On Lily Pads and Rivers: The Theology of Data Types

Every semester I teach a statistics class at ACU. That's one of the classes you get to teach when you are the experimental psychologist in the Psychology Department. I'm the stats geek.

Just about every statistics class opens up with a lecture about data types. It's a fundamental issue because the data you have determines the statistics you should use. So when people call me on campus to ask "What statistic should I use?" I start by asking them about what kind of data they have.

One way to describe data types is the contrast between nominal versus numerical data, categorical versus continuous data, discrete versus dimensional data, or qualitative versus quantitative data. People use different words for this distinction. But the general idea is that nominal, categorical, discrete, or qualitative data represents a difference of kind and is often a grouping variable. By contrast, numerical, continuous, dimensional, or quantitative data represents a difference of degree and is often a measured variable where people can score high or low on some dimension. In my classes I tend to use the labels nominal versus numerical to get at this distinction. So in my classes the question gets asked a lot, "Now, is this variable nominal or numerical?" I like to talk about lily pads (discrete groups) and rivers (continuous flow).

Examples of nominal variables are gender and political affiliation. These are differences of "kind" rather than degree. Men aren't more or less than women. They are just different groupings. Republicans aren't more or less than Democrats. They are just different groupings.

By contrast, your age, weight or IQ are numerical variables where a number--your age, weight or IQ--represents where you fall on some continuum. Thus, we can say you are older or younger, overweight or underweight, or possessing a high IQ.

All this seems clear until you run into situations where there is a bit of overlap. For example, think of Olympic medalists--the gold, silver or bronze. These are groupings. And yet, the groupings were based upon an underlying numerical assessment, for example your elapsed time in crossing the finish line. Thus, we have groupings that are trying to communicate differences of degree. The gold medalist was faster than the silver medalist. But a medal isn't a score. You often run into situations like this where an underling dimension is "cut up" to make groupings, like when a teacher cuts up 0% to 100% test scores into the letter grade groupings A, B, C, D and F.

Okay, if you are normal person I've just bored the hell out of you. If so, you are just like my students. After 30 minutes of explaining all this to my students most, by the looks on their faces, seem about ready to fall asleep.

So, it's at this point in the lecture where I stop and say the following, "I know all this seems boring and irrelevant, but I've actually just handed you an analytical tool that can help you sort out some of the most controversial debates in the world today. In many, many disagreements what you'll find is that people are disagreeing about the 'data type' that best fits the situation they are discussing."

Let me explain this. When we wander out into the world and pick out a bit of it to talk about we often have to decide how we are going to model that bit of the world in our minds. And one of the choices we can make is to see the situation as a difference in kind, category, or quality or as a difference in degree or quantity. Is the data nominal or numerical? A lumpy discrete grouping or a smooth underlying continuum? Is it a lilly pad or a river?

It often can go either way. Consider extroversion and introversion. When Carl Jung first coined these terms he thought of introverts and extroverts as types. There were Introverts over here and Extroverts over there, two groups, two kinds of people. That's how Jung decided to model this bit of human psychology, as a nominal variable. And assessment instruments like the Myers-Briggs, which was inspired by Jung, continue to use the typology approach where you get a letter designation--an I or an E--to show which group you are in.

However, most psychologists no longer think of introversion and extroversion in this way. Rather, we've replaced Jung's difference of kind with a difference of degree. While we still speak of "introverts" and "extroverts" we are really talking about an underling continuum where people could be in the "middle." An "extrovert" is someone who is just high on the extroversion side of the continuum. And you can be more or less extroverted or introverted. It's more a matter of degree than a difference of kind.

You see this issue all through the field of psychology. Is parent/child attachment best understood as a type--Secure vs. Anxious vs. Avoidant--or as a matter of degree? Is ADHD best understood as a mental illness--a diagnosis is a grouping variable--or simply as the extreme point on an underlying continuum (e.g., There are very tall people in the world and they don't get diagnosed. So why diagnose kids on the extreme end of human attentional abilities? Isn't this just natural human variation?).

Okay, that's psychology. How does any of this relate to theology?

Well, if you stop to think about it, a lot of the debates you find in theology and ethics often boil down to how people are modeling the data under discussion. One group is modeling the data as a difference of kind. The other group is seeing it as a matter of degree. It's a black/white frame against a shades of gray frame.

Consider the following debates:

1. Abortion
2. Sexual Orientation
3. Salvation
4. Evolution
5. Orthodoxy

In each of these situations there is some debate (although the parties often don't recognize this) about the proper way to model the data/phenomenon under consideration:

Does life begin at conception or is life a continuous biological process?

Is sexual orientation a gay versus straight distinction or is human sexual orientation best understood to be a continuum between these two poles?

Justification seems to be an either/or (Saved versus Lost) while sanctification seems to be a continuous process. Which is the better way to understand the Christian life? And how do the two views fit together?

Evolution is a continuous process. Creation is not. How do we make the two fit together to explain humanity's unique spiritual status among the animals?

Is orthodoxy best understood as either/or with the Orthodox on the one side and the Heretics on the other? Or should we see orthodoxy as a "degree of similarity " with people varying in greater or lesser ways across a host of theological issues?

Hopefully you can see the point I'm trying to make. Many of these disagreements (and many others) are due (at least partly) to disagreements about a fundamental theoretical assumption: What data type is this? On any given issue conservatives are framing the data as a difference of kind while progressives are framing it as a difference of degree. Or vice versa. In fact, did you just see what I did? I framed theological viewpoints as a nominal variable: Conservative vs. progressive. That is fine to do, but we all know that these "types" are not pure and that the labels obscure the underling continuum and diversity. So we have to be careful to not take those labels too seriously. They are theoretical abstractions I'm imposing on the world.

And that's the point. In these very hot debates we are often unaware that we are deploying theoretical models that might be questioned. Paying attention to these assumptions--like the data type you are using--might help us create more light than heat when we discuss these contentious issues.

Which makes me wonder: Perhaps even theology classes should begin with a lecture on data types.