Survivorship bias

Survivorship bias, or survival bias, is the logical error of concentrating on the people or things that "survived" some process and inadvertently overlooking those that did not because of their lack of visibility. This can lead to false conclusions in several different ways. The survivors may be actual people, as in a medical study, or could be companies or research subjects or applicants for a job, or anything that must make it past some selection process to be considered further.

Survivorship bias can lead to overly optimistic beliefs because failures are ignored, 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. For example, if three of the five students with the best college grades went to the same high school, that can lead one to believe that the high school must offer an excellent education. This could be true, but the question cannot be answered without looking at the grades of all the other students from that high school, not just the ones who "survived" the top-five selection process.

Survivorship bias is a type of selection bias.

Examples

In finance

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 which 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, 90% 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.

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). 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, when 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, applying entry and exit dates to gain the appropriate return during inclusion in the index, would allow for a bias-free output.

Financial writer Nassim Taleb called the survivorship bias "silent evidence" in his book The Black Swan.

In the military

During World War II, the statistician Abraham Wald took survivorship bias into his calculations when considering how to minimize bomber losses to enemy fire. Researchers from the Center for Naval Analyses had conducted a study of the damage done to aircraft that had returned from missions, and had recommended that armor be added to the areas that showed the most damage. Wald noted that the study only considered the aircraft that had survived their missions — the bombers that had been shot down were not present for the damage assessment. The holes in the returning aircraft, then, represented areas where a bomber could take damage and still return home safely. Wald proposed that the Navy instead reinforce the areas where the returning aircraft were unscathed, since those were the areas that, if hit, would cause the plane to be lost.

In 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. 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.

Another possible explanation for this phenomenon would be survivorship bias. The fact that cats who 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.

As a general experimental flaw

Survivorship bias (or survivor bias) is a statistical artifact in applications outside finance, where studies on the remaining population are fallaciously compared with the historic average despite the survivors having unusual properties. Mostly, the unusual property in question is a track record of success (like the successful funds).

For example, the parapsychology researcher Joseph Banks Rhine believed he had identified the few individuals from hundreds of potential subjects who had powers of ESP. His calculations were based on the improbability of these few subjects guessing the Zener cards shown to a partner by chance.

A major criticism which 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 the track record of success he had found purely by chance.

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 naïveté, 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 typical 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:

"Eventually, 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".

If enough 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. 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".

Survivorship bias is one of the issues discussed in the provocative 2005 paper "Why Most Published Research Findings Are False".

In business law

Survivorship bias can raise truth-in-advertising problems when the success rate advertised for a product or service is measured with respect to a population whose makeup differs from that of the target audience whom the company offering that product or service targets with advertising claiming that success rate. These problems become especially significant when

1. the advertisement either fails to disclose the existence of relevant differences between the two populations or describes them in insufficient detail;
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 pass this test because they fail the first two prongs but not the third: 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 who possess traits that increase their likelihood of finding and maintaining relationships and lack traits that pose obstacles to their doing so (1), and 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 (2), but the company does not charge a fee for administration of its pre-screening test, with the effect that its prospective customers face no "downside risk" other than losing the time and expending the effort involved in completing the pre-screening process (negating 3).

Similarly, many investors believe that chance is the main reason that most successful fund managers have the track records they do.

See also

• Econometrics
• Fooled by Randomness by Nassim Nicholas Taleb
• Meta-analysis
• Multiple comparisons problem
• Selection bias
• Selection principle
• Texas sharpshooter fallacy