Percentiles in Tableau

The Tableau Support Communities contain several threads on how to calculate percentiles. Here is one that dates back to 2011 and is still going strong. It seems that historically (i.e. pre version 9), the calculation of percentile required all sorts of homegrown calculated fields that use Tableau's LOOKUP() and WINDOW_*() functions and other abstruse and barely documented features of Tableau's inner workings.

Now that we have the PERCENTILE() function and Level-of-Detail calculations, it seems to be a lot simpler. Here is the code that I use to tercile the items on all the orders in Tableau's "superstore" dataset by sales value:

IF [Sales] > {FIXED : PERCENTILE([Sales], 0.667)}
    THEN "H"
ELSEIF [Sales] > {FIXED : PERCENTILE([Sales], 0.333)}
    THEN "M"

Dropping this dimension into a crosstab confirms that (i) each tercile contains the same number of items and (ii) the minimum and maximum of each tercile do not overlap.

tercile minimum sale/$ maximum sale/$ count
H 127.96 22,638.48 3,329
M 25.20 127.95 3,334
L 0.44 25.18 3,331

Isn't there a term missing from the LOD expression?

Yes. All the documentation I have found suggests that the first of my LOD expressions should look like this:

{FIXED [grain] : PERCENTILE([Sales], 0.667)}

Omitting the "grain" qualifier seems to cause the expression to be evaluated at the finest grain possible, namely the individual row within the dataset. In this case, that is just what I want.

Sidebar: Why do I want to tercile anyway?

Splitting a continuous variable into discrete ranges aids communication and non-experts' interpretation of results. But how many discrete ranges should one use? Well, that depends on (i) the question you are trying to answer and (ii) the established practice in that particular discipline. For example, in pharmaceutical sales everything gets split into deciles: the things that a pharma rep does with a decile 10 physician are very different to the things she does with a decile 1 physician.

Personally, I like splitting into an odd number of ranges as it allows some items to be average. That central category contains the peak of the bell-curve and some stuff either side: in many cases I have found that this provides a better mapping of my analysis to the real-world problem that the analysis is attempting to solve. (I suspect that this is the flip-side of the problem in social sciences about whether a Likert scale should contain an odd or even number of terms; see link for discussion.)

Here is more evidence to support the odd-is-better-than-even position: Beyond the median split: Splitting a predictor into 3 parts.