# Variable-labels and Variables

Theories and Theories of Change are written down in Theorymaker as connections between Variables; so first we need to learn how to write down Variables.

Variables have labels like this…

The security alert level was ((green < orange < red))

… which we call, unsurprisingly, Variable-labels. (In this case, the three options are arranged into some kind of order of importance or severity, as shown by the < symbol.)

This Variable-label is a kind of template which can be used in any of the following Statements:

The security alert level was *green--* ((green < orange < red))
The security alert level was *orange--* ((green < orange < red))
The security alert level was *red--* ((green < orange < red))

… we call this set of possible Statements the corresponding language-Variable.

Loosely, Theorymaker native speakers also use the word “Variable” for whatever the written language-Variable refers to, or, as Theorymaker native speakers say, whatever the written language-Variable reports.

This security alert level is ((red, orange, green))

Any line like of text like the one above is called a Variable-label. It is like a Statement but without any particular Level being marked as factual.

The set of all the Statements associated with a Variable-label is called a language-Variable.

A Variable-label on its own doesn’t really say very much. We only ever see them as part of Theories, see xx. It just says that these various possibilities exist. A Variable-label isn’t a Statement, it can’t be true or false. On its own, it is more an expression of the boundary conditions, part of the Context. So “the Ambassador’s support for the project, yes/no” cannot be uttered in Theorymaker on its own.

But we will need to be able to write Variable-labels once they join up into Theories, as part of claims about impact and effect, attribution and contribution, e.g.:

The Ambassador’s support was the main factor leading to the building of the airport.

A candidate’s approval rating depends partly on their social media presence.

In Theorymaker diagrams, Variable-labels look like this:

The security alert level is ((red, orange, green))

Loosely, Theorymaker native speakers also use the word “Variable” for whatever the written language-Variable refers to.

Surprisingly often, there is no need to distinguish between Variables and language-Variables.

## Classifying Variables according to their Levels

Perhaps the most important way to distinguish different types of Variable is according to the different kinds of Levels they can have and the different ways we can order those Levels7.

We aren’t used to the idea of a whole zoo of different kinds of types of Variables. As an extreme example, some statistics software packages like SPSS teach us that there are only really two kinds of Variable, string and numerical. But the Variables we meet in real life have all kinds of different shapes or types.

## Multiple Variables

There are plenty of concrete phenomena which we tend to think of as being expressed in terms of simple Variables, but if we try to model them mathematically we end up with multiple simultaneous dimensions. “The colour of this pixel” is like that - we tend to think of it as a single Variable, but in most technical implementations of colour we need three or more Variables to model it, e.g. the intensity of the red, green and blue lights which we need to create that colour.

The Theorymaker language is quite relaxed about this; one minute we are talking the colour of a pixel as “the Variable” and the next minute we are talking about it as a multiple set of three red, green and blue colour Variables.

### Example: personality

Psychiatric and psychological classifications are often multi-dimensional, e.g. the Big Five or the 16PF personality dimensions. One can argue about whether these can really only be understood as packages of, say 5 constituent Variables or whether it makes sense to understand them as a single Variable with 5 dimensions.

### Example: location

My house is at *45--* degrees North, 1 degree West ((from the set of points on the Earth's surface))

Whether you think of position on the map in terms of x and y coordinates, or latitude and longitude, or polar coordinates, you still need two dimensions.

### Example: multiple ordinal variables

So-called “Multi-choice Variables” are very popular in questionnaire research. You can think of these as blocks of individual yes/no Variables but you can also think of them as single Variables too.

Given any bunch of Variables, you can always think of any more or less complex combinations of them as a single, more complicated Variable and vice versa.

### Quality & Quantity (Q&Q)

Very often in project design we encounter Variables which express the quantity and quality of something - for example, “more and better services to the poor” - at the same time.

Theorymaker is quite relaxed about this kind of multiple Variable. Sure, if we tried to “break it down” into a quality component and a quantity component, we might find there are various, not necessarily equivalent, ways to do it. But this does not mean that the idea of such a “Q&Q” Variable is incoherent or useless.

### Unusual dimensionality

A good example of a two-dimensional Variable is Ainsworth’s “attachment style” (Ainsworth, Waters, and Wall 1978) which is neither totally linear nor merely ordinal, because the first and third have a common element.

• Anxious-Avoidant Insecure Attachment
• Secure Attachment
• Anxious-Resistant Insecure Attachment

## Note for Nerds: Why not just define Variables in terms of numbers and equality?

Most traditional approaches in empirical social science (see (To be completed)) parses Statements as essentially saying that one thing is equal to another, namely to a number. For example, “the child’s height = 102cm”. So we can object to the number part but we can also have a wider objection object to the whole “equality” approach.

So, above we said that the Level of the language-Variable in this Statement is 50:

The average age was *50--* ((from a range of likely human ages))

So this is like the traditional treatment, essentially “age=50”.

But no because:

The child was *smiling--* ((smiling, frowning, laughing, crying, ...))

and here the part that varies, each different Level, is a verb.

But this is uselessly philosophical. So what?

Well it has very practical consequences. it allows us to see that there are whole classes of Variables which have been ignored because they are hard to understand in the “x = a number” paradigm, such as “((lo-hi))” Variables.

### Variables: the acts of people and Gods?

The Levels of a Variable represent the possible outcomes of a decision or the consequences of a decision; Variables are the bits of the universe we can fiddle with, or imagine fiddling with, and/or their consequences. Arguably we can extend the idea to phenomena like the weather which seem to us to be like the decisions of people, or Gods. Pearl argues (Pearl 2000) that this is how causation was seen right up until the European Middle Ages. Perhaps they were right.

### Levels of a Variable: collectively exhaustive and mutually exclusive?

We normally only consider language-Variables in which the corresponding set of English sentences are mutually exclusive and collectively exhaustive. So we wouldn’t normally consider

This security alert level is ((red, orange))

… to be a language-Variable because there is a missing possibility; and normally we wouldn’t consider

This security alert level is ((red, orange, green, red or orange))

… to be a language-Variable because the possibilities overlap with one another.

What do we mean by “the Levels of a Variable have to be mutually exclusive and collectively exhaustive”?

Formally, one can argue that there is really no problem. Given any bunch of language-Variables, we can define their Cartesian product, i.e. the space of all possible combinations of their Levels and say “this is the Context within which all language-Variables are to be understood”.

So in a sense, every Theory is preceded by “… in the context which is all the possible combinations of all these different Levels of all these different Variables”. See xx.

#### Do Levels of Variables have to be mutually exclusive?

In a loose sense, we can think of both “30 degrees” or “really hot” as Levels of the language-Variable “current temperature outside this room”, even though they are specified with different Levels of precision and possibly overlap. Often we restrict what we count as the Levels of a Variable, and say they have to be mutually exclusive as well. Sometimes this exclusivity is sold as being critical to the definition of a Variable. But I think we can get along fine for now without insisting on it.

### References

Ainsworth, M D S, E Waters, and S Wall. 1978. Patterns of attachment: {A} psychological study of the strange situation. Lawrence Erlbaum Associates.

Pearl, Judea. 2000. Causality: Models, reasoning and inference. Cambridge Univ Press. http://journals.cambridge.org/production/action/cjoGetFulltext?fulltextid=153246.

1. Note for nerds: Actually, it is probably more consistent to say that what we are classifying here is actually pairs {Variable, some ordering of the Levels} - where the ordering is something like “greater than” or “happier than”. For example, you could order the Eurovision contestants not only in terms of their final score but also alphabetically.