2303: Error Types

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Error Types
Type IIII error: Mistaking tally marks for Roman numerals
Title text: Type IIII error: Mistaking tally marks for Roman numerals

Explanation[edit]

This comic is another comic in a series of comics related to the 2020 pandemic of the coronavirus SARS-CoV-2, which causes COVID-19.

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.


Explanation of error types
Type Description Explanation
Type I False positive 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.
Type II False negative 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.
Type III 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 himself to have COVID-19 but incorrectly believes so on the basis of living near a 5G tower.
Type IV 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 himself to not have COVID-19 but incorrectly attributes this result to wearing a tinfoil hat.
Type V 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.
Type VI 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. 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.
Type VII 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.
Type VIII 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.)
Type IX The Rise of Skywalker Star Wars: The Rise of Skywalker is the ninth and final film in the Star Wars Skywalker saga. It 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.
Type IIII 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.

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.

Transcript[edit]

[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

Trivia[edit]

  • 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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Discussion

As of the time of this post, the title text is "Type IIII error: Mistaking tally marks for Roman neumerals". Is "neumerals" a typo, or is there a joke in there that I'm missing? Cosmogoblin (talk) 22:52, 6 May 2020 (UTC)

Looks like a typo to me. Randall's patrons should have caught this for him!
ProphetZarquon (talk) 23:07, 6 May 2020 (UTC)
That particular mistake is actually just called a type error.
162.158.62.221 23:12, 6 May 2020 (UTC)
"Not sure if humorous or just wrong..." to paraphrase a Fry meme... It does appear to be a typographical error; Though I suppose it could be a misspelling?
ProphetZarquon (talk) 17:46, 9 May 2020 (UTC)
Or, surely, a Type-0. 162.158.159.82 01:09, 7 May 2020 (UTC)
I am Type-O and as a Type-O Negative, I'm VERY popular at the blood bank! (Universal Donor) 108.162.216.48 01:25, 7 May 2020 (UTC)
Actually, that's an over-simplification. Type-O-neg is only universal for whole blood donations, and only truly universal for whole blood if you are also CMV-negative. For plasma donations, Type-AB (both -pos and -neg) are universal donors. For platelets, only Type-AB-pos is universal donor. 162.158.74.81 16:11, 7 May 2020 (UTC)
When I play Type-O Negative at the blood bank I get asked to turn it down. I'm sure it's loud enough to wake the dead, but the vampires should be glad I woke them in time to make a withdrawal.</badjokes>
Side note, my last name starts with O, so I sign high-score boards with 00O.
ProphetZarquon (talk) 17:46, 9 May 2020 (UTC)
I was hoping it could be bent to be a tribute to John von Neumann. 172.68.189.223 05:00, 7 May 2020 (UTC)
Looks like same type of typo he made at word "blag": [Intentional.] 172.69.54.189 08:04, 7 May 2020 (UTC)
Perhaps a reference to Neumes? 162.158.158.211 09:47, 7 May 2020 (UTC)
But according to [1530] this is an impossible typo to make ?!? Gunterkoenigsmann (talk) 07:27, 24 May 2020 (UTC)

108.162.216.48 01:24, 7 May 2020 (UTC) The explanation builds on definitions of terms in statistics. That's fine, but there are also non-statistical usages, just for example whether someone has now (or had before) the COVID-19 virus. A false positive is a test result which incorrectly indicates that a particular condition or attribute is present, and a false negative is a test result which incorrectly indicates that a particular condition or attribute is absent. A particular test is useful when its incidence of Type I and II errors is low. Types III and IV in that context would be given by poorly designed tests which, even if they give correct results, do it for unsupportable reasons and are therefore unreliable for future results. Types V, VI, VII, and VIII are necessary fillers in the sequence, once you decide that calling The Rise of Skywalker a mistake has to be error type IX simply because it's the ninth film in the series. JohnB (talk) 00:54, 7 May 2020 (UTC)

I could convince myself that the errors are a reference to each Star Wars movie. Definitely a stretch but I'd believe it. 162.158.106.24 02:00, 7 May 2020 (UTC)

Surely an Error of the Third Kind is when an Alien gets lost and lands on Earth. Arachrah (talk) 11:28, 7 May 2020 (UTC)

Can we please stop categorizing every comic about scientific research and methods as COVID-19 related? This is getting quite silly.162.158.187.201 14:31, 7 May 2020 (UTC)

While some members of the public this year are hearing about false positive and false negative for the first time in connection with SARS-COV2 and swab testing, usually in some counterfactual argument that getting tested now increases the probability that you got infected last week or something - I don't see that coronavirus needs to be mentioned in an explanation of the comic, given that it's xkcd and science happens here all the time. If this script ran in Arlo & Janis then a justification like that would be required... although today (May 7th) they're discussing Pavlov's dogs... is there a web page that explains Arlo & Janis? Robert Carnegie [email protected] 162.158.158.225 01:26, 8 May 2020 (UTC)

I spent some time musing about whether the Skywalker saga could be taken as an exemplar of each of the types (e.g. the hypothesis for #1 is that Anakin Skywalker could bring balance to the Force, and the experiment was assigning him a tutor), but it's a stretch. I do like the idea that #9 is the epitome of errordom.16:07, 7 May 2020 (UTC)

I suspect that people who like Episode IX would disagree, but I haven't found evidence that they even exist, so I can't say for sure. GreatWyrmGold (talk) 22:02, 7 May 2020 (UTC)

I'm not sure where this would fit in, but a correct answer that is viewed by the experimenter as being incorrect because of a misunderstanding, so that he changes the recording of the measurement, resulting in an incorrect measurement that he view as correct. This happened in a college classroom exercise involving Reynolds numbers. Above a certain value of Reynold's number, laminar flow will change to turbulent flow. However, that number is not where the change occurs but where laminar flow becomes unstable. One student changed all the measurements to indicate that the flow changed to turbulent almost immediately. I wondered what could have sped up the transition, thinking of things like loud noises and vibrations affecting the apparatus. The student immediately and loudly yelled that he "hadn't changed the numbers", with the vehemence indicating that he had actually changed the numbers. One problem with analog meters was that some people staring at the meters actually thought that the needle moved when it actually hadn't. Digital meters with automatic logging tended to get rid of this problem. 17:17, 7 May 2020 (UTC)

Everyone knows that of all the Reynolds numbers, only two actually matter. Burt and Debbie. (You're gonna say Ryan as well, I suppose...) 162.158.159.82 00:12, 8 May 2020 (UTC)

Wikipedia on Roman Numerals says: at some early time the Romans started to use the shorter forms IV and IX. But originally their numbers included 4 as IIII and 9 as VIIII. I wasn't sure if the Roman Empire used IV and IX at all, and I still am not sure, but if the change came early, so called, then I guess so. I wonder if there's a particular issue of stone cracking if you try to carve IIII on it, or it takes longer. Robert Carnegie [email protected] 162.158.159.74 01:36, 8 May 2020 (UTC)

IIII is a clock error.172.69.63.173 23:13, 8 May 2020 (UTC)

I notice in the wikipedia article for type III errors, which mentions several people's proposed definitions, some of them mention one not listed here: a correct answer, but they were investigating the wrong question to begin with.--162.158.74.81 17:58, 9 May 2020 (UTC)

Roman numerals are tally marks. Duh. —Kazvorpal (talk) 20:09, 16 May 2020 (UTC)