Graphs: tips from Briefings - comparing across countries

This is the third of several emails that look at the UK Coronavirus Briefings on TV. This one is on graph type (and I appreciate that when fighting pandemics, sorting out graphs isn’t key).

Should the Briefings' graphs show lines or columns? Daily or cumulative figures? Etc. This is a huge topic, plus political goals muddy the waters. So I limit this review to one topic: how to compare exponential growth for total infections over time across different countries.

Figure 1 is what we ended up with after the typography tips in the last review (click here for those tips) - it shows fictional numbers for total infections for four countries, A, B, C, D. Study it and ponder this: which countries are bringing down their spread of infection? Which countries are failing to? I don’t know… I struggle to compare exponential-growth lines. Is line D getting more or less exponential over time than line C..?

Figure 2 re-plots it as a log graph. The actual data are the solid lines - and all the way back to Day 0 now. You can also just about see dotted lines alongside each country's solid line - more on this later.

Log scales are great for exponential growth. They appeared often in the media, but surfaced just twice in the Briefings – on 29 April and 6 May.

Now for those dotted lines... they're straight, and because it's a log scale, straight lines show constant daily percentage changes in infections, e.g. D's dots plot a constant 70% increase in infections every day - and A's dots plot a constant 25% increase a day.

And lo, from about Day 12, D's solid line starts to dip under its dotted line - hence its daily increase in infections moves down from 70%. It's making inroads into the spread of infection. A is worsening though – its solid line moves over its dotted line, so its daily increase in infections moves up from 25%. Log graphs help us compare exponential changes.

But it's still not ideal. Readers must squint at gaps between a country’s solid line and dotted line - and that's neither that easy nor intuitive. But what to do instead?

Well, to see if the daily percentage change in infections gets higher or lower, the answer is: plot the daily percentage change in infections. Obvious, really.

See Figure 3. Readers easily see that, for the first 11 days, the increase in infections doesn’t change for any country – D rises at 70% a day, A rises at 25%, etc. Then at day 12, things happen, e.g. D drops linearly from 70% a day to 50% by Day 16 - it's making inroads. And over the same period, A rises from 25% to close to 40% - things are getting worse in country A. Much easier. And a lead-in title would make it even easier.

In real-life though, numbers are rarely as linear or smooth as in Figure 3, hence 7-day rolling averages help… and the Briefings do such graphs thankfully.

Time to summarise. Firstly, we struggle to compare exponential-growth lines (albeit it's not often we wish to make such comparisons...). Secondly, don't force readers to squint at small gaps between lines - or columns.

And at work, we force people to squint a lot. Figure 4 shows cumulative sales, Actual versus Budget - "Now let's see... the grey line is just above the black line there, but just beneath it there... hmm"). And Figure 5 is the percentage of calls answered in Target time - Actual is dark grey, Target light grey. (Notice that Target is always 96%, so there's a 'helpful' horizontal line at 96%...I see this a lot.)

No. Instead, plot the monthly variances between Actual and Budget sales. Or the Unders or Overs against Target.

Or do a table. Figure 6 rejigs the numbers from Figure 4 - it shows the percentage variance from budget by month. As seen from the table, the first five months' variances are tiny, the next four are huge. Bet you didn't spot that from Figure 4. (Notice that numbers are in a column, not a row. We find it easier to scan down columns than across rows.)

There's more on this topic, e.g. people tell me: "But cumulative graphs help because blah, blah"). Let's stop there though.

Time for a really bad Covid graph. Figure 7 is how the US State of Georgia showed statistics. Study the x-axis: April 28, April 27, April 29, May 1, etc.... what order is that?! Truly weird. It's fascinating to read Georgia's 'reason' for it - click here for the full story. With thanks to Mike van de Water for drawing it to my attention, and to Joey Devilla for the original post on social media.

Til next month.

Clarity and Impact Ltd | +44 20 8840 4507 | jon@jmoon.co.uk | www.jmoon.co.uk

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