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>box plots always make distributions look bell shaped I feel like this is where the confusion stems from for the author and everyone else here. Box plots don't
by sigmoid10 2y ago
>box plots always make distributions look bell shaped
I feel like this is where the confusion stems from for the author and everyone else here. Box plots don't make anything bell shaped (they don't change the distribution), they assume that your data follows a bell/gaussian shape. This is correct in cases where the central limit theorem can be applied (which is almost everywhere) - but when that is not the case, the assumption is wrong and you shouldn't use a box plot anyways, because the values it shows have no real use. There are very real use cases for box plots, but people need to understand the basics of statistics before they can use them.
- blueflow 2y agoThis should be the topmost comment. Box plots are made for visualizing generalized normal distributions and nothing else. Edited to preempt nitpick.
- cjk2 2y agoThis is also wrong. Gaussian curves are symmetric. Box plots do not have to be. In fact representing skew in a batch is one of the fundamental purposes of them.
- crazygringo 2y agoBut representing skew is precisely to show how "off" from a Guassian it is. Because real data is never perfectly Guassian, or perfectly anything. But the idea of a box plot is that it's for data which is in theory Gaussian or a similar unimodal kind of bell-shaped curve. Then you can look at the box plot and see if it actually is -- are the two boxes roughly equal-sized? Are the lines a bit longer than the boxes but not insanely so?
- blueflow 2y agoYou model skew in Gaussian distributions by adding an exponential parameter.
- pocketsand 2y agoWhy? They’re non-parametric and make zero assumptions of normality.
- blueflow 2y agoHow else would you calculate the quartiles to render the boxes?
- munch117 2y agoCount data points in each quartile. You can do that for any sortable data, independent of distribution.
- blueflow 2y agoIf you do that in your paper, you better write next to the graph that you did that.
- thaumasiotes 2y agoArguing that nobody who might be professionally expected to look at a box plot can be reasonably expected to understand how box plots are defined doesn't make a compelling case that using them is a good idea.
- blueflow 2y agoIf the method how the plot boxes are calculated is not clear (this thread references at least two different methods), you'll need to explicitly write it down which methods you did use.
- thaumasiotes 2y ago> this thread references at least two different methods No, as the sidethread comment notes, there is only one way you can compute quartiles. You seem to be arguing that the correct thing to do is to impute them, and that calculating them is such a deviant practice that it would need to be specially remarked on.
- munch117 2y agoBut is that what they're actually used for? The data has been reduced to three numbers, throwing away most of the information that you would need to assess whether the distribution is gaussian or not. If it's not, how will you ever know?
- cjk2 2y agoExactly this on the last point. Although rereading this the distribution point is explained poorly. People waltz in with assumptions and then complain when they don’t work because they don’t really understand the tools they are using. The author is one of them. It’s a bad article and the author should not be using or demonstrating things they clearly don't understand.
- munch117 2y agoIsn't that the whole point? That the graph type is very easy to misunderstand. If you are right, and not even a professional data visualization consultant properly understands the graph, then who will?
- cjk2 2y agoSome of us are perfectly qualified to understand them and the nuances.
- munch117 2y agoA plot that requires the reader to be perfectly qualified is a bad plot.
- cjk2 2y agoThey teach this to 15 year olds in the UK. If it's a bad plot, perhaps some introspection is required...
- magicalist 2y agoThey also teach pie charts and use color scales with non-uniform brightness. Just because it's possible to read a plot doesn't make it a good plot.
- Beldin 2y ago> Box plots [...] assume that your data follows a bell/gaussian shape. Not sure how to square that with this statement on Wikipedia's page on box plots: Box plots are non-parametric: they display variation in samples of a statistical population without making any assumptions of the underlying statistical distribution[3]
- sigmoid10 2y agoIf you want to see why that is not fully correct you should read the article. For a box plot you need to calculate mean, variance and certain percentiles. These values don't make sense if your distribution does not follow a certain shape (because these values unambiguously define such a shape). See the examples in the article for what happens if you still try to use them in those cases. You can still extract the values of course (hence probably why wiki says they don't assume anything), but you lose significant information about the distribution. So you can no longer reverse the process.
- rcxdude 2y agoThe mean and variance are not features of a box plot. Box plots show the quartiles, which are about the cumulative distribution.
- lolc 2y agoWhich is why I find the article so compelling because I'd always read box plots as being about variance. To me the plot implied a quite normal distribution.
- fjkdlsjflkds 2y agoNote that "not knowing how to correctly interpret a boxplot" is not equivalent to "boxplots are useless".
- lolc 2y ago
- treflop 2y agoI agree. The author simply used the wrong chart. The author's example has a bimodal distribution (TWO peaks) and chooses a type of chart that has ONE peak (a box plot). A little baffling tbh.
- rcxdude 2y agoWell, to start with, how would you determine that about your distribution in the first place? And if that works well enough, why use a box plot afterwards?
- cjk2 2y agoBecause it's very hard to rationally compare multimodal batches without single test statistics. And they present five summary figures for each batch, each of which are reasonable metrics to compare batches with.
- treflop 2y agoWell usually when you are analyzing some data, you toss it into the most basic chart like a histogram. And a histogram for the author's example is perfectly acceptable to show that single data series. But imagine if you have 10 different normal data series and you want to compare their medians and distributions between each other... well are you going to put 10 histograms side by side and expect the reader to compare them? No -- that's where the box and whisker plot shines.
- smcin 2y agoSimple, use a histogram. The author's first histogram clearly shows most of the distribution lies in [20,100), then the [10,20) bin is empty but the [0,10) bin is quite full. Hence, that's not a single-mode distribution. It has two modes, one around [50,60) and the other in [0,10).
- WWWWH 2y agoYes, exactly! Just plot all the bloody data and be done with it. No one is doing this by hand anymore so it is no extra work. To my mind, if you have a genuine EDA attitude you plot it all.
- ozyschmozy 2y ago> There are very real use cases for box plots, The author argues otherwise, can you give an example of a use case where box plots would be preferable to the alternatives the author suggests?
- ohmyiv 2y ago> There are very real use cases for box plots, > The author argues otherwise No, in the article he says he wouldn't recommend them _in most_ situations. It's a part that a lot of people here seemed to have missed whether arguing for or against box plots. >Despite making more visual sense than box plots, I still wouldn’t recommend these design concepts or box plots in most situations because… (Emphasis mine)
- Ringz 2y agoFrom the article: „So, no, I can’t think of any situations when a box plot would be the truly best choice, other than those in which the audience demands box plots because that’s what they’re used to seeing. If you can think of any such situations, though, please let me know on LinkedIn or Twitter.“ „Other reviewers suggested that the conclusion should be that box plots are a useful chart type, but only for statistically savvy audiences. Again, I’m going a step further, suggesting that even those audiences would be better served by other chart types in virtually all situations.“
- cjk2 2y agoComparing location, spread and skew of multiple batches.
- rzmmm 2y agoOften people are interested in exact quantitative statistics like IQR, median, top/bottom deciles which are commonly represented in box plots. The alternatives are visually simpler but they contain less quantitative information.
- oefrha 2y agoThe alternative plots in TFA after > Design concepts such as the ones below make more ‘visual sense’ than box plots: present the exact same info in much less visually confusing ways, through the use of brightness (weight) and area. Just better box plots. And of course you can always draw some lines for the quartiles on any kind of plot with a linear scale for the value.
- rcxdude 2y agoNah, there's nothing in a box plot which assumes a bell-shape. It does, however just visualise the parameters which reasonably well characterize a smooth single-mode distribution regardless of the underlying distribution. So it's a valid criticism of using box plots, especially when the alternatives can just as well visualise a bell-shaped distribution, as well as showing when it is not.
- deleted 2y ago[deleted]
- quietbritishjim 2y ago> smooth single-mode distribution That IS a bell curve. While it's true that the Guassian distribution is often called a bell curve or even "the" bell curve, a non-Guassian single mode distribution is still absolutely bell shaped in a general sense. So, although you started your comment with "nah", you're actually in agreement with the content you replied to.
- conformist 2y agoIn the mathematical sense this is clearly not true - it’s easy to come up with a smooth single mode distribution that doesn’t look like a bell.
- thaumasiotes 2y agoIs it? How? You could include a lot of little bells far from the single mode, but that's reading a little too much into the literal meaning of "single mode" - a "bimodal" distribution isn't one where the two most common values are both modes. It's one where there are two distinct local maxima. The tails to the left and right must asymptotically approach zero (or you don't have a smooth distribution, because you have discontinuities somewhere), and if there's just one local maximum, your curve will look like a bell.
- commathingy 2y ago
- wesleywt 2y agoThis is exactly why the author says you should stop using Box plots. The plot is easy to misinterpret.
- IanCal 2y ago> they assume that your data follows a bell/gaussian shape No they don't. They show quartiles mostly, and don't assume symmetry or any parameters of a gaussian.
- kamma4434 2y agoWhat you say is technically correct, but in the sense where you can put rat poison in One of those ceramic cookie jars they sell in houseware shops. There is nothing wrong in doing it, but it may lead to interesting failure modes Because someone can have implicit assumptions about what’s in there.
- afiori 2y agoQuartiles are relevant for almost any distribution
- crazygringo 2y agoIf by "almost any" you mean "unimodal". Quartiles are not relevant, i.e. can be highly misleading, for a bimodal distribution or beyond...
- afiori 2y agothey are misleading if you assume unimodality, but are always relevant. If you care about how many modes there are then likely you would prefer deciles or centiles. But even in the first image of the article the fact that two quartiles are close together means that there some density peak around there. I agree with the author that box plots are not good plots, but quartiles/deciles/medians are useful even for multimodal distributions
- amelius 2y agoA bell shape has no minimum/maximum, like the box has.
- Hendrikto 2y agoIn theory. In pratice you always have a finite sample size and thus a min and max.
- lkdfjlkdfjlg 2y agoBoxplots don't assume anything about your data. They just measure percentiles and put them on the y-axis.
- vehemenz 2y agoThe argument is more about the relation between the visualization and the audience, not the data and the visualization. I see a lot of commenters missing this point.
- jncfhnb 2y ago> people need to understand the basics of statistics before they can use them. > they assume that your data follows a bell/gaussian shape. This is correct in cases where the central limit theorem can be applied (which is almost everywhere) You sir just failed basic statistics
- fnordpiglet 2y agoSorry I don’t understand. The central limit theorem describe the distribution of the sample means from a population. It describes the distribution of the mean, not the distribution of the population itself. The shape of the distribution of the sample mean isn’t super interesting when you’re interested in the distribution of the samples themselves as a proxy for a population. So I’m not sure I understand your assertion. Could you explain more your reasoning? Maybe I’m missing something, but the estimation of the sample mean distribution isn’t the only metric that’s useful, and almost nothing in nature is normally distributed otherwise. Normal distributions are generally a useful assumption mostly because of the analytic form of the Gaussian and our understanding of how to work with it. But that estimation isn’t useful as it might seem. A Poisson distribution is much more common for instance.
- sigmoid10 2y agoI't appears you don't understand the central limit theorem fully. You gave the definition you find in textbooks, but you don't see how it applies to real world measurements and already explains your question. I can only recommend to visit a university level statistics course at this point. Maybe you will understand when you actually deal with some real data. Then you will indeed see its consequences pop up everywhere. The issue (also for the blog author) is that it is often implicitly assumed. It is one of many common pitfalls in statistics. You should also learn what the difference is between a poisson and a gaussian distribution. They may look similar, but there is a drastic difference in their definition and they are used in very different circumstances.
- jncfhnb 2y agoThe GP here did not claim a poisson was the same thing as a Gaussian. They also don’t look similar. As far as I can tell you’re making the introductory student error of thinking the central limit theorem means any sufficiently large sample makes a distribution look normal.
- fnordpiglet 2y agoYes precisely. I’m also frankly shocked at the condescension. If you weren’t making that typical mistake then please explain the uses you meant. I would rarely use a box plot for a CLT distribution. Why? I would most often use it with a population sample I want to get the distribution of. Yes the mean of those would be a Gaussian under the CLT but it’s not useful useful as such. Most natural distributions are not Gaussian upon sampling even if they’re bell shaped. They often have fatter tails, model some complex process, etc. The box plot is sometimes deceptive as is demonstrated in the original link. I don’t think that’s easy to argue against as they provide a totally reasonable and common sample distribution and show it failing to be descriptive of the most important features. I fail to see how the CLT even remotely addresses the concerns or obviates them in any useful sense. The CLT and box plots aren’t very often applied together for these reasons.
- crazygringo 2y agoYes. A lot of people here are commenting that no, technically box plots don't assume any distribution. And I mean, technically you can ride from NYC to SF in a lawnmower. But I completely agree that box plots shouldn't ever be used for anything but unimodal distributions similar enough to a bell/gaussian distribution. All of the criticism of the article seems to be that they're misleading when the distribution is not bell/gaussian, e.g. bimodal. To which my reply is, of course. Box plots shouldn't be used then. But if your distribution is bell/gaussian, they seem fine and I see no particular issue with them.
- pictureofabear 2y agoThis article is very click-baity. Boxplots are a single tool for data analysis. They do not apply in every situation, nor do any other tools. The same goes for pie charts, which are constantly being accused of always distorting data. Pie charts, like box plots, have their place.
- hoosieree 2y agoMurphy's law for data viz: If a plot can mislead, it will.
- theamk 2y agoWell, how do you readers know if your distribution is bell/gaussian? Sure, sometimes you plot means of large samples, and then it is true by construction; but a lot of time people use box plots when there is no intrinsic reasons for data to be gaussian. Like most experimental papers. Or take the first example from wikipedia page on box plot [0]: "Box plot of data from the Michelson experiment", which is just 20 points per run. Would I want to see this in the paper? No please. There is no evidence that the experimental data is gaussian (or even single-modal). Or further down that page, "A series of hourly temperatures" - why would one box-plot it either? And even if you claim your data is gaussian by construction, maybe because you surveyed lots of people - I still want to see the evidence, as it's pretty simple to make experimental mistakes that turns data non-gaussian (say you only surveyed two neighborhoods with very different properties) In other words, the domain where box plots are sufficient is very small. Most publications should never use them. [0] https://en.wikipedia.org/wiki/Box_plot https://en.wikipedia.org/wiki/Box_plot
- imachine1980_ 2y agoCould you please elaborate on the reason? I assume it’s related to a unique null derivative instead of multiple maxima, but I couldn’t find any papers or information on this. Additionally, I find the article informative but believe it could be improved with this clarification. As someone who has worked with data analytics but is not a mathematician or actuary, I know people who probably review these types of graphs. Now, I understand that it is essential to check the underlying data distribution to avoid being misled by the information, even if the source and axes seem trustworthy
- sigmoid10 2y ago>related to a unique null derivative instead of multiple maxima I think the word you're trying to use is "bimodal" and yes, that is one example where the author's reasoning fails. But it's not the only one. >I couldn’t find any papers or information on this. You said you have no formal higher education in mathematics - how would you even go about finding (let alone understanding) papers? Regardless, just to be clear, this is not something you would learn from papers but from introductory textbooks and university courses. Everyone who has to deal with statistics in science needs to go through a whole lot of extra education exactly because there are many pitfalls like this. >it is essential to check the underlying data distribution to avoid being misled by the information That is another half-truth that everyone on the outside seems to agree on, but it is useless in practice. What do you do if the underlying data is not accessible. And what if you don't have the means to process it for every paper you read (which is what usually happens)? Then you have to rely on the actual tricks of the trade, which will come naturally if you worked with tons of statistics before. There are lots of telltale signs that let you spot bad analyses by only looking at a plot or summary chart. Granted, you won't catch all of them, but it often takes real malice and deep statistical competence on the author's side to cover up these things.
- kylebenzle 2y agoYes! You are right and my gears were grinding the whole time reading that article because right of the bat they make some gross and incorrect assumptions. A box plot isn't trying to show the same thing a histogram is, it's like saying we should stop using Venn diagrams because they confuse people when trying to show the exact amount of overlap, so pie charts are better... It's silly.
- chipdart 2y ago> Box plots don't make anything bell shaped (...), they assume that your data follows a bell/gaussian shape. Not true. Box plots represent low and and high quantiles independently and support the representation of outliers. This alone is enough to make it clear for everyone that they don't require a distribution to be symmetric, let alone bell shape.