Different kinds of Variables: discrete Variables

This chapter begins the attempt to classify Variables (and language-Variables) according to their Levels and the relationships between them, looking first at discrete Variables.

The alert status is ((green < orange  < red)).

The law was passed ((no,yes))

The most affected area was ((North, South, East, West)) Province.

The black on/off symbol next to the Variable “The law was passed” shows at a glance that this is a so-called “no,yes” Variable.

The black symbol with a block going up to the right, next to the Variable “The alert status”, shows at a glance that this is a so-called “ordinal” Variable - a discrete Variable whose Levels can be compared with one another, which allows the Variable to express a sense of “more” or “less”.

In this chapter we also look at some more unusual examples of discrete Variables such as “hierarchical” and “circular”.

Discrete Variables

Discrete Variables are quite familiar to empirical social scientists and to M&E professionals.

A discrete Variable has Levels which can be listed in advance.

Reminder: we normally don’t distinguish between Variables and language-Variables

So where above we perhaps should have said this:

A discrete language-Variable has Levels which can be listed in advance

Yet when feeling lazy we might also say that the Variable which the language-Variable refers to “has a discrete set of Levels” or “is discrete”.

Actually lots of people don’t bother making the distinction at all (not sure that Pearl does).

Binary Variables

If it can be true, it can be false too. So there’s your Variable.

((no,yes)) Variables are Variables too.

Sometimes, when writing a Theory of Change, it is easy to overlook that ((no,yes)) Variables are Variables too. So when a Variable is numeric, say, number of children attending a session, it is quite easy to recognise it as a Variable. But when a Variable is expressed as a no/yes proposition or statement, it is sometimes harder to grasp that it too is a Variable, with just two Levels.

Many sentences can best be seen as expressing binary, yes/no Statements. But not all sentences are like this8

The law on social protection was *passed--* ((no,yes)).

Dichotomised continuous Variables

You can always dichotomise continuous Variables, and sometimes it makes things simpler. But how advisable is it? You can see this as an empirical question as well as a theoretical one. For example the argument in psychiatry about whether no/yes diagnoses are more adequate and useful than a continuous or dimensionally-based approach to diagnosis.

Intensity Variables with just two Levels (“dichotomised”)

Example:

President's overall approval level ((negative, positive))

You can think of this as like a dichotomised intensity Variable (President's overall approval level ((lo-0-hi))). See intensity Variables.

Nominal Variables

The winning team in the final was ((Germany, Brazil).

The most successful East African country was *Kenya--* ((Tanzania, Burundi, Rwanda, Uganda, Sudan, South Sudan, Ethiopia, Kenya, Eritrea, Djibouti, Somalia)).

The meaning of the list inside the double brackets should be fairly obvious: it is a direct listing of the alternatives. Here, Kenya could be the Level of a Variable which could have taken the Level Sudan or Eritrea or any of the other countries in the list. (Actually, Theorymaker native speakers use a rather colourful clicking noise; the asterisks are just a way to indicate this delightful sound).

These Statements correspond to what are often called“Nominal Variables”. In Theorymaker, calling a Variable “nominal” usually means it is not binary: the Levels are not numbers and do not follow any other special rules or relations like, say, greater than or less than.

The Variable’s Levels are discrete, with no consistent ordering.

Nominal variables: Statements with an implicit list

Sometimes Theorymaker native speakers can’t be bothered to list all the options, and who can blame them. So they just name the list without actually spelling everything out.

The winning team was *Germany--* ((list of all the finalists)).

The country worst hit by the typhoon was *the Philippines--* ((list of countries in S.E. Asia))

Ordered Variables

The vast majority of Variables we meet in M&E are ordered: for any two members of the Domain, we can ask and answer the question “which of the two is bigger/more important/more something” (and usually it is also possible that the two are the same.)

A Variable is ordered if it is possible to say, for each of its Levels, whether it is in some sense bigger or smaller than any other Level.

By convention, Theorymaker native speakers also treat no/yes Variables as ordered too, with the “yes” Level being greater than the “no” Level.

Examples: a child’s height, or achievement, or a country’s GDP.

Common exceptions are:

  • Variables for which although they have an obvious order, it is not clear without further information which we are to interpret as large and which as small, even if numbers have been assigned to them arbitrarily. Example: season of the year.
  • Nominal Variables, like “the current leader of the English Premier League”
  • More complicated Variables “colour” which can be understood as involving more than one dimension (e.g. brightness, hue, etc.)

Ordinal Variables (step-by-step ordering)

Whenever we see these kinds of Statements, we know that there are not only a fixed number of alternatives but that in some sense they are ordered from “less” to “more”.

Ordinal Variables (step-by-step ordering; explicit listing)

The medal she won at the 2016 Olympics was a *silver--* ((bronze < silver < gold)).

The most frequent answer was *quite bad--* ((very bad < quite bad < quite good < very good)).

The alert status is *orange--* ((green < orange < red)).

Written Theorymaker uses a “less than” symbol < to separate these discrete but ordered alternatives.

Ordinal Variables (Step-by-step ordering; implicit listing)

Sometimes Theorymaker native speakers cannot be bothered to list all the alternatives but simply specify the endpoints and the number of stages. It is only important that there is at least one < in the Statement so that we know we are dealing with a step-by-step Variable.

The most frequent answer was ((very bad < bad <... very good (in five stages))).


The most frequent answer was ((very bad < ... neutral < ... very good (in five stages))).

Hierarchical Variables (classification)

The animal she identified was a *East-Asian Tiger--* ((hierarchical classification of species and sub-species,)).

You can think of the Variable the animal she identified as hierarchical - she might have said just Tiger, or East Asian Tiger, and both of these have a place on a hierarchical classification tree.

Circular

Any cyclic variable is likely to have some circular form, for example the passing of the seasons. This is often presented really as a circle in temperate climes. It is interesting how this circular format changes as you move to other climates.

 The current season is *somewhere between winter and spring--* ((the seasons as a continuous, circular Variable))
 The current season is *spring--* ((the four seasons - an ordered yet circular Variable))

Similar is the debatable idea that political parties can be put on a broadly left-right spectrum which however meets at the extreme ends (such a 20-th century idea, isn’t it?).


  1. Unfortunately, some analyses of causation like to forget that Variables and Statements, from global warming to inflation rate to a child’s attachment style, frequently have more than two Levels. See xx..