In scientific writing, the typical ways to report uncertainty are with the friendly plus-or-minus sign, e.g., 1.5 ± 0.05, or the more concise parenthesis notation, e.g., 1.5(5).

These representations are understood to give a range within which the true value is likely to fall – the textual equivalent of error bars in a plot. While it can be tricky to pin down the precise meaning of the stated uncertainty (a 95% confidence interval? the standard error? a Bayesian credible interval?), authors can spill a little extra ink to indicate what kind of range they have shown and the notation works just fine.

In popular writing, it seems more common to avoid any technical notation (e.g., ±). Instead, you are likely to see either a range of values (e.g. “between 1 and 3”) or just some fuzzy modifier (e.g., “about 2”). This approach trades detail about the uncertainty for approachability, which makes perfect sense for a more informal target audience.

Where I think both approaches come up short is in conveying an intuition of what values are likely. Sure, the information is there, but we know that probability is hard and uncertainty often misunderstood.

My uncertaintext project is a little experiment aimed at delivering this intuition. Let’s take advantage of the fact the webpages need not be static, and see what happens if we display uncertain values as a simple text-only animation of samples from some underlying distribution.

Uncertaintext in action

Take this example sentence about the current estimate of sea level rise provided by NASA:

Satellite sea level observations show 101 ± 4.0 mm rise in global sea level since 1993.

Let’s jazz it up a bit using the uncertaintext library. Taking a guess that the measurement uncertainty is Gaussian, and that the stated 4.0 mm range is two standard deviations, we can tell uncertaintext to display samples from a normal distributes with mean 101 and standard deviation 2.0 mm. Observe the fun!

Satellite sea level observations show mm rise in global sea level since 1993.

Maybe that’s too much precision? We can update the format to give fewer digits.

Satellite sea level observations show mm rise in global sea level since 1993.

Maybe that update cadence is too fast and giving you a headache? We can specify the update in “frames-per-second” to slow things down. The previous example updates 5 times per second, so let’s reduce that to 2.

Satellite sea level observations show mm rise in global sea level since 1993.

Maybe you want a different distribution? We can try a uniform distribution instead, here with a minimum of 97 and a maxium of 105.

Satellite sea level observations show mm rise in global sea level since 1993.

Personally, I find this dynamic representation informative, if a bit silly. I think that it does impart a more visceral feel for the certainty of the estimated value.

As a final example, say we have two estimates with the same expected value but different standard deviations. Displaying these with uncertaintext hammers home the difference in a quite satisfying way:

Standard Notation 1 ± 0.01 1 ± 0.5

How to use it

Uncertaintext is a javascript module which finds HTML elements with class=uncertaintext, parses special dataset attributes that define the distribution, format, and update interval, and then inserts random samples into the element’s innerHTML.

First, download uncertaintext.js and put it somewhere accessable to your webpage.

Then, import the main uncertaintext function into your page and run it, like so:

<script type=module>
  import uncertaintext from "include/uncertaintext.js";

I’ve found that using a monospace font is essential too. Otherwise, the changing character widths nudge the surrounding text and make the page layout unstable. A little bit of styling does the trick:

  .uncertaintext {
    font-family: monospace;

Lastly, add <span> elements where you want uncertaintext to display random samples from a given distribution. For example: <span class=uncertaintext data-uct-distrib=normal data-uct-mu=1 data-uct-sigma="0.01"></span>

This is, in fact, exactly how this blog post uses uncertaintext. For more details on available distributions and other formatting options, take a look at the README for the project.