Different kinds of Variables: vague Variables
In this chapter, we look at what happens when Variables aren’t clearly defined but still have too much going on to be thrown away.
Most of our actual Theories of Change are full of Variables like this (even though we might have to squash them into a more precise format if we want to use them to manage a project.)
It is quite easy to say and understand:
The child's weight is *25kg--* ((continuous)).
even though we would find it hard to agree on a precise lower or upper bound to this range, and even though the only weighing machine we have is rather inaccurate.
It is remarkable how often we have to deal with Variables for which we are quite confident in some middle part of the Variable’s range, but we could never say what are the absolute maximum or minimum. Obviously it makes no sense to say that a child weighs 0g, and in a different way it hardly makes sense to say a child weighs 100000000kg.
Any kind of Variable can be more or less vague. And often we aren’t even sure exactly which kind a Variable is, but still it might be useful to us.
Very often, with the Variables we already looked at - discrete, intensity and numerical - there is some vagueness about the Levels the Variable can take. In particular, numerical Variables are often vaguely defined at the extremes. For example, what is the maximum possible score on reading age? On the age of a person? On intelligence? We call Variables which are based on one of the three previous types but fail to completely specify the Levels “vague Variables”.
Because most Variables are vague, Theorymaker native speakers assume by convention that any Variable is at least in some way vague unless it is specifically specified otherwise.
Vagueness is however not the same as uncertainty, where a Variable certainly has some specific Level but we just aren’t sure which one. Uncertainty is a property of Reporting.
Right now I can’t think of any scales in evaluation which can really be as large as you like. Still, we often have to deal with numerical Variables which suggest that there is no limit to the Levels. There is of course some natural limit, so in a sense of course the number of Levels is actually finite. The point is though that the Levels are in fact specified using some iterative rule and are not explicitly listed.
Very often we won’t be able to list all of S, the set of Levels of a Variable, but we can a) make a machine which will recognise if the sentence belongs to S and/or b) make a machine which will produce any given one at some point in time: so you can’t now produce a complete list of all the meaningful sentences “I am y centimetres away from you” but you can start a machine off which will print out any given such sentence at some point in the future, i.e. it will print out “I am 1 centimetres away from you”, “I am 2 centimetres away from you” etc. Although the machine would at some point run out of power or paper, it is a good illustration of the iterative principle.
So the Levels of “current temperature outside this room” is somehow all the rational numbers (positive when expressed in degrees Kelvin). But in practice, we are not too sure if we really understand what “all” the continuous numbers are, or whether absolute zero is really a possible Level of this Variable, or 100,000,000,000 degrees Kelvin, and if not where the barriers actually are.
Think of IQ score or reading age, or almost anything else you care to measure. Does a reading age of 200 or an IQ of 10000 (or 3) make sense?
So when we say this …
This week there were about *20--* ((count)) visitors to the centre.
we know there is some vague upper limit to possible scores, we aren’t really thinking about visitor numbers in the hundreds of billions.
I have *minus 200--* ((continuous)) EUR in my bank account.
Example: reading age
Even some Variables which seem like robust, quantitative, non-fuzzy Variables at first glance can be more problematic on a closer look. So even lo-hi Variables can turn out to be quite fuzzy on a closer look.
Take reading age. We can assume every child has a reading age which just needs measuring. So the answer to “what is the child’s reading age” comes on a scale of numbers, say “8 years” or “10 and a half”.
OK, but which is the lowest possible number here? 0? Which is the highest? We can decide these ages by decree but there is no obvious answer. The Education Ministry or the leading Universities might have defined reading age to start at 4 years, but even people who don’t know that can communicate quite nicely about children with reading ages of 8, 9 and 10.
Which is the highest possible number? “40” probably wouldn’t make sense and we can all agree that “about 2000” is nonsense. But 17? 22?
Of course we can more or less arbitrarily define some kind of standard to answer these kinds of questions. But the point is that we managed to communicate using the idea of “reading age” without such a standard.
Even without such an agreement, the idea of reading age works pretty well most of the time. If my daughter has a reading age of 10, this may imply a whole load of other things depending on the context, but we can be quite clear that her reading age is not 6, or 7, or 8, or 15. So in some contexts, even without a definitional decree, we can treat reading age as a formal Variable, even though it fades into fuzziness at the edges.
Vague underlying definitions
Example: smartphone ownership
The number of people owning a smartphone in the world today is a Variable even though we can’t measure it with 100% accuracy.
The number of people owning a smartphone in the world today is a Variable even though, when we start thinking about it, there might be some serious dispute about the edges of the definition - how smart does a phone have to be to count as a smartphone, do I still own a phone if I left it on the bus two hours ago, is it still a smartphone if the bus ran over it, etc.
So this example is somewhat problematic but only at the fringes.
We can still make some serious statements about vague Variables.
Yet, even without some tortuous definition, we can still be perfectly sure of statements like “more people own smartphones than 10 years ago”.
Suppose we know child A’s reading age is 8, and child B’s reading age is about 10. We can conclude that child A has a higher reading age than child B, even if the Variable “reading age” is not clearly defined at its extremes.
How do we as evaluators manage to manipulate and even do calculations with such inherently indefinite facts?
Soft Arithmetic can help us with many of these problems.