2303: Error Types
Title text: Type IIII error: Mistaking tally marks for Roman numerals
The comic is inspired by the COVID-19 pandemic, as there is a lot of medical testing for the disease being done, including detection of the virus itself, usually by qPCR, or of antibodies present in people who have had the disease (sometimes unknowingly). The quality of these tests is often mediocre and never perfect, leading to discussion of different types of errors that can occur, including "false positives" (calling presence of the virus/antibodies when they are not really there) or false negatives (failing to see the virus/antibodies which are present). The comic is riffing on Type I and type II errors, also known as "false positive" and "false negative", respectively. The first two rows of the comic's table are correct definitions for established terms in statistics. Further rows contain suggestions for new terminology.
|A false positive is a result that indicates a correlation, when there is no correlation in reality. For example, a person may test positive (indicating that they have a disease), but in actuality they do not have the disease. Most diseases are only present in a small fraction of a population, so a test for that disease will usually produce more false positives than false negatives; this is why tests are usually not administered universally but only to patients with other diagnostic criteria, and sometimes multiple tests are used for additional certainty before embarking on serious, invasive treatments.
|A false negative is a result that indicates no correlation, when there is a correlation in reality. For example, a person may test negative (indicating that they do not have a disease), but in actuality they do have the disease. Several previous XKCD comics have been about trivial "tests" for rare conditions that always return a negative result (e.g. 2236: Is it Christmas? and 937: TornadoGuard). Because most days it is not Christmas, and most people are not near a tornado, the "test" is technically correct a high percentage of the time, but for those circumstances when the condition is true, a false negative may be extremely costly.
|True positive for incorrect reasons
|"Type III error" is a nonstandard term meant to build off the notion of type I and II errors. Randall's explanations of this and of Type IV errors line up with some relatively common definitions of them, but others have also been proposed. None have yet been widely adopted. The Type III and Type IV definitions given here correspond to the Gettier Problem in philosophy. In the case of COVID-19, this type of error might be committed by a person who correctly believes themselves to have COVID-19 but incorrectly believes so on the basis of living near a 5G tower.
|True negative for incorrect reasons
|Randall's proposed Type III and Type IV errors refer to when a correct correlation or lack thereof is determined, but on faulty grounds. Although harmless in the present, this may lead to false faith in the results at a later date, as the faulty grounds of the result may lead to a type I or type II error in different circumstances. In the case of COVID-19, this type of error might be committed by a person who correctly believes themselves to not have COVID-19 but incorrectly attributes this result to wearing a tinfoil hat.
|Incorrect result which leads you to a correct conclusion due to unrelated errors
|Here we get into errors entirely made up by Randall. The idea behind this one is that a botched statistical test might accidentally result in a true conclusion due to completely unrelated errors in the other direction--perhaps during data collection or aggregation. This could be the type of error experienced by a person whose test result is a false positive or negative, but which is then mis-typed into the electronic medical record, so that the correct result is returned to the doctor and patient after all.
|Correct result which you interpret wrong
|An unfortunately common occurrence. For example, statistical tests on observational data can only determine correlation, not causation, yet press releases and subsequent popular articles often imply or explicitly state a causal relationship ("Jelly beans cause acne!" or whatnot). This has actually been proposed as a definition of a Type IV error. Coincidentally, "Type VI" could be misread as "Type IV", making an incorrect reading be interpreted as the older definition of Type IV (which would, ironically, be a Type V error). Some kinds of coronavirus antibody tests have been found to return positive if the patient has ever had an infection by any coronavirus (e.g. some common colds), not just SARS-CoV-2, so the patient could test positive but incorrectly attribute that result to COVID-19.
|Incorrect result which produces a cool graph
|It is commonly believed that data is beautiful. Sometimes, that's still true even when the data is bogus! A few days after this comic was released (May 9th), the Georgia Department of Public Health published a graph purporting to show a decline in cases of COVID-19 over the previous two weeks, but which had actually been arranged so that the days were ordered by decreasing cases, rather than by time.
|Incorrect result which sparks further research and the development of new tools which reveal the flaw in the original results while producing novel correct results
|A hypothetical example might be if the Fleischmann–Pons cold fusion experiment, discredited as it was, had by its investigation successfully prompted the discovery of a truly usable alternate technique. (So far, in reality, it seems not to have.)
|The Rise of Skywalker
|Star Wars: The Rise of Skywalker is the ninth and final film in the Star Wars Skywalker saga, usually written using Roman numerals as Episode IX. It was received far less critical acclaim than the previous two films in the sequel trilogy. The poor reviews suggest that the movie as a whole could be considered an error. Closing with an "error" that refers to Star Wars and has no discussion of statistics also serves as a non sequitur punchline.
|Mistaking tally marks for Roman numerals
|Title text. "I", "II", and "III" could be representations of the numbers one, two, and three in either tally marks or Roman numerals. It's only when you get to "IV" or "IIII" that it becomes apparent which system is being used. Some clocks use Roman numerals but with "IIII" instead of "IV" at the four o'clock position; the exact reason for this is unknown, but several plausible hypotheses have been advanced.
Additionally, before the adoption of the printing press, "IIII" was the standard way of writing "4" in Roman numerals.
Coincidentally, Randall seemed to have initially made a typographical error of his own in this title text spelling the word "numerals" as "neumerals". The error has since been corrected.
- [A list with nine entries. The left side has 9 types of errors numbered with Roman numerals. The right side has a description of each type of error:]
- Type I Error: False positive
- Type II Error: False negative
- Type III Error: True positive for incorrect reasons
- Type IV Error: True negative for incorrect reasons
- Type V Error: Incorrect result which leads you to a correct conclusion due to unrelated errors
- Type VI Error: Correct result which you interpret wrong
- Type VII Error: Incorrect result which produces a cool graph
- Type VIII Error: Incorrect result which sparks further research and the development of new tools which reveal the flaw in the original results while producing novel correct results
- Type IX Error: The Rise of Skywalker
- Randall seems to have, ironically, made a typographical error of his own when spelling the word "numerals" in the title text.
- This was corrected later, but initially, the title text was: "Type IIII error: Mistaking tally marks for Roman neumerals."
- This may be intentionally mispronouncing, because of his hobby.
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