Demystifying Tufte's data-ink ratio | Hacker News Reader

Demystifying Tufte's data-ink ratio

tuftesrazor.scienceux.org

78 pointss407443348 comments

I think the idea that a bar chart is usually improved by narrowing its bars while keeping them in the same positions is pretty silly. Yes, the article does say that one can take it too far, but I think that's the wrong framing. It's not that using less ink is good, but sometimes if you take that too far then it competes with visual clarity. Visual clarity is always the goal; sometimes clearer designs have more non-data ink, sometimes less; many designs are too busy so "less non-data ink" is usually good, but not always.

Tufte's "data-ink ratio" is a pretty good heuristic, but e.g. it would probably become a better match for actual visual clarity if what you counted wasn't "amount of ink" but something that measures spatial change in ink. It's the transitions that feel like noise, much more than patches of constant colour. But "data-ink ratio" is easier to say and easier to read than "ratio of integral of norm of gradient of colour".

Also, I think this sort of graph is better with very light gridlines than with no gridlines, though I think Tufte would disagree.

Also also, in Tufte's book, immediately before the section about "data-ink" there is an copy of a graph drawn by Playfair showing a country's balance of trade over time. Tufte gives it as an example of a good informational graphic. You can see it at https://en.wikipedia.org/wiki/William_Playfair#/media/File:P... if you like. This graph uses shading to indicate which direction the balance of trade goes in; that information is completely redundant with the curves by which the shading is bounded; but it would very much not be improved by removing that "redundant" ink even though according to his principles as interpreted by the page linked here that would make a huge improvement in the data-ink ratio.

Narrowing the bars is not reducing non-data ink ratio imo and against the spirit. The bars are the data. And they therefore should be maximally visible, the same way that you BOLD text (make it thicker) that you want to emphasize rather than thin it to "reduce non-message ink ratio."

For the width of the bar there is practically speaking a middle ground that uses thick bars but not too thick/close together such that it harms legibility.

Exactly, in this case the middle ground is right, just as with text, if everything is highlighted as BOLD UPPER CASE, then effectively nothing in the message is highlighted

If you only take that idea in one direction then I agree that it is pretty silly. However, the spirit of the visualization suggests finding a balance and optimizing the data-ink ratio rather than searching for a perfect value. If you follow the link you'll find the article I wrote talking about this: https://scienceux.org/articles/data-ink-ideal-vs-minimal

All the points that you make are very much valid, and it is good that you have pointed these things out because I wouldn't want people to follow these principles blindly without thinking about it for themselves.

I haven't considered the 'ratio of integral of norm of gradient of colour' too much (because it is easier to start simple and build on it), but I hope you might consider elaborating on it.

I've always hated the data-ink ratio metric. It's totally invalid.

The proof of this is right there in one of the examples in The Visual Display of Quantitative Information.

He shows an example where the axes of a scatter chart are shortened to the range of the data in each direction. This is a data-ink win-win! You get more information (the range of the data, at a glance), and it doesn't matter how little importance that is because you also have less ink!

But of course it actually looks terrible. To think otherwise, you have to be so busy thinking about metrics that you ignore your eyes. The axes no longer overlap in the corner, so the whole thing looks like a soup of visual fragments rather than a single cohesive thing.

Imagine you had several of these on a page side by side. It would be far harder to visually focus on one for a moment, because the fragments of different subfigures would be one big visual soup.

The solution is to put boxes around them (they don't have to be big thick black boxes, just something to visually separate the different things). But of course Tufte hates boxes. They add ink for no information content.

It's just bad science. Or brains don't process black pixels, one at a time, spending mental energy on each one. They see different visual fragments, having been heavily pre-processed by the CNN in our optic nerves before reaching our frontal contexts. The thing you actually need to minimise is visual complexity. Often, adding ink (for no information) helps with that.

I refer you to the article I wrote about optimizing data-ink ratio (rather than maximizing it as many people believe the intent to be): https://scienceux.org/articles/data-ink-ideal-vs-minimal

Many principles and concepts are based on ideal scenarios when we know that realistically there are different contexts and situations when you also need to break the rule. I am not suggesting that we should cut everything out, but rather that we try to understand good graph design rules and what effects it has on the data-ink ratio. You'll find that some best practices actually increase the data-ink ratio, while others reduce it.

Thanks, I love it! Like Tufte's Visual Display... book, it's a great article because it has loads of good examples so the reader can form their own views, regardless of what the text says.

It seems like it proves my point but somehow it skirts around the real conclusion. You say "example cases where more ‘chartjunk’ improve clarity, comprehension, and attention" but I think what you really mean is that sometimes extra ink *isn't* chartjunk.

As I said, the real goal is to maximise the data-visual complexity ratio. That sounds like I'm agreeing with the article but I think there's a subtle difference: Some of the examples you called "too minimal", I would argue, are not minimal. They use less ink but more visual complexity. You actually do want minimalism, but adding more ink or sometimes even more separate elements can create that minimalism.

Your figure 1(a) is an excellent example of Tufte's nonsense, even better than partial axes example I gave. I'm definitely going to link to this article in future when Tufte comes up.

That page is a lot of ink for very little data. It's also somewhat wrong - no, you can't claim the axis marks and labels aren't data ink at all just because it doesn't directly reflect the measure. They are still data that's extremely relevant to reading the chart. Yes, even if Tufte says otherwise.

Meanwhile, even Tufte's advice was explicitly to grey them down, but not completely remove them.

(And we can debate Tufte's advice - lots of other comments on this page how he had great aesthetic sensibility, but his advice wasn't grounded in reason or actual readability research, and so is limited to the examples he chose)

There is a distinction between non-data-ink and redundant data-ink that is being made here. Whereas non-data-ink is usually easier to identify, redundant data-ink is somewhat subjective to how we view the information and process it. But you can argue that something is redundant if removing it doesn't change the amount of information contained within the chart that is required to understand and interpret it. However, you could also argue that different people interpret things differently, and therefore having different ways to do that will have some use.

Rather than trying to create unnecessarily debate, the intent is to try and help people understand the metric beyond a simple value but how the concept can be applied.

More importantly, it is not about simply chasing a perfect value that doesn't exist, but to optimize it within a specific context for your audience.

I remember getting Tufte's book ("The Visual Display of Quantitative Information") and being really excited because I'd heard all these great things about it, and then being disappointed because it had no real justification for its claims. The "data ink" thing is a typical example. I'm willing to accept the general concept that many graphs are too cluttered. But there's no particular reason to suppose that quantifying the proportion of "data ink" and trying to optimize it is the best way to handle that. A lot of the book is just taking subjective aesthetic judgements and trying to frame them as some kind of objective truth.

If we really wanted reliable guidelines on how to format graphs, we would want to ground them in psychological research that actually demonstrates that, for instance, some versions result in better understanding or recall of certain information. But as far as I can see Tufte's book makes no attempt to do this. (Perhaps he or those who built on his works did it later on?)

William Cleveland is who you are looking for. He actually did studies like you are looking for on the display of information and its relation to psychological perception. His work is authoritative and predates Tufte significantly. I’m not sure why anyone pays attention to Tufte at all except that he is good at marketing himself. He is kind of the antithesis of quantitative information in that sense. All style and no substance.

Any book recommendation from William Cleveland on the subject?

I agree. I think Tufte has good aesthetic judgement and is often right in his criticism of why certain examples of visual data presentation are flawed. But a researcher on this subject he is not.

To your question, I recommend this recent review as one good example: https://doi.org/10.1177/15291006211051956

This is actually a great paper to read (and as you say, quite recent for this type of review), and it does touch on the topic of "How to Design a Perceptually Efficient Visualization", which I think is most relevant to what an optimal data-ink ratio will provide for the audience (i.e. clarity and reduced amount of clutter). However, the only mention it makes about data-ink ratio (it doesn't do this directly) is that:

"Despite strong calls to declutter visualizations (e.g., Tufte, 1983), there is only mixed evidence that this practice improves aesthetic ratings and little evidence that the prescription affects objective performance. Several studies have measured aesthetic ratings for cluttered versus decluttered charts, and some have shown clear preferences for decluttered versions (Ajani et al., 2021) and others, surprisingly, showing the opposite (Hill et al., 2017; Inbar et al., 2007). Researchers who have found the opposite have typically argued either that viewers’ higher level of familiarity with cluttered charts make those charts more attractive or that decluttered charts that are too minimalistic become boring. Another possibility is that users may prefer particular depiction styles for particular purposes, mindful of their audience and goals (Levy et al., 1996). Objective performance measures, such as the speed with which viewers can compute means across values in a bar graph, also present mixed evidence. For example, that speed can be slightly faster when some forms of “clutter,” such as axis tick marks, are removed but slower when other elements are removed (Gillan & Richman, 1994). Given the large number of design elements that could count as clutter, combined with the large number of tasks that one could complete on a visualization, some have argued that a simple rule for whether to declutter is unlikely to arise and have discouraged further empirical testing given the small and mixed effects found so far (Ajani et al., 2021)."

I am certainly not arguing for the fact that the data-ink ratio is a magic number, but quite the opposite - I believe that even trying to maximize or minimize a ratio is full of dangers and traps, but instead we should understand our design decisions and be aware of its impact in a more considered and objective way. The discussions here suggests people don't believe it is a magic number, but it also shouldn't be discarded when it does have some value.

Tufte doesn't really move far beyond exploring examples he likes, and as a result, it's hard to take away any generalizable set of principles. Some of the few "rules" like this data-ink ratio are framed as generalizations but depend on idiosyncratic aesthetic judgments.

I think this is why every Tufte-inspired CSS framework or LaTeX style ends up just cargo-culting the style of his books: Bembo/Palatino/ETBook typography, italicized subheads, an asymmetric wide margin layout, margin notes replacing footnotes, illustrations/diagrams in the margins. (Like the linked website.) Few people are really confident after reading the books to stake out their own approach. It's not a bad aesthetic, but if the books were truly successful at their goal, varied application of the ideas would be as common as imitation.

I think what you said about 'trying to optimize it' is actually on the spot. I think what too many people try to do is to 'maximize' or 'minimize' it without really understanding the impact of designing based on metrics. But I think what we can do is use a metric to understand some of the impact of our design decisions, and help clarify why it might make sense to do something. Even the best designers will know when it makes sense to break rules (because there are often good reasons to do so).

You are right in that there is a lack of empirical evidence in how to apply the data-ink ratio to design. This is one of the reasons why I am trying to sift through the previous research that makes claims without really testing them properly, so that I can hopefully make better sense of it with better research.

It makes me think of https://xkcd.com/688/

Ha! Yes. One of my favorites.

A zoom button would have been cool for this one :-)

Despite knowing the correct answer to the question in the first section, the diabolical wording on it absolutely threw me:

"Erase the shaded background: does the share of ink that shows the five numbers go up, down, or stay the same?"

In the spirit of the project, try asking me instead,

"Remove the shaded background: is the amount of ink now left on the chart more useful, less useful or the same as before?"

Damn...even that was hard to write.

And the same question was answered in the opposite sense in section 4, in which adding a colored background was deemed not to affect the data/ink ratio.

... Mumble mumble metric vs. target. Data/ink is a useful thing to keep in mind, but it's just one factor in selecting designs that communicate your data.

... Mumble mumble LLM-generated document problems.

It's even more frustrating/hypocritical considering that the underlying topic is about carefully and clearly communicating to other humans.

That’s interesting. However, with charts, reducing the amount of ink can sometimes compromise readability.

An excellent point that is very well covered in the linked article.

I wrote the article thinking that I won't need to explain some of the points explicitly with examples that are going to be subject to some criticism. But of course people who read the article asked for that and so I tried to illustrate some of the points as best as I can, but it is hard to please everyone. Nonetheless, I prefer to try and make a point for the sake of moving towards clarity rather than to continue circling in a place that I am not so happy with at the moment.

There should be a similar metric for information density in an article. This one is so repetitive that it's hard to keep reading since the whole point was already contained in the first section. The rest keeps just repeating again and again. Too bad the slop density is off the charts on this one.

To be fair, if someone wanted to present that exact dataset efficiently, they would have probably proposed something much different, like an horizontal chart with thin lines, eg

North [------------] 7

South [--------] 5

East [--------] 5

West [-----] 3

or something, which would have saved a lot of data/ink ratio

You could just remove the bars and present the numbers in a table. In this case I think that would be a considerable improvement (unless the chart is one of several similar charts that one might want to compare, in which case being able to compare their shapes at a glance would have value).

That's Tufte's first guideline, anyway. Present data in a table unless it's better visualized as a graph.

For sure! It is all about context of use and the audience. I think the pie chart also serves its purpose in the right context and in front of the right audience. I would probably write a much longer article using different charts to illustrate all the various contexts but I don't want to be writing a textbook in the era of short attention spans. In this case, picking a bar chart to illustrate some principles clearly isn't going to satisfy everyone :p

But I will perhaps add a couple more examples based on all the comments and feedback so far. If nothing else I certainly enjoyed getting more people thinking and talking about how we can improve data visualization design!

The example with the two light grey horizontal lines is apparently wrong, but I found it by far the easiest to visually compare bar heights, which is the entire point of the chart, no?

I think your point illustrates that optimizing data-ink ratio is not as simple as the concept of data-ink sounds, when it comes to best practices for data visualization design.

If you want to encourage people to compare bar heights, you can certainly leave the grey horizontal lines. But if you directly labeled the bars with values then you don't need to scan from the vertical axis across individual bars to do that processing in your head. And if you removed the vertical axis labels that don't represent values being charted while also sorting the categories by their value, you can further remove another step in the process.

The point is that you can try to optimize in either direction of the data-ink ratio, but you should be aiming to just blindly increase or decrease it. Often it ends up making very little difference to the actual ratio value (which relates more to information density), and you need other design techniques to improve clarity and reduce clutter.

I agree. Labels at the top was a nice touch.

But this does not help with the visual inspection of the difference.

If it was enough, we didn’t need the chart and could just publish the numbers instead.

The point of the graph is a visual inspection of the differences. I feel like adding the one thing actually showing this relative comparison is therefore almost mandatory

I think I prefer the 10-12% range myself.

This isn't a great example, because they're effectively using a chart to show a handful of data points. The key with the data/ink ratio is to densify the amount of data shown so that the ink that is used can show additional dimensions or statistics -- such as using a 2 dimensional plot, turning the axes into box plot equivalents, or other relationships.

I plan to add another example to compare the density of data contained in different types of charts. However, in that case you are picking chart type based on what best shows the relationships contained within the dataset; optimizing the data-ink ratio is secondary to that, because it doesn't matter how high or low your data-ink ratio is if the chart type used is not the best one for your use case.

Mistifying Tufte’s data-ink ratio (by blasting it into a fine mist with my slop cannon).

What in the slop?

"The data to ink ratio is the ratio of data to ink. The data to ink ratio can be increased by decreasing the amount of ink. Decreasing the ink, while keeping the data constant, will increase the data to ink ratio. Here, we decreased the amount of ink in the diagram, and you can readily see that the data to ink ratio went up. The data to ink ratio should be increased, except when it shouldn't."

I don't see that text anywhere in the article.

It sounds like you're parodying the article but putting it in quotes is misleading.

How else would you format such a parody?

By either preceding the quote with something indicating you're making it up or not putting it in quotes. Like, "This article is basically just saying the data to ink ratio is the ratio of data to ink."

Italics are also a good option. They're annoying to read, but I think that actually helps when you're parodying that type of prose.

I am parodying the article. Agree to disagree!

Viewing in dark mode, so most of the ‘ink’ is used to render the empty background. Every suggested change here decreases the ink/data ratio.

Paper isn’t ink.

Wouldn't "dark mode" be the equivalent of using black paper? :)

It does exist btw, I've used it before myself.

Yes, it would. And if you use black paper, then it is the white ink (I assume you use white ink) that you need to calculate for the data-ink ratio.

Just out of curiosity, what do you use black paper for?

> what do you use black paper for?

Just for something different, nothing too special about it. :)

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