====== Spurious accuracy ====== A statistical indicator is presented with a level of precision that cannot be justified by the measured data. This error can probably best be explained by the following joke: > During a guided tour of a natural history museum, the guide explains: “This dinosaur skeleton is 100 million and 5 years old!” > A visitor asks: “How can you know that so precisely?” > He replies: “Well, I was told it was 100 million years old when I started here – and that was five years ago.” Clearly, the figure of “100 million years” is not nearly as precise as the “5 years” that the museum guide simply added to it. This overly precise total is therefore misleading. ===== Other names ===== * False precision * Overprecision * Drama digits ===== Description ===== It may be tempting to give one’s figures a veneer of “scientific precision” by presenting them to several decimal places. Even more so if one can even back up these figures with observation data. However, stating such a supposedly “precise” figure also implies a level of accuracy and methodological reliability that may not actually be justified. Such an error typically arises when figures with different levels of precision are combined, or when a factor of uncertainty (such as the [[wp>Margin of error|margin of error]]) is ignored. It would be sensible to reflect the uncertainty in the data by the way the figures are presented. This can be done by actually stating the margin of error, or by specifying a range of possible values (such as “approximately 350 to 400”), or indeed by using a rounded figure instead of an overly precise one. ===== Examples ===== ==== Budget planning for building a house ==== The budget for building a private house might look something like this: ^ Construction | € 350 000.—| ^ Land | € 80 000.—| ^ Service connection | € 12 000.—| ^ Refreshments for construction workers | € 145.—| ^ Land Registry stamp duty | € 4.16| ^ TOTAL | **€ 442 149.16**| Even without ever having been involved in the construction of a house yourself, it is easy to see that the total price of exactly **€ 442 149.16** surely cannot be accurate to such a degree: it is more likely that the construction costs will amount to only //around// 350 000 euros (anyone with experience in this field would say: rather //significantly// more!). Stating the total price down to the last cent is therefore misleading, as it gives the impression of a level of precision that isn’t really justified. In this case, a more appropriate estimate would probably be “around 450 thousand”. ==== Vaccine efficacy ==== The manufacturer of a new vaccine stated in its press release that the vaccine has an “efficacy of 94.5 %”.(([[wp>Moderna|Moderna]] press release dated 16 November 2020: [[https://web.archive.org/web/20201116215012/https://investors.modernatx.com/news-releases/news-release-details/modernas-covid-19-vaccine-candidate-meets-its-primary-efficacy|Moderna’s COVID-19 Vaccine Candidate Meets its Primary Efficacy Endpoint in the First Interim Analysis of the Phase 3 COVE Study]], archived on the same day.)) Indeed, tests conducted on around 30 000 participants had identified 95 cases of the disease by the time of the announcement, 90 of which were in the control group and 5 in the treatment group. This actually corresponds to an efficacy of 94.5 %. Whilst this undoubtedly points to the vaccine’s high effectiveness, presenting the figure to one decimal place suggests that it can be determined with a level of accuracy that is not justified given the very low number of cases. In fact, we are only seeing an interim result at a very specific point in time; if just one more person falls ill the next day (whether in the control or the experimental group), the percentage will shift significantly. It would therefore have made more sense to state it like: “well over 90 %”. ==== Body temperature ==== As we have all surely learnt at school, the [[wp>Thermoregulation#Normal_human_temperature|normal body temperature for humans]] is 37 °C (degrees [[wp>Celsius|Celsius]]). Similarly, schoolchildren in North America are taught that the normal body temperature is 98.6 °F (degrees [[wp>Fahrenheit|Fahrenheit]]); and indeed, 98.6 °F is exactly 37 °C. However, the normal body temperature is only //around// 37 °C. In fact, it typically fluctuates between approximately 36.3 and 37.4 °C (approx. 97 to 99 °F) over the course of the day and can also be significantly higher (for example, in the brain) or lower in certain parts of the body (e.g. in the toes). The conversion from //Celsius// to //Fahrenheit// has therefore introduced a fractional digit, which suggests a level of accuracy that was not implied by the original figure and which does not accurately reflect the reality. It would probably be better to state the normal temperature as 98 °F. This corresponds to 36.7 °C, which is close enough to the average. ==== Cold sensitivity of plants ==== A website providing information on //plants// took the opposite approach. Regarding a specific plant (a [[wp>Acer japonicum|Japanese maple]]), it stated: > Frost-hardy down to ‑17.8 °C That is a remarkably //precise// figure. Does that mean the plant dies at exactly ‑17.9 °C? Probably not. The figure “‑17.8 °C” given corresponds almost exactly to 0 °F (rounded to one decimal place). It is likely that the figure was simply taken from a US source and converted in this way. Moreover, there is evidence to suggest that the figure given in the source was already incorrect: In its native Japan, this tree species also grows in the often much harsher climate of the northern island of [[wp>Hokkaido|Hokkaido]]. It is likely that the figure of “0 °F” was simply a placeholder value that would never be reached in the Southern US anyway. ==== Ussher’s Date of Creation ==== In the mid-17th century, the Irish theologian [[wp>James Ussher|James Ussher]] had concluded, on the basis of a detailed analysis of the Old Testament, that the world had been created on 23 October 4004 BC. To this end, he drew on the [[wp>Genealogy|genealogies]] – that is, family trees – which are abundant in the Bible, as well as the reigns of kings, and filled in the (numerous!) gaps with somewhat bold assumptions and theological considerations. This led him to a rather //vague// (and, as we now know, also //wildly inaccurate//) estimate of //around four millennia// before the birth of Christ. However, even in Ussher’s time it was already known that the basis of our calendar must be flawed, as [[wp>Herod the Great|King Herod]], who plays an important role in the biblical narrative, had already died in 4 BC. Ussher therefore added these four years to his calculation, arriving at 4004 BC. He went on to deduce that, as the [[wp>Hebrew calendar|Hebrew calendar]] begins with [[wp>Tishrei|Tischrei]] [תִּשְׁרֵי] in autumn, the Creation must have taken place on 23 October of that year((A further clarification – namely that creation must have begun at 9 o’clock in the morning – comes from another source.)). The mixing of very vague and very precise data follows a pattern very similar to the one we saw above in the equally absurd calculation of house-building costs. ===== See also ===== * [[abstraction:index|Fallacies of abstraction]] * [[knowledge:epistemic_fallacy|Epistemic fallacy]] * [[mathematics:statistics:misrepresentations:relational|Relational error]] ===== Further information ===== * [[wp>False precision]] on //Wikipedia// * [[https://www.fallacyfiles.org/fakeprec.html|Overprecision]] on //Fallacy Files// {{page>templates:banner#Short-BG-Article&noheader&nofooter}}