Survivorship Bias

Abraham Wald

rhine zener

Survivorship 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. The concept applies to actual people (e.g. subjects in a medical study), as well as companies, or anything that must make it past some selection process to be considered further (e.g. job applicants).

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 always have some special property, rather than just benefiting from coincidence. For example, if the 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.

In finance, survivorship bias often causes the results of studies to skew higher because only companies which are 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.

Survivorship 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, 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 survivor bias in subject selections. He was accused of failing to take into account the large effective size of his sample (all the people he didn’t choose as ‘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.

In discussing the Rhine case, science writer Martin Gardner explained that he didn’t 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.’

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 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 the advertisement either fails to disclose the existence of relevant differences between the two populations or describes them in insufficient detail; 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 the company offering the product or service charges a fee for the privilege of attempting to become a customer (especially if is non-refundable or not disclosed in the advertisement).

For example, the advertisements of online dating service 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, 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. However, the company doesn’t 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.

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