu wrote in Vice that "for every Mark Zuckerberg, there's thousands of also-rans, who had parties no one ever attended, obsolete before we ever knew they existed." [13]

In his book The Black Swan, financial writer Nassim Taleb called the data obscured by survivorship bias "silent evidence". [14]

History

Diagoras of Melos was asked concerning paintings of those who had escaped shipwreck: "Look, you who think the gods have no care of human things, what do you say to so many persons preserved from death by their especial favour?", to which Diagoras replied: "Why, I say that their pictures are not here who were cast away, who are by much the greater number." [15]

Susan Mumm has described how survival bias leads historians to study organisations that are still in existence more than those that have closed. This means large, successful organisations such as the Women's Institute, which were well organised and still have accessible archives for historians to work from, are studied more than smaller charitable organisations, even though these may have done a great deal of work. [16]

Architecture and construction

Just as new buildings are being built every day and older structures are constantly torn down, the story of most civil and urban architecture involves a process of constant renewal, renovation, and revolution. Only the most beautiful, useful, and structurally sound buildings survive from one generation to the next. This creates a selection effect where the ugliest and weakest buildings of history have been eradicated (disappearing from public view, leaving the visible impression that all earlier buildings were more beautiful and better built).

Highly competitive career

Whether it be movie stars, athletes, musicians, or CEOs of multibillion-dollar corporations who dropped out of school, popular media often tells the story of the determined individual who pursues their dreams and beats the odds. There is much less focus on the many people that may be similarly skilled and determined, but fail to ever find success because of factors beyond their control or other (seemingly) random events. There is also a tendency to overlook resources and events that helped enable such success, that those who failed didn't have. [17]

This creates a false public perception that anyone can achieve great things if they have the ability and make the effort. The overwhelming majority of failures are not visible to the public eye, and only those who survive the selective pressures of their competitive environment are seen regularly.

Military

This hypothetical pattern of damage of surviving aircraft shows locations where they can sustain damage and still return home. If the aircraft was reinforced in the indicated areas, this would be a result of survivorship bias because crucial data from fatally damaged planes was being ignored; those hit in other places did not survive. Survivorship-bias.svg
This hypothetical pattern of damage of surviving aircraft shows locations where they can sustain damage and still return home. If the aircraft was reinforced in the indicated areas, this would be a result of survivorship bias because crucial data from fatally damaged planes was being ignored; those hit in other places did not survive.

During World War II, the statistician Abraham Wald took survivorship bias into his calculations when considering how to minimize bomber losses to enemy fire. [18] The Statistical Research Group (SRG) at Columbia University, which Wald was a part of, examined the damage done to aircraft that had returned from missions and recommended adding armor to the areas that showed the least damage. [19] [20] [21] The bullet holes in the returning aircraft represented areas where a bomber could take damage and still fly well enough to return safely to base. Therefore, Wald proposed that the Navy reinforce areas where the returning aircraft were unscathed, [18] : 88  inferring that planes hit in those areas were the ones most likely to be lost. His work is considered seminal in the then nascent discipline of operational research. [22]

Cats

In a study performed in 1987, it was reported that cats who fall from less than six stories, and are still alive, have greater injuries than cats who fall from higher than six stories. [23] [24] It has been proposed that this might happen because cats reach terminal velocity after righting themselves at about five stories, and after this point they relax, leading to less severe injuries in cats who have fallen from six or more stories. [25] In 1996, The Straight Dope newspaper column proposed that another possible explanation for this phenomenon would be survivorship bias. Cats that die in falls are less likely to be brought to a veterinarian than injured cats, and thus many of the cats killed in falls from higher buildings are not reported in studies of the subject. [26]

Studies of evolution

Large groups of organisms called clades that survive a long time are subject to various survivorship biases such as the "push of the past", generating the illusion that clades in general tend to originate with a high rate of diversification that then slows through time. [27]

Business law

Survivorship bias can raise truth-in-advertising issues when the success rate advertised for a product or service is measured by reference to a population whose makeup differs from that of the target audience for the advertisement. This is especially important when

  1. the advertisement either fails to disclose the relevant differences between the two populations, or describes them in insufficient detail; and
  2. these differences result from the company's deliberate "pre-screening" of prospective customers to ensure that only customers with traits increasing their likelihood of success are allowed to purchase the product or service, especially when the company's selection procedures or evaluation standards are kept secret; and
  3. the company offering the product or service charges a fee, especially one that is non-refundable or not disclosed in the advertisement, for the privilege of attempting to become a customer.

For example, the advertisements of online dating service eHarmony.com fail a truth in advertising test because they fail the first two prongs and pass the third, when all three must be passed:

  1. they claim a success rate significantly higher than that of competing services while generally not disclosing that the rate is calculated with respect to a viewership subset of individuals who possess traits that increase their likelihood of finding and maintaining relationships and lack traits that pose obstacles to their doing so, and
  2. the company deliberately selects for these traits by administering a lengthy pre-screening process designed to reject prospective customers who lack the former traits or possess the latter ones, but
  3. the company does not charge a fee for administration of its pre-screening test; thus its prospective customers face no "downside risk" other than wasting their time, expending the effort involved in completing the pre-screening process, [28] and suffering disappointment.

See also

Related Research Articles

The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the belief that, if an event has occurred more frequently than expected, it is less likely to happen again in the future. The fallacy is commonly associated with gambling, where it may be believed, for example, that the next dice roll is more than usually likely to be six because there have recently been fewer than the expected number of sixes.

In statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. It results in a biased sample of a population in which all individuals, or instances, were not equally likely to have been selected. If this is not accounted for, results can be erroneously attributed to the phenomenon under study rather than to the method of sampling.

<span class="mw-page-title-main">Statistics</span> Study of the collection, analysis, interpretation, and presentation of data

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.

<span class="mw-page-title-main">Ganzfeld experiment</span> Pseudoscientific test for extrasensory perception (ESP)

A ganzfeld experiment is an assessment used by parapsychologists that they contend can test for extrasensory perception (ESP) or telepathy. In these experiments, a "sender" attempts to mentally transmit an image to a "receiver" who is in a state of sensory deprivation. The receiver is normally asked to choose between a limited number of options for what the transmission was supposed to be and parapsychologists who propose that such telepathy is possible argue that rates of success above the expectation from randomness are evidence for ESP. Consistent, independent replication of ganzfeld experiments has not been achieved, and, in spite of strenuous arguments by parapsychologists to the contrary, there is no validated evidence accepted by the wider scientific community for the existence of any parapsychological phenomena. Ongoing parapsychology research using ganzfeld experiments has been criticized by independent reviewers as having the hallmarks of pseudoscience.

Post hoc ergo propter hoc is an informal fallacy which one commits when one reasons, "Since event Y followed event X, event Y must have been caused by event X." Its a fallacy in which an event is presumed to have been caused by a closely preceding event merely on the grounds of temporal succession. This type of reasoning is fallacious because mere temporal succession does not establish a causal connection. It is often shortened simply to post hoc fallacy. A logical fallacy of the questionable cause variety, it is subtly different from the fallacy cum hoc ergo propter hoc, in which two events occur simultaneously or the chronological ordering is insignificant or unknown. Post hoc is a logical fallacy in which one event seems to be the cause of a later event because it occurred earlier.

Statistical bias, in the mathematical field of statistics, is a systematic tendency in which the methods used to gather data and generate statistics present an inaccurate, skewed or biased depiction of reality. Statistical bias exists in numerous stages of the data collection and analysis process, including: the source of the data, the methods used to collect the data, the estimator chosen, and the methods used to analyze the data. Data analysts can take various measures at each stage of the process to reduce the impact of statistical bias in their work. Understanding the source of statistical bias can help to assess whether the observed results are close to actuality. Issues of statistical bias has been argued to be closely linked to issues of statistical validity.

<span class="mw-page-title-main">Cherry picking</span> Fallacy of incomplete evidence

Cherry picking, suppressing evidence, or the fallacy of incomplete evidence is the act of pointing to individual cases or data that seem to confirm a particular position while ignoring a significant portion of related and similar cases or data that may contradict that position. Cherry picking may be committed intentionally or unintentionally.

Selection bias is the bias introduced by the selection of individuals, groups, or data for analysis in such a way that proper randomization is not achieved, thereby failing to ensure that the sample obtained is representative of the population intended to be analyzed. It is sometimes referred to as the selection effect. The phrase "selection bias" most often refers to the distortion of a statistical analysis, resulting from the method of collecting samples. If the selection bias is not taken into account, then some conclusions of the study may be false.

Anecdotal evidence is evidence based only on personal observation, collected in a casual or non-systematic manner.

The representativeness heuristic is used when making judgments about the probability of an event being representional in character and essence of a known prototypical event. It is one of a group of heuristics proposed by psychologists Amos Tversky and Daniel Kahneman in the early 1970s as "the degree to which [an event] (i) is similar in essential characteristics to its parent population, and (ii) reflects the salient features of the process by which it is generated". The representativeness heuristic works by comparing an event to a prototype or stereotype that we already have in mind. For example, if we see a person who is dressed in eccentric clothes and reading a poetry book, we might be more likely to think that they are a poet than an accountant. This is because the person's appearance and behavior are more representative of the stereotype of a poet than an accountant.

<span class="mw-page-title-main">Planning fallacy</span> Cognitive bias of underestimating time needed

The planning fallacy is a phenomenon in which predictions about how much time will be needed to complete a future task display an optimism bias and underestimate the time needed. This phenomenon sometimes occurs regardless of the individual's knowledge that past tasks of a similar nature have taken longer to complete than generally planned. The bias affects predictions only about one's own tasks. On the other hand, when outside observers predict task completion times, they tend to exhibit a pessimistic bias, overestimating the time needed. The planning fallacy involves estimates of task completion times more optimistic than those encountered in similar projects in the past.

<span class="mw-page-title-main">Response bias</span> Type of bias

Response bias is a general term for a wide range of tendencies for participants to respond inaccurately or falsely to questions. These biases are prevalent in research involving participant self-report, such as structured interviews or surveys. Response biases can have a large impact on the validity of questionnaires or surveys.

Statistics, when used in a misleading fashion, can trick the casual observer into believing something other than what the data shows. That is, a misuse of statistics occurs when a statistical argument asserts a falsehood. In some cases, the misuse may be accidental. In others, it is purposeful and for the gain of the perpetrator. When the statistical reason involved is false or misapplied, this constitutes a statistical fallacy.

<span class="mw-page-title-main">Abraham Wald</span> Hungarian mathematician

Abraham Wald was a Jewish Hungarian mathematician who contributed to decision theory, geometry and econometrics, and founded the field of sequential analysis. One of his well-known statistical works was written during World War II on how to minimize the damage to bomber aircraft and took into account the survivorship bias in his calculations. He spent his research career at Columbia University. He was the grandson of Rabbi Moshe Shmuel Glasner.

The overconfidence effect is a well-established bias in which a person's subjective confidence in their judgments is reliably greater than the objective accuracy of those judgments, especially when confidence is relatively high. Overconfidence is one example of a miscalibration of subjective probabilities. Throughout the research literature, overconfidence has been defined in three distinct ways: (1) overestimation of one's actual performance; (2) overplacement of one's performance relative to others; and (3) overprecision in expressing unwarranted certainty in the accuracy of one's beliefs.

In social psychology, illusory superiority is a cognitive bias wherein people overestimate their own qualities and abilities compared to others. Illusory superiority is one of many positive illusions, relating to the self, that are evident in the study of intelligence, the effective performance of tasks and tests, and the possession of desirable personal characteristics and personality traits. Overestimation of abilities compared to an objective measure is known as the overconfidence effect.

The "hot hand" is a phenomenon, previously considered a cognitive social bias, that a person who experiences a successful outcome has a greater chance of success in further attempts. The concept is often applied to sports and skill-based tasks in general and originates from basketball, where a shooter is more likely to score if their previous attempts were successful; i.e., while having the "hot hand.” While previous success at a task can indeed change the psychological attitude and subsequent success rate of a player, researchers for many years did not find evidence for a "hot hand" in practice, dismissing it as fallacious. However, later research questioned whether the belief is indeed a fallacy. Some recent studies using modern statistical analysis have observed evidence for the "hot hand" in some sporting activities; however, other recent studies have not observed evidence of the "hot hand". Moreover, evidence suggests that only a small subset of players may show a "hot hand" and, among those who do, the magnitude of the "hot hand" tends to be small.

Funding bias, also known as sponsorship bias, funding outcome bias, funding publication bias, and funding effect, refers to the tendency of a scientific study to support the interests of the study's financial sponsor. This phenomenon is recognized sufficiently that researchers undertake studies to examine bias in past published studies. Funding bias has been associated, in particular, with research into chemical toxicity, tobacco, and pharmaceutical drugs. It is an instance of experimenter's bias.

<span class="mw-page-title-main">Success</span> Meeting or surpassing an intended goal or objective

Success is the state or condition of meeting a defined range of expectations. It may be viewed as the opposite of failure. The criteria for success depend on context, and may be relative to a particular observer or belief system. One person might consider a success what another person considers a failure, particularly in cases of direct competition or a zero-sum game. Similarly, the degree of success or failure in a situation may be differently viewed by distinct observers or participants, such that a situation that one considers to be a success, another might consider to be a failure, a qualified success or a neutral situation. For example, a film that is a commercial failure or even a box-office bomb can go on to receive a cult following, with the initial lack of commercial success even lending a cachet of subcultural coolness.

References

  1. ↑ Shermer, Michael (3 August 2011). "Deviations: A Skeptical Investigation of Edgar Cayce's Association for Research and Enlightenment". Skeptic.com. Retrieved 21 May 2018.
  2. ↑ Fads and Fallacies in the Name of Science, Martin Gardner, p. 303, 1957, Dover Publications Inc.
  3. 1 2 Ioannidis, J. P. A. (2005). "Why Most Published Research Findings Are False". PLoS Med . 2 (8): e124. doi: 10.1371/journal.pmed.0020124 . PMC   1182327 . PMID   16060722.
  4. ↑ Goodchild van Hilten, Lucy. "Why it's time to publish research "failures"". Elsevier Connect. Elsevier. Archived from the original on 2 June 2021. Retrieved 31 May 2021.
  5. ↑ Redelmeier, Donald A.; Singh, Sheldon M. (2001-05-15). "Survival in Academy Award–Winning Actors and Actresses". Annals of Internal Medicine. 134 (10): 955–62. doi:10.7326/0003-4819-134-10-200105150-00009. ISSN   0003-4819. PMID   11352696.
  6. ↑ Sylvestre, Marie-Pierre; Huszti, Ella; Hanley, James A. (2006-09-05). "Do Oscar Winners Live Longer than Less Successful Peers? A Reanalysis of the Evidence". Annals of Internal Medicine. 145 (5): 361–3, discussion 392. doi:10.7326/0003-4819-145-5-200609050-00009. ISSN   0003-4819. PMID   16954361. S2CID   13724567.
  7. ↑ "How to think about diversification - Page 3 - Bogleheads.org". www.bogleheads.org. Archived from the original on 2020-10-29. Retrieved 2020-10-26.
  8. ↑ Elton; Gruber; Blake (1996). "Survivorship Bias and Mutual Fund Performance". Review of Financial Studies . 9 (4): 1097–1120. doi: 10.1093/rfs/9.4.1097 . S2CID   154097782. In this paper the researchers eliminate survivorship bias by following the returns on all funds extant at the end of 1976. They show that other researchers have drawn spurious conclusions by failing to include the bias in regressions on fund performance.
  9. ↑ Michael Shermer (2014-08-19). "How the Survivor Bias Distorts Reality". Scientific American. Archived from the original on 2019-04-29. Retrieved 2015-07-20.
  10. ↑ Carmine Gallo (2012-12-07). "High-Tech Dropouts Misinterpret Steve Jobs' Advice". Forbes. Archived from the original on 2019-04-02. Retrieved 2017-09-15.
  11. ↑ Robert J Zimmer (2013-03-01). "The Myth of the Successful College Dropout: Why It Could Make Millions of Young Americans Poorer". The Atlantic. Archived from the original on 2019-04-09. Retrieved 2017-03-11.
  12. ↑ Karen E. Klein (11 August 2014). "How Survivorship Bias Tricks Entrepreneurs". Bloomberg. Archived from the original on 2016-03-07. Retrieved 2017-03-11.
  13. ↑ Alec Liu (2012-10-03). "What Happened to the Facebook Killer? It's Complicated". Motherboard - Tech by Vice.
  14. ↑ Taleb, Nassim Nicholas (2010). The Black Swan: The Impact of the Highly Improbable (2nd ed.). New York: Random House. p.  101. ISBN   9780679604181.
  15. ↑ Cicero, De Natura Deor., iii. 37.
  16. ↑ Mumm, Susan (2010). Women and Philanthropic Cultures, in Women, Gender and Religious Cultures in Britain, 1800-1940, Eds Sue Morgan and Jacqueline deVries . London: Routledge.
  17. ↑ Karen E. Klein (2014-08-11). "How Survivorship Bias Tricks Entrepreneurs". Bloomberg Business. Archived from the original on 2017-05-23. Retrieved 2017-04-11.
  18. 1 2 Wald, Abraham. (1943). A Method of Estimating Plane Vulnerability Based on Damage of Survivors. Statistical Research Group, Columbia University. CRC 432 — reprint from July 1980 Archived 2019-07-13 at the Wayback Machine . Center for Naval Analyses.
  19. ↑ Wallis, W. Allen (1980). "The Statistical Research Group, 1942-1945: Rejoinder". Journal of the American Statistical Association. 75 (370): 334–335. doi:10.2307/2287454. JSTOR   2287454.
  20. ↑ "Bullet Holes & Bias: The Story of Abraham Wald". mcdreeamie-musings. 23 April 2019. Archived from the original on 2020-04-16. Retrieved 2020-05-29.
  21. ↑ "AMS :: Feature Column :: The Legend of Abraham Wald". American Mathematical Society. Archived from the original on 2020-05-27. Retrieved 2020-05-29.
  22. ↑ Mangel, Marc; Samaniego, Francisco (June 1984). "Abraham Wald's work on aircraft survivability". Journal of the American Statistical Association. 79 (386): 259–267. doi:10.2307/2288257. JSTOR   2288257. Reprint on author's web site Archived 2019-08-17 at the Wayback Machine
  23. ↑ Whitney, WO; Mehlhaff, CJ (1987). "High-rise syndrome in cats". Journal of the American Veterinary Medical Association. 191 (11): 1399–403. PMID   3692980.
  24. ↑ "Highrise Syndrome in Cats". Archived from the original on 2015-02-21. Retrieved 2014-06-13.
  25. ↑ Falling Cats Archived 2007-07-12 at the Wayback Machine
  26. ↑ "Do cats always land unharmed on their feet, no matter how far they fall?". The Straight Dope. July 19, 1996. Archived from the original on 2012-04-16. Retrieved 2008-03-13.
  27. ↑ Budd, G. E.; Mann, R. P. (2018). "History is written by the victors: the effect of the push of the past on the fossil record" (PDF). Evolution. 72 (11): 2276–2291. doi:10.1111/evo.13593. PMC   6282550 . PMID   30257040. Archived (PDF) from the original on 2019-04-28. Retrieved 2018-12-12.
  28. ↑ Farhi, Paul (May 13, 2007). "They Met Online, but Definitely Didn't Click". Washington Post . Archived from the original on May 16, 2017. Retrieved September 15, 2017.
  29. ↑ "Archived copy" (PDF). Archived (PDF) from the original on 2019-07-05. Retrieved 2019-07-05.{{cite web}}: CS1 maint: archived copy as title (link)
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