What is the difference between d3.scale.quantize() and d3.scale.quantile()?

Question

From the docs, the definitions are:

quantize

..a variant of linear scales with a discrete rather than continuous range. The input domain is still continuous, and divided into uniform segments based on the number of values in (the cardinality of) the output range.

quantile

...map an input domain to a discrete range. Although the input domain is continuous and the scale will accept any reasonable input value, the input domain is specified as a discrete set of values. The number of values in (the cardinality of) the output range determines the number of quantiles that will be computed from the input domain

These both seem to map continuous input domains to a set of discrete values. Can anybody illuminate the difference?

Looking up quantile outside of their use in D3 is what helped me. Quantiles are very simple once they are explained in the context of medians: https://www.statisticshowto.com/quantile-definition-find-easy-steps/ — cyclingLinguist, Dec 06 '22 at 14:44

score 23 · Answer 1 · edited Oct 09 '13 at 12:42

In general terms, the difference is similar to the difference between the mean and median.

The difference is only really apparent when the number of values in the input domain is larger than the number of values in the output domain. Best illustrated by an example.

For the quantize scale, the input range is divided into uniform segments depending on the output range. That is, the number of values in the domain doesn't really matter. Hence it returns 1 for 0.2, as 0.2 is closer to 1 than 100.

The quantile scale is based on the quantiles of the input domain and as such affected by the number of values in there. The number of values in the output domain only determines how many quantiles are computed. By their very nature, the quantiles reflect the actual list of values rather than just the range. Thus, an input of 0.2 returns 100 as the corresponding quantile is closer to 100.

Are you writing "domain" when you should be writing "range" and vice-versa, at least in your first two paragraphs? — cyclingLinguist, Dec 05 '22 at 20:45

score 11 · Accepted Answer · answered Jul 20 '17 at 07:42

Coloring Maps has a great visual explanation.

Quantize:

Quantile:

On the scatter plot, the previously horizontal bars are now vertical as the colors of each place is determined by its rank, not value.

Here's a code snippet in D3 v4 that shows different results in quantize and quantile.

const purples = [
  'purple1',
  'purple2',
  'purple3',
  'purple4',
  'purple5'
]
const dataset = [1, 1, 1, 1, 2, 3, 4, 5] // try [1, 2, 3, 4, 5] as well
const quantize = d3.scaleQuantize()
  .domain(d3.extent(dataset)) // pass the min and max of the dataset
  .range(purples)
const quantile = d3.scaleQuantile()
  .domain(dataset) // pass the entire dataset
  .range(purples)
console.log(quantize(3)) // purples[3]
console.log(quantile(3)) // purples[4]

Dave · Answer 3 · 2017-06-17T23:22:42.500

9

I had this same question myself. So I made a visualization to help understand how they work.

edited Jun 17 '17 at 23:22

answered Oct 26 '16 at 16:15

Dave

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I don't understand the static version of this visualization. Can you post it on bl.ocks? – Jonathan Schneider Oct 26 '16 at 22:50
1

@jkschneider The link was already above, but now I've linked the image to it as well. – Dave Jun 17 '17 at 23:23
I love this graphic, but it doesn't answer this particular question. You should incorporate a situation where there are more inputs than outputs like in Lars Kotthoff's answer. I gave it an up-vote. – Phillip Scott Givens Dec 24 '17 at 22:52
@PhillipScottGivens The nice thing about bl.ocks is that it's just a Github gist. So you can fork it and make the changes you'd like to see :) – Dave Jan 04 '18 at 17:03

score 5 · Answer 4 · answered Oct 09 '13 at 03:59

The difference is, as far as I can tell, simply that statistically quantiles are finite, equal, and evenly-distributed discrete blocks/buckets into which your results simply fall. The difference being that a quantized scale is a continuous function based on your discrete input.

Basically: quantize allows interpolation and extrapolation, where as quantile forces the value into the subset.

So, for example, if a student's calculated grade is 81.7% in a quantized scale, a quantiles scale of percentiles would simply say that it is of the 81st percentile. There's no room for flexibility there.

What is the difference between d3.scale.quantize() and d3.scale.quantile()?

quantize

quantile

4 Answers4

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