2696: Precision vs Accuracy

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Precision vs Accuracy
'Barack Obama is much less likely than the average cat to jump in and out of cardboard boxes for fun' is low precision, but I'm not sure about the accuracy.
Title text: 'Barack Obama is much less likely than the average cat to jump in and out of cardboard boxes for fun' is low precision, but I'm not sure about the accuracy.

Explanation[edit]

Ambox notice.png This explanation may be incomplete or incorrect: Created by BARACK OBAMA IN A CARDBOARD BOX. Further detail, sortable table? - PLEASE CHANGE THIS COMMENT WHEN EDITING THIS PAGE. Do NOT delete this tag too soon.
If you can address this issue, please edit the page! Thanks.

This comic parodies the difference between 'accuracy' and 'precision' with a table. Accuracy and precision are common concepts to be encountered in the scientific field and often students have issues with the differences between them. Accuracy concerns whether a statement is true, while precision concerns how detailed it is; it is possible for a statement to be one but not the other. The comic explores this concept by comparing Barack Obama, former President of the United States, with cats. Confusingly, he measures different statistics of both Barack Obama and cats (sometimes measuring them in terms of cats) leaving the unwary reader even more confused.

Being precise is typical of calculations that roll out an excess of significant digits, often in the form of trailing decimals. Precision is lowered by using more rounded figures, or merely being comparative, but largely unaffected by whether the original values used were accurate or even correct. Accuracy is a cumulative function of the accuracy given to the intermediate values used for any calculation, and can be degraded by using figures that are themselves in some way inaccurate or imprecise. One part of confusion between the two is because being too precise usually decreases accuracy.

The numbers mentioned in the top row (high precision) of the table all use exactly the same digits, dictating that a full five digits of precision are used in them all. The most "valid" or correct value is a number that's very accurate and precise (see table). For the medium accuracy the number is an anagram of the 1st entry, giving a value that is reasonable but would be overly exact, whilst the low accuracy number is just a repeat of the first entry's digits with a shifted decimal but clearly at the wrong scale, as Randall could have shifted the decimal point one further place to the left to be closest to the true measurement. Instead, he replaces the thousands separator with the decimal point, perhaps for the visual pun.

The title text compares Obama's and cats' enjoyment of playing with cardboard boxes. While cats are known to do this,[citation needed] we don't know whether Obama does.

The day prior to the publication of this comic (November 8, 2022) was election day in the United States, so Randall may have been remembering Barack Obama's presidency at this time.

Precision Accuracy Statement Explanation
High High Barack Obama was president for 70,128 hours This is the official length in hours of Barack Obama's 8-year presidency, including 2 leap days. Obama served from January 20, 2009 through January 20, 2017, and his term officially began and ended at noon on those days. (There were three leap seconds during his presidency, though.)
High Medium Barack Obama weighs as much as 17.082 cats The accuracy would depend on the mass of the cats in question. Also a human's mass can vary by a few pounds in a small amount of time as meals are consumed, resources are used in metabolism and wastes are eliminated, and thus this may be overly precise due the margin of error in both the mass of cats and the mass of Mr. Obama. In 2016, Obama was officially reported to weigh 175 lb (79.3787 kg). Google claims that an average cat weighs between 8.8 and 11 lbs, so this statement may be close to accurate.
High Low Barack Obama is 70.128 feet tall A highly precise (5 significant digits) measurement, but far from his actual height, published as 6'1".

The given value is more than an order of magnitude different from both him and almost any other known human, whilst one of 7.0128 would only be about 15% off – still a low accuracy, but not outside the realms of possibility for an otherwise unknown person. Coincidentally, Barack Obama is approximately 70 cat feet tall, using the paw size of a house cat to measure his height. Given the number of cat-related facts in the rest of the chart, this could be seen as rather appropriate.

Medium High Most cats have 4 legs Like many mammals, cats are quadrupeds, which means "four feet". Unless there is a genetic or other developmental issue, or an an injury that causes the loss of a limb, then cats generally have 4 legs.
Medium Medium Barack Obama is 6'1" While only as precise as the nearest inch, a common degree of rounding in that scale of measurement, that is the former president's published height.

In 2016, Obama was said to have "grown" 0.5 inches in height, so there is a definite lack of consistency of exactly how tall he is. The examinations may have been made at different times of their respective days, with some spinal compression occurring all the time not laid in bed, and his current height is also not publicly recorded; several years of gradual aging could also reduce his posture slightly, or sustaining his fitness (since experiencing the travails of office) may counteract this to a greater or lesser effect.

Medium Low Barack Obama has 4 legs Barack Obama, being a mammal, does qualify as a tetrapod, but as a primate, his ancestors' forelimbs evolved into arms and hands. Like other humans, he does not generally use them for locomotion,[citation needed] but to manipulate his environment. Thus calling these limbs "legs" runs counter to normal definitions, and is inaccurate.
Low High Most cats have legs A true (high accuracy) statement without much information (low precision).
Low Medium Barack Obama has fewer legs than your cat Again, this will depend on the cat (not to mention whether or not you actually have a cat), but in general, true.
Low Low Barack Obama's cat has hundreds of legs This statement has low accuracy, as Barack Obama owns a four-legged dog named Sunny, but is not known to have owned a cat, much less one with more legs than normal. And cats tend not to have hundreds of legs.[citation needed] It also has low precision, as "hundreds" could reasonably range from 200 to 900. (From a strict logician's point of view, this could however be considered a vacuously true statement.)
Low Unsure Barack Obama is much less likely than the average cat to jump in and out of cardboard boxes for fun Barack Obama has never publicly jumped in and out of cardboard boxes for fun,[citation needed] but the possibility exists that he does so in private. Cats, on the other hand, are commonly known for jumping in and out of cardboard boxes for fun.

Transcript[edit]

[The comic shows a table with 3 rows and 3 columns. Each row and column has a label, and then nine statements are given for the 3x3 grid.]
High
accuracy
Medium
accuracy
Low
accuracy
High
precision
Barack Obama was president for 70,128 hours Barack Obama weighs as much as 17.082 cats Barack Obama is 70.128 feet tall
Medium
precision
Most cats have 4 legs Barack Obama is 6'1" Barack Obama has 4 legs
Low
precision
Most cats have legs Barack Obama has fewer legs than your cat Barack Obama's cat has hundreds of legs


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Discussion

87.532% of all statistics are just made up. 172.70.178.220 11:10, 9 November 2022 (UTC)

Why is 'Barack Obama is 6'1"' and 'Barack Obama has 4 legs' medium precision? It seems to give exact value, so high precision. Tkopec (talk) 11:44, 9 November 2022 (UTC)

OK, I get it. 6'1" means something between 6'0.50" and 6'1.49". For height it's OK, but when counting legs, it seems like a stretch. Tkopec (talk) 12:30, 9 November 2022 (UTC)
The four legs are probably considered to be only medium precise, not because of the number but because of the imprecise term "leg". While humans can walk on all four extremities, thereby using them as legs, the upper two are commonly referred to as arms. Bischoff (talk) 14:54, 9 November 2022 (UTC)
(ECed by Bischoff) Plus a person's height (excluding differences to footwear and perhaps hairstyle) varies by an inch or so over the course of a day, as the spine compresses whilst mostly upright (would depend a bit upon your daily activities, but "an inch" or 2-3cm is the typical quoted value, with all the questions about precision as well as accuracy). Within an inch of such a foot-and-inch value is basically between slightly over a percentage point of drift across a continuum of ultimately non-integer values.
The number of legs is generally a whole number (perhaps lower-limb amputees could claim "half a leg", but is that for above the knee or below or... that's beyond my wish to define, I would leave it up to the individual amputee to finesse to their own liking) and assigning decimals, even .000(recurring), would be over-precise. A definite plain figure (however inaccurate) being the happy and acceptable medium between that and the vague imprecision (never mind inaccuracy) of the kind in the cell below. 172.71.178.137 15:00, 9 November 2022 (UTC)
The medium is because it says most, and not all! --Kynde (talk) 08:08, 10 November 2022 (UTC)
It says "most cats", indeed, but the above was about Obama, singular. Though I think it's covered anyway... 172.70.85.25 09:44, 10 November 2022 (UTC)
All the statements about 'Barack Obama' ought to be medium precision at best, because there could be more than one Barack Obama, and it doesn't give any further contextualisation to identify, for example 'the Barack Obama who was president of the United States of America'. 141.101.107.157 09:29, 11 November 2022 (UTC)
Compare with 6'1"1/50 or 4.0000 legs, both of which would imply a higher degree of certainty.--162.158.126.204 08:58, 13 November 2022 (UTC)

Someone should add an explanation of the difference between precision and accuracy. Nutster (talk) 13:13, 9 November 2022 (UTC)

Tried it myself. Maybe made it too compact, but I often go on too long so I tried made it as brief and snappy as I felt I could. Over to other editors to rewrite or replace. 172.71.178.137 15:00, 9 November 2022 (UTC)
That there is confusion over this was a bit of a surprise to me, about 20 years ago, when I worked (as I did for many years) in the outdoor pursuits trade. GPS units would give a 12-character grid reference (1m2), but couldn't be relied upon to that level. I would tell people they're more precise than they are accurate, until it became apparent that they were waiting for me to complete the joke they thought I'd begun, as I was so clearly contradicting myself, what with the two words meaning identical things.
Having gone on to explain the difference between the words, the neat brevity I'd sought was lost.
Obviously they can be used sort of interchangeably in casual conversation, but I thought the difference was well enough known that, when talking about a navigational instrument, it would be obvious what was meant.
Nope. Yorkshire Pudding (talk) 20:18, 9 November 2022 (UTC)
I deal with OS Grid References a lot, in a similar context, and a number of people who give 10-digits or more (2x5, for 1m res) from devices that typically don't ever settle down to less than 3m, and provably can be tens of metres off if there happens to be a small tree or shrub nearby.
(In fact, the other day I was geohashing myself, and my device was insisting I was in a totally different bit of the open field, 50m or so, no matter how much I sat it down at the provably correct point and wandered away so that even I wasn't obscuring its view of the sky. But it was good enough for me, which was all I do it for, so after giving it 5 minutes I counted it as done.)
And, in yet another activity, the publicised information for an event included a 12ish-DP reference for the starting area (vaguer than that), but just the postcode for the HQ (a very definite building that you could bullseye on a map), in a rural area where it covered half the valley! 172.70.86.12 22:19, 9 November 2022 (UTC)

How is 17.082 palindromic? Barmar (talk) 14:54, 9 November 2022 (UTC)

My error, I meant an anagram! (Was going for "anagramic", and my brain clearly rebelled.) 172.71.178.137 15:00, 9 November 2022 (UTC)

High Precision High accuracy, Randall Munroe misses when Obama was president. Low precision Medium-rare accuracy, so do we, Randall, so do we. 172.70.130.154 (talk) (please sign your comments with ~~~~)


It is so annoying that the US uses . and , to mean the opposite of what most European countries (including Denmark where I live). So when I read this it states that Obama was president less than 3 days (70 hours) but it more than 70000 feet tall. :-) Of course I now the difference but I have to think about it more than if everyone used the same standard. Also height should use SI units as everyone should ;-) (weight given in number of cats is the new SI unit as far as I know, but don't use inches and feet ;-D ) --Kynde (talk) 08:17, 10 November 2022 (UTC)

Well, as a UKian, I was happy enough. Tell you what, though, let's develop a new and mutually-acceptable standard notation... ;) 172.70.85.25 09:44, 10 November 2022 (UTC)
Good idea. Lets meet on 11/12/22 to discuss the details. --Lupo (talk) 13:41, 10 November 2022 (UTC)

I think Randall missed an opportunity to clarify how high precision can make something inaccurate. He could have said that Obama is 6’ 1.02173” tall, which would clearly be very precise, and also clearly inaccurate, simply because of the excessive precision. John (talk) 15:22, 10 November 2022 (UTC)

Saying 6'1.0278 would have been more in theme, there. And it would be not really more inaccurate (might even be closer to the truth...) but would convey a false precision.
Interstingly, when Andrew Waugh measured Mount Everest (before it was so named) he got a diffraction-adjusted figure of 29,000 feet, but decided to announced that it was 29,002 so that it didn't just like a rough figure rounded to the nearest hundred or even thousand feet. This made him the first person to put two feet on the top of Everest!
(...The actual error was not bad, given his measurements had to be made from hundreds of miles away. Current official measurements with on-the-spot modern GPS say 29,031.7 feet (for the snow-peak, which is all that Waugh could mention), after 170ish years of (by some estimates, but contested) about a foot of extra height per decade through the continuing techtonic raising of the Himalaya. And any unknown differences in snow-depth. Certainly it was within tens of feet, i.e. a dozen or so metres. With a bit of an error-bar, but not really that big when you consider it...)
So, arguably, that case was a deliberately false accuracy to help convey the true precision. 172.70.90.3 16:15, 10 November 2022 (UTC)
I don't get your point? Unless you just made up everything after the decimal point: How would it be less acurate? --Lupo (talk) 09:37, 11 November 2022 (UTC)
The only thing I can imagine is, that these kinds of numbers happen due to conversions. E.g. 6ft1in would be 185.42cm (according to the first calculator I found), but it is unlikely that 6ft1in was as precise as a cm-value with 2 digits after the decimal point would be. And in the other direction 185cm (which would be the usual precision of a height in m or cm - while 186cm could still be correct as it would be 6ft1in in the "usual precision") would calculate as 6ft and 0.83in --Lupo (talk) 10:18, 11 November 2022 (UTC)
If Obama's height is provided with this much precision, you can assume that the numbers are made up. 0.0278 inches are - in real measure units ;-) - 0.07mm. That's the diameter of a strain of hair. Nobody's height gets measured to that kind of precision. Kimmerin (talk) 08:10, 17 November 2022 (UTC)

I'm not sure the current explanation's claim that 'being too precise usually decreases accuracy' is, er, accurate (or perhaps it's just imprecise). It might be reasonable to claim that increasing precision tends to decrease accuracy relative to the level of precision, but not so much in absolute terms, or even necessarily relative to the size of the thing being measured.141.101.107.156 09:38, 11 November 2022 (UTC)

I think it's badly phrased. The assumed accuracy can be degraded and disadvantageous.
For example, to use someone's figures from just above, looking for an individual with a height of 185.42cm might seem to rule out the one that you find is 185.57cm tall, though they are indeed the one initially measured/estimated at 6'1" and would definitely be within an inch or so in this latest attempt to match them.
An old phrase that I grew up with is "don't try to be accurate over inaccurate details" (courtesy of a chemistry teacher, where we frequently used mmol-like measurements in analyses like titrations). The number of articles that say "the probe flew past the asteroid at a distance of about 20 miles (32.187 kilometres) ...", where clearly the accuracy is misleading, especially if the conversion ends up being back-converted by someone else with no idea ("...which is 20.0000746 miles"), and may have come from an original figure actually deliberately pegged at 35km (21.748 miles!), within a few metres or less.
Really, you should be taking the level of precision/accuracy inherent in the initial values, preserving the awkward fractions throughout the intermediate steps and converting the inherent ranges by the same process then clearly presenting the final figure to no more exactitude than the initial smudge of "all actual values that would be given by this type of input value", and maybe less. The write-up might be then be realistically "...of around 21¾ miles (35km)", if using a better primary source, or "20 miles (~30km)" in a case of the detail already being likely lost by intermediate chinese-whispers.
But this is what confuses people. And how even those that are not confused can confuse others... 172.70.86.10 12:16, 11 November 2022 (UTC)
It gets even better when different units also use different 0s. So for a persons height we can assume that as 0ft0in and 0cm is the same, 185cm is one order of magnitude more precise than 6ft1in, as it is 3 significant digits vs 2 at the same height. However a persons body temperature in 38°C with 2 significant digits and 311K with 3 is the same level of precision and only .15°C (Or .15K) apart, while 100°F (37.77...°C) is also very close but a bit more precise. --Lupo (talk) 14:10, 11 November 2022 (UTC)
One of many reasons that Celsius and Fahrenheit are not considered as true units - their connection to kelvins is affine, not linear. 172.71.142.75 05:49, 13 November 2022 (UTC)
Acknowledging that Celsius degrees equal Kelvin degrees, which remains a useful equivalence, even though degrees Celsius does not equal degrees Kelvin. (Ditto with Fahrenheit and Rankine.)
...and I'm partial to Delisle, anyway. ;) 172.70.162.134 11:28, 13 November 2022 (UTC)

I was expecting maybe a reference to Schrödinger's President when I first read the comic - but later realized that this could have been misconstrued as a threat. Oops!

As far as I recall, isn't the transcript supposed to avoid tables? I understand blind people with text reading programs use the transcripts to follow this comic, and thus it should avoid visual elements wherever possible? NiceGuy1 (talk) 04:49, 12 November 2022 (UTC)

Generally, yes, though some useful additional description went in before I might have 'flattened' the description again, and there are ther extant table-transcripts
Best practice would be to not rely on screen-readers to say nice informative things about tabulation and instead say it all explicitly (like they can't be relied on parsing MathML stuff), but there's good manual description and bad, too. 172.70.85.25 13:13, 12 November 2022 (UTC)

In the fewer-legs-than-your-cat category, any interest in adding a link to the "How many legs does a dog have if you call the tail a leg?" riddle often attributed to Lincoln? The best link I found is https://quoteinvestigator.com/2015/11/15/legs/ which makes it clear the riddle was already in circulation by 1825, well before Lincoln's usage. 108.162.246.163 05:30, 13 November 2022 (UTC)