Some of the comments at the bottom of the article lament the "innumerancy" of the general public. But let's be honest: logarithmic scales take effort to read. And like any kind of communication, you should make it easy to read.
As a person who creates and looks at charts all day, I can read complex charts. But I really prefer other people use linear charts of simple bars or trend lines. You're conveying a new idea to me, so don't assume I have all the context you do when reading the chart.
If you want to show acceleration, remember to use different units. Choose a unit that can be shown on a linear scale. E.g., the ratio of today's cases over the cases from a week ago.
They take effort to read even when you know what they are; on top of that it's easy to not notice that they're logarithmic, and I'd bet a lot of people don't even know what "logarithmic" means.
In my experience, all of the following words cannot be used in general discourse: Quadratic, linear, logarithmic, exponential, orthogonal, asymptotic, etc...
The second you use any of those words, people's eyes glaze over and there's an audible mumble sigh of "Ugh! Maths!"
I observe that "exponentially", along with "minimal", and "inflection point" are frequently used in the popular press -- wrongly, or at least without understanding of the first, quantitative sense of the term.
In all honesty, I know what I'm looking at and I still find it hard to understand by comparison. It's also poor graphing.
Graphs should have a purpose and communicate information as clearly as possible. Scales and units should be chosen to most effectively convey information. Logarithmic scales are a poor choice for the information being displayed.
The logarithm is appropriate because disease transmission is an exponential process.
For a given set of parameters (of measures such as social distancing, mask wearing, weather, etc.) new infections will not rise by some specific, absolute number. Rather, similar environments result in similar rates of new infections as a percentage of existing, active infections.
But that's not what the graphs are showing. The graphs are showing continuous infections over February, March and April. Those are not unknown future times. Those are past times with existent data. There's no reason not to represent those data as clearly as possible. Which a logarithmic scale does not.
Again graphs should serve one purpose. The purpose of those graphs is clearly, by the axis labels, supposed to display continuous deaths over a set period of time.
The linearly scaled graph displays this clearly, the logarithmic one does not. If the x-axis displayed into some future time, yes I'd agree a logarithmic scale may be more appropriate. But that would be displaying a graph of predictions at that point, which is something totally different than the two example graphs are showing.
Simply asserting that graphs should communicate one purpose does not make it so. Multiple audiences require multiple techniques for visualization and analysis. A logarithmic scale communicates the characteristics of an exponential curve better than a linear scale.
Well log scale is intended to make it easier to read... In general it is used in cases where a linear scale would be unreadable.
Your suggestion about changing what is represented in order to avoid a log scale is good but does not solve the root of the issue: many members of the public will not understand the information however it is represented because the concept itself is too complex.
I've found that, if somebody has trouble understanding a type of statistic (log-scaled, survival rate, confidence interval), it's because they never use them. You could say we should teach these things in high school, but why? So we can effectively communicate data they still won't use?
Throwing more math, tech notes, or gentle introductions at the communication problem has never worked for me. What has worked is expressing the concept in the most "real" terms possible.
Epidemiologists are worried about exponential growth because it means hospitals will be swamped. That worry should be the topic when communicating with the public. How long until that's projected to happen? Maybe show the linear trend with a horizontal line for capacity and dotted line for a forecast of need. Put a huge red circle around where they intersect. Even better: just write "X days predicted until overrun."
Also, charts are terrible for reading data. They're good for comparisons, trends, and distributions. I only use them for exploring or summarizing. Tables are for readable numbers.
Blaming the people you're trying to communicate with is not a winning move.
When you look at the 2 graphs side-by-side, as in the article, it's apparent which conveys more meaning (the linear one), unless I suppose you read log graphs all day. The public does not.
Blaming would be to claim that it is their fault for not understanding.
Here it is not blame, it is a statement that anything above the most basic maths concepts will stump a surprisingly large number of people. I'm not sure 'surprisingly' is the right word but here it is.
What actually happened? Some people were shown linear data on a linear scale, others were shown the same linear data on a logarithmic scale. The people who saw a straight line, because the scale matched the data, were better able to interpret and extrapolate the data.
The spread of the novel coronavirus in the USA used to be exponential, but it was linear at the time the subjects were asked to analyse.
You don't say! Before the the authors recruited 2000 subjects to investigate that, maybe they could have enrolled in Physics Practical 101 and listened to the demonstrator. If they went to an old-school physics department, they would have seen some real semi-log graph paper, designed for people to read actual values off. It doesn't look anything like the scales on their graphs.
Oh, but the subjects who saw a linear graph were more likely to accept the authors' opinion on what to do about that data.
The authors are right: the USA and UK should do more to contain the coronavirus. But it's still propaganda to advocate that data be presented in a certain format because that makes readers agree with your opinion, even when your opinion is right.
> [...] we find that the group who read the information on a logarithmic scale has a much lower level of comprehension of the graph: only 40.66% of them could respond correctly to a basic question about the graph (whether there were more deaths in one week or another), contrasted to 83.79% of respondents on the linear scale.
> Admittedly, we cannot know which policy preferences are superior. However, we do know that unlike the people who saw the graph on a logarithmic scale, the people exposed to a linear scale graph can form their preferences based on information that they can understand better.
While they're using pandemic data, they're asking people about their basic understanding of data in the graph.
> The public do not understand logarithmic graphs used to portray Covid-19
- does the public include our leaders? Very likely.
- although I know what a log plot is, I didn't have an intuitive answer to the question posed in the article. So instead of informing people, it adds further confusion.
Related:
- the Santa Clara (Bay Area) hospitals dashboard is confusing and takes about 2 minutes to load, so another example of poor crisis communications - inexcusable in 2020:
Logarithmic scales are such a common and useful tool, it's a hard pill to swallow that the general populace doesn't have the knowledge or interest to understand them. I'm not talking from an elite academic point of view; if you make it through sophomore year of high school, you have at least been exposed to them, and if you graduate highschool you've been tested on their use.
I use them regularly (nearly every time I plot data to figure out trends or whatever), and have a hard time imagining not having them for problem solving.
Yesterday I was looking at a COVID-19 log graph and I was interested in a point of the curve right at the middle between the 100 and the 1000 tick mark. It's hard to have an intuition on what the value was.
edit: I double checked for the record, the value halfway between 100 and 1000 is 316.2.
The financial times has a covid tracker with log vs linear, daily vs cumulative and absolute vs per capita toggles. I understand log scales and even so, changing these settings really makes me look at the data differently. For example - look at absolute daily data on a log scale and Brazil seems headed for destruction, overtaking the UK amd US. Look at cumulative per capita data on a linear scale and things don't seem so bad for Brazil, but Belgium looks like a disaster.
Well even tech folk don’t read charts correctly, even if they understand a logarithm.
I have seen all kinds of junk nonsensical charts in my career that somehow made it into reports, because nobody thought it was necessary to take the time to READ the chart and ask a few questions to see if it made any sense.
As a person who creates and looks at charts all day, I can read complex charts. But I really prefer other people use linear charts of simple bars or trend lines. You're conveying a new idea to me, so don't assume I have all the context you do when reading the chart.
If you want to show acceleration, remember to use different units. Choose a unit that can be shown on a linear scale. E.g., the ratio of today's cases over the cases from a week ago.