Developing a vibrant accessible colour palette

7 Apr 2019 13:29 GMT

I have been working with ggplot2 themes lately, including developing a theme for the House of Commons Library. In my spare time I have also been working on a plotting theme for personal projects. For this theme I wanted a vibrant colour palette for representing discrete categories that is accessible to people with the most common kinds of colour blindness.1

I don't have any expertise in colour vision, but there are lots of good tools to help you test how a given set of colours look to different people, including Susie Lu and Elijah Meeks' Viz Palette and the Coblis colour blindness simulator.

I spent a while playing around with colours in Viz Palette, trying to come up with a set that are visually distinct for most people. I was interested to see how many categories it was possible to safely represent.

I managed to come up with a six colour palette that seems to work reasonably well in most cases. I stress, this was just the result of my own inexpert trial and error. I am sure there is room for improvement. The colours are:

  • blue [#0080e8]
  • sky [#70d0ff]
  • mint [#98f098]
  • yellow [#ffa000]
  • green [#009900]
  • magenta [#c00060]

There are two caveats to bear in mind. First, this palette still fails for people with the most severe and least common types of colour blindness, such as tritanopia and monochromacy.

Second, the palette takes advantage of differences in the perceived brightness of different colours, so colours that look different to people with no colour deficiency appear as different shades of the same colour to people with protanopia and deuteranopia.

In practice, this means you need to take care if you interpolate between the colours in this palette to represent more than six categories. Doing this may reduce accessibility, as it risks creating colours that are not visually distinct to some people. The sequence of the colours in the palette has been chosen to reduce this risk, but it needs to be considered. To be on the safe side, use the same number of colours from the palette as there are categories and don't interpolate.

Column charts

The following charts approximate how this palette looks as a basic column chart to people with different types of vision. The colours shown are based on the transformations shown on Viz Palette, which I assume are a good approximation.

If you are colour blind in one of the ways listed here, I would love to know if you can in fact distinguish between the colours in the first chart in the way the colour blindness simulators suggest you are able to.

A simple bar chart showing how the colours look to a person with normal vision

A simple bar chart showing how the colours look to a person with deuteranomaly

A simple bar chart showing how the colours look to a person with protanomaly

A simple bar chart showing how the colours look to a person with protanopia

A simple bar chart showing how the colours look to a person with deuteranopia

Scatter plots

I wanted to test the palette in the most difficult case. So here is the same comparison using a messy scatter plot with all six categories. The charts show turnout in Parliamentary constituencies at the 2017 General Election by median age, with each constituency shaded according its settlement class, based on the Library's city and town classification of constituencies.

A scatter plot showing how the colours look to a person with normal vision

A scatter plot showing how the colours look to a person with deuteranomaly

A scatter plot showing how the colours look to a person with protanomaly

A scatter plot showing how the colours look to a person with protanopia

A scatter plot showing how the colours look to a person with deuteranopia

Line charts

And finally, here is the same comparison again with a line chart, showing an index of the value of various technology stocks over the last decade.

A line chart showing how the colours look to a person with normal vision

A line chart showing how the colours look to a person with deuteranomaly

A line chart showing how the colours look to a person with protanomaly

A line chart showing how the colours look to a person with protanopia

A line chart showing how the colours look to a person with deuteranopia

The palette is available as ggplot2 scales in the pilot package, which is my general purpose plotting theme. You are more than welcome to use or fork it, but I make no guarantees that the theme elements won't change in future.


1. A quick note about the spelling of colour. I'm British so I spell colour “colour”. But in most English-based programming languages the word colour is spelled “color”. Consequently, I've developed a habit of using “color” everywhere in source code, and “colour” in all other contexts. But it's leaky. Is a GitHub readme source code? Probably, if it includes function signatures.

Experimenting with grid histograms

11 Mar 2019 08:38 GMT

A few months ago, when ONS published their population estimates for Parliamentary constituencies in mid-2017, I worked on an analysis of constituencies by median age. This included some interacive charts produced with D3, which I was never able to publish as the online part of the project didn't get off the ground. Rather than see that work go to waste, I decided to publish the charts here for posterity.

The charts in question are grid histograms, which show the distribution of Parliamentary constituencies by median age at the 2017 General Election. In these charts, each square represents a single constituency, and each chart shows the squares shaded by another variable: such as party, turnout and majority. Click on the image below or the link above to see the interactive versions of these charts.

A set of four charts each showing the distribution of constituencies by median age and their relationship with another variable

On average, median age was lower in seats won by Labour and higher in seats won by the Conservatives. Turnout tended to be higher in seats with a higher median age. And some of Labour's biggest majorities were in seats with the lowest median age.

As a way of showing the strength of the relationship between two variables, I think this type of chart is probably less succesful than a scatterplot. But as a way of showing the distribution of one variable within another, I think it works quite well. Although perhaps better for the continuous variables than the categorical variable.

Web scraping for BBC More or Less

10 Feb 2019 17:27 GMT

During my career as a journalist I used to work for BBC Radio Current Affairs, where I would often work on Radio 4's pop stats programme More or Less. I don’t think anyone would be surprised to hear it was my favourite programme.

I am still in touch with the team that make the show, and every now and again the editor Richard Vadon sends me a message to chat about something statistical. Last year he sent me a DM with an interesting question.

A direct message from the editor of More or Less asking me to web scrape data on the position of the planets over time

More or Less wanted to work out which planet was closest to Earth on average, given how their relative positions change over time. They were exploring ways of getting the data and wanted to know if I could help. They did the story on the programme a couple of weeks ago, and they have produced a special version of that show for the BBC’s new interactive web player.

I want to be clear about how I helped with the story, because Tim Harford was very generous with his praise on the programme, which was kind of him and the team, but it was essentially a web scraping exercise.

I'm not an astronomer. I do use computational statistics in my job but I work primarily with social, economic and political data. Richard asked if I could help them with the story by scraping the data from the web, which I did. I’m not even sure this is the best source for the data, but it is a source, and one that was relatively easy to use.

Here’s a chart of the data that I gathered for the story — these are the “wiggly lines” Professor David Rothery talked about during the piece. It shows that on average over the last fifty years Mercury was the planet that was closest to Earth.

A chart showing how the distances of Mercury, Venus and Mars from Earth vary over time

If you want to reproduce the chart yourself, you can download the Python code to gather the data and generate the image from this gist.

R and Python packages for the Parliamentary data platform

27 Jan 2019 18:26 GMT

I recently published two software packages for downloading and analysing data from the new Parliamentary data platform.

The data platform is an ambitious project, which aims to be a canonical source of integrated open data on Parliamentary activity. The data is stored in RDF and is available through a publicly accessible SPARQL endpoint. You can see the structure of the data stored in the platorm visualised with WebVOWL.

These packages provide an easy way to use the data platform API in both R and Python. They are aimed at people who want to use Parliamentary data for research and analysis. Their main feature is that they let you easily download data in a structure and format that is suitable for analysis, preserving the links between data so that it is easy to combine the results of different queries.

The packages provide two different interfaces to the data platorm:

  • A low level interface that takes a SPARQL SELECT query, sends it to the platform, and returns the result as a tibble (R) or a DataFrame (Python), with data types appropriately converted.
  • A high level interface comprising families of functions for downloading specific datasets. This currently focuses on key data about Members of both Houses of Parliament.

I think the data platform is great. It's a really valuable piece of public data infrastructure that has the potential to become a comprehensive digital record of what Parliament does. I hope to expand these packages as more data is added to the platform in future.

A bestiary of undead statistics

30 Oct 2018 19:47 GMT

For some time now, statisticians and fact-checkers have talked about zombie statistics: false statistical claims which have found their way into public debate that are repeated endlessly and uncritically. They are called zombies because no matter how many times you beat them to death with evidence, they keep coming back to life.

A few months ago I described a particular false claim as a vampire statistic, because it survives in the shadows of semi-public discourse and avoids the daylight of scrutiny that could kill it.

I've been wondering what other kinds of undead statistics there are, and seeing as it's Halloween I've had a go at a typology. This is a little schematic, so I'd welcome any suggestions to flesh it out.

  • Zombie statistic — The classic undead statistic; it survives all attempts to destroy it with facts and keeps on claiming victims.
  • Vampire statistic — A statistic that never dies because it is never exposed to daylight. It is too wrong to appear in the usual arenas of public debate, so it keeps circulating through viral channels. Vampire statistics survive in the dark corners of the internet where paranoia and conspiracy theories flourish.
  • Phantom statistic — A statistical claim with no apparent source. It is either asserted without evidence or attributed to a source that does not contain the statistic.
  • Skeleton statistic — The bare bones of a statistical claim that has been removed from the body of knowledge that gives it life and meaning. This kind of statistic is often true in a narrow or technical sense, but is untrue in the way it is presented without context.1
  • Frankenstein statistic — a false statistical claim produced by stitching together statistics from different sources that shouldn't be combined.2
  • Werewolf statistic — A statistical howler that comes up with predictable regularity at certain events or times of year.3
  • Mummy statistic — A statistic that was once true but is no longer true. It has somehow been embalmed in the public imagination and keeps coming back to life when it should have died a long time ago.4

Happy Halloween!


1. An example of a skeleton statistic is the claim that more than 90% of communication is non-verbal. Albert Mehrabian's finding was that, in certain experimental settings, more than 90% of the content of communications about feelings and attitudes was non-verbal.

2. An example I can recall is this article, which compared the number of EU migrants living in the UK with the number of British migrants living in the EU using datasets that had different definitions of a migrant. To the FT's credit they quickly corrected the story (because they have a brilliant data team).

3. See Blue Monday, for example. See also the recurring confusion between the net change in the number of people in work and the number of new jobs that accompanies ONS's regular labour market statistics.

4. I once accidentally created a mummy statistic. In 2014, I tweeted that the Telegraph was wrong to say net migration was above 250,000. The tweet was picked up by a fact-checking bot, which intermittently cited me saying this over the next two years, as net migration rose to around 330,000.