Using axis lines for good or evil

I guess this is fine, but I'm not convinced. This mostly just seems like you pushing your personal aesthetic preferences, but it feels like I could easily come up with arguments for following exactly the opposite advice.

This post reminds me of lots of writing advice: seems fine, so long as you have the same aesthetic sensibilities as the person giving the advice.

↑ comment by Mo Putera (Mo Nastri) · 2024-03-07T11:48:12.186Z · LW(p) · GW(p)

I was wondering about this too. I thought of Eugene Wei writing about Edward Tufte's classic book The Visual Display of Quantitative Information, which he considers "[one of] the most important books I've read". He illustrates with an example, just like dynomight did above, starting with this chart auto-created in Excel: 

and systematically applies Tufte's principles to eventually end up with this:

Wei adds further commentary:

No issues for color blind users, but we're stretching the limits of line styles past where I'm comfortable. To me, it's somewhat easier with the colored lines above to trace different countries across time versus each other, though this monochrome version isn't terrible. Still, this chart reminds me, in many ways, of the monochromatic look of my old Amazon Analytics Package, though it is missing data labels (wouldn't fit here) and has horizontal gridlines (mine never did).

We're running into some of these tradeoffs because of the sheer number of data series in play. Eight is not just enough, it is probably too many. Past some number of data series, it's often easier and cleaner to display these as a series of small multiples. It all depends on the goal and what you're trying to communicate.

At some point, no set of principles is one size fits all, and as the communicator you have to make some subjective judgments. For example, at Amazon, I knew that Joy wanted to see the data values marked on the graph, whenever they could be displayed. She was that detail-oriented. Once I included data values, gridlines were repetitive, and y-axis labels could be reduced in number as well.

Tufte advocates reducing non-data-ink, within reason, and gridlines are often just that. In some cases, if data values aren't possible to fit onto a line graph, I sometimes include gridlines to allow for easy calculation of the relative ratio of one value to another (simply count gridlines between the values), but that's an edge case.

For sharp changes, like an anomalous reversal in the slope of a line graph, I often inserted a note directly on the graph, to anticipate and head off any viewer questions. For example, in the graph above, if fewer data series were included, but Greece remained, one might wish to explain the decline in health expenditures starting in 2008 by adding a note in the plot area near that data point, noting the beginning of the Greek financial crisis (I don't know if that's the actual cause, but whatever the reason or theory, I'd place it there).

If we had company targets for a specific metric, I'd note those on the chart(s) in question as a labeled asymptote. You can never remind people of goals often enough.

And I thought, okay, sounds persuasive and all, but also this feels like Wei/Tufte is pushing their personal aesthetic on me, and I can't really tell the difference (or whether it matters).

Replies from: dynomight

↑ comment by dynomight · 2024-03-07T14:46:11.364Z · LW(p) · GW(p)

One way you could measure which one is "best" would be to measure how long it takes people to answer certain questions. E.g. "For what fraction of the 1997-2010 period did Japan spend more on healthcare per-capita than the UK?" or "what's the average ratio of healthcare spending in Sweden vs. Greece between 2000 and 2010?" (I think there is an academic literature on these kinds of experiments, though I don't have any references on hand.)

In this case, I think Tufte goes overboard in saying you shouldn't use color. But if the second plot had color, I'd venture it would win most such contests, if only because the y-axis is bigger and it's easier to match the lines with the labels. But even if I don't agree with everything Tufte says, I still find him useful because he suggests different options and different ways to think about things.

Replies from: nathan-helm-burger, jkaufman

↑ comment by Nathan Helm-Burger (nathan-helm-burger) · 2024-03-08T19:04:24.465Z · LW(p) · GW(p)

Yeah, agreed that getting people to answer questions using the chart, and measuring their speed and accuracy is the key objective metric of design quality. Also, I like it when both color and line styles are used together. Keeps it clear for colorblind people, and makes it extra clear for colorsighted people. Choosing colors should be done carefully to balance contrast with the background color. And can be done in such a way as to be visible even to the most common colorblindness types.

↑ comment by jefftk (jkaufman) · 2024-03-21T11:07:45.647Z · LW(p) · GW(p)

Yes! But not just time, you should also compare them on accuracy.

As someone who's spent a while designing charts for published books, I have generally been strongly against axis lines. One thing that has really influenced my approach to using lines is the section of Butterick's Practical Typography on tables.

Nowadays I remove all lines on tables and charts unless there's a strong argument in favor of one; implied lines are much easier on the eye.

This post overall moved me toward using gridlines a little bit more, for intuitively measuring distance when that's important.

One downside of not using lines, it makes it harder to tell where one plot ends and the next begins.

I mean a plot like this is just a mess. You could probably get situations where it wasn't even clear which plot a data point belonged to.

At least with the boxes, you have a nice clear visual indicator of where the data ends. Here it's not obvious at a glance which numbers match up with which plots, and the ticks are easy to confuse for point markers.

All right it's a bit of a mess with the edges in too. But at least it's crisper.

(Rant about philosophical meaning of “0” and “1” and identity elements in mathematical rings redacted at strenuous insistence of test reader.)

I'm curious about this :)

I'm sad that the post doesn't go on to say how to get matplotlib to do the right thing in each case!

ax.spines['top'].set_visible(False) # or 'left' / 'right' / 'bottom'
ax.set_xticks([0,50,100],['0%','50%','100%'])
ax.tick_params(axis='x', left=False, right=False) # or 'y'
ax.set_ylim([0,0.30])
ax.set_ylim([0,ax.get_ylim()[1]])

This could be expanded to show good examples of using logarithmic scale.

These suggestions seem plausible. A few notes:

• Tick marks for years are ambiguous. Is the tick mark indicating the start of the year? The middle of the year? The end of the year? I have worked with chart libraries, and sometimes it's even the current date, n years ago. Like a tick mark labelled "2010" = March 9, 2010. A better alternative to tick marks is to have "year separators", where the "2010" is placed between two "tick marks" rather than under one, which can only be interpreted as start and end of the year.
• Regarding temperature. Physically speaking, only 0 Kelvin is an objective zero point, such that something with 20 Kelvin has "twice as" much temperature as with 10 Kelvin. Kelvin is a "ratio" scale. Celsius and Fahrenheit are only "interval" scales, so 20°C is not twice as hot as 10°C, but only ~3.5% hotter. (See also this interesting Wikipedia article on the various types of scales.) This is even though 0°C (water freezes) seems more objective than 0°F.
  Nonetheless, Kelvin is not relevant to what we perceive as "small" and "large" differences in everyday life. We wouldn't say 20°C only feels a mere 3.5% warmer than 10°C.
  I guess it helps to include two familiar "reference points" in the temperature axis of a chart, like freezing and boiling of water (0°C and 100°C, or explicit labels for Fahrenheit) or "fridge temperature" and "room temperature". That should give some intuitive sense of distance in the temperature axis.

There's something about the way you write introductions that reminds me of good YouTube videos. It's a combination of easy-to-understand illustrations, simple words, and starting with an interesting question.

The problem I see here is that you are trying to use functions at all. Take the years/GDP line. If your measure the GDP once a year, you should use a bloc graphic.

Else you have a lot of imaginary points per month, day and hour, that, in reality, are not there. Take black friday - lots of changing , take holidays, when the shops are closed - little changing.

Days - lots of changing, nights - little changing. And you can´t really know the GDP for the next year - there can always be a drastic change.

Take the cannabis/homeowner plot graph on the other hand. You have a lot of (x,y) pairs  (homeowners, cannabis supporters)

Some of these points have the same place on the x - axis, but different places on the y - axis. That is the reason you can´t just draw a function through all this points.

Such a set of points is called a relation in mathematics. Just because you can draw a line through them does not mean you should.

And just because it is customary to draw orthogonal x- and y- axes in mathematics does not mean that is always the best way.

Especially If the points of a relation are not stochastically independent it might not be a good idea.

After all, you draw on a euclidean plane and your are free which axes to chose on a euclidean plane.

GDP is an absolute quantity. If GDP doubles, then that means something. So readers should be thinking about the distance between the curve and the x-axis.

But 1980 is arbitrary. When comparing 2020 to 2000, all that matters is that they’re 20 years apart. No one cares that “2020 is twice as far from 1980 as 2000” because time did not start in 1980.

This is the difference between a ratio scale and a cardinal scale. In a cardinal scale, the distance between points is meaningful, e.g., "The gap between 1 and 2 is twice as big as the gap between 2 and 4." In a ratio scale, there is a well-defined zero point, which means the ratios of points are also meaningful, e.g., "4 is twice as large as 2."

My first impression was also that axis lines are a matter of aesthetics. But then I browsed The Economist's visual styleguide and realized they also do something similar, i.e. omit the y-axis line (in fact, they omit the y-axis line on basically all their line / scatter plots, but almost always maintain the gridlines). 

Here's also an article they ran about their errors in data visualization, albeit probably fairly introductory for the median LW reader.

Curated. Beyond the object level arguments for how to do plots here that are pretty interesting, I like this post for the periodic reminder/extra evidence that relatively "minor" details in how information is presented can nudge/bias interpretation and understanding.

I think the claims around bordering lines become strongly true if there were established convention, and more weakly so the way currently are. Obviously one ought to be conscious in reading and creating graphs for whether 0 is included.

In ggplot (R statistical language) the defaults include a subtle grid and no axes. They also put in the extra random space. 

Here is some code in case someone else using R wants to try out things discussed here:

library(ggplot2)
qplot(wt, mpg, data = mtcars, colour = factor(cyl)) +
theme(axis.line.x = element_line(color="black", size = 0),
axis.line.y = element_line(color="black", size = 1)) +
scale_x_continuous(expand = c(0, 0), limits = c(0,8)) + 
scale_y_continuous(expand = c(0, 0), limits = c(0,36))

I promise that readers will recognize a plot even without lines around it.

I'm not so sure. Without lines or tick marks, it's not all that clear what the squiggly line is. I'm sure some squiggly lines would be more obvious, and a scatter plot without axis lines or ticks would be more obvious still.

Suppose your data is how the GDP of some country changed over time, so the x-axis is years and the y-axis is GDP.

When you introduce tick marks and tick labels, I think you've already done most (if not all) of the work that the axis lines do. Now it's way more clear what we're looking at, and to the extent that the reader is invited to make ratio- or interval-level comparisons, the tick marks and labels provide most (all?) of the relevant information.

The LessWrong Review [? · GW] runs every year to select the posts that have most stood the test of time. This post is not yet eligible for review, but will be at the end of 2025. The top fifty or so posts are featured prominently on the site throughout the year.

Hopefully, the review is better than karma at judging enduring value. If we have accurate prediction markets on the review results, maybe we can have better incentives on LessWrong today. Will this post make the top fifty?