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.

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15 thoughts on “On Lily Pads and Rivers: The Theology of Data Types”

  1. Like all good psychology, it's all so obvious just AFTER you've read it!  Brilliantly simple, simply profound - as always, professor!

    BTW, are you familiar with the case from a while back of the psychologists called in to advise the US military? 

    When the researchers presented their first set of findings - a lot of hard work under the bridge - the joint chiefs turned to one another and then gave their verdict with smiling condescension:  "That's all obvious - we already knew all that."

    The psychologists' disappointment turned to frustration when the second year findings received the same response.

    In their third and final year presentation, the research team decided to reverse every single finding.  They reported the complete opposite effect to what they actually found.

    The top brass consulted briefly before giving their verdict:  "That's all obvious," they smiled condescendingly.  "We already knew all that."

  2. Here's a question. Within the various Protestant traditions, sin is viewed as nominal: all sins are equally repellant to God. Within Roman Catholicism, there are mortal and venial sins, which are maybe still two nominal groupings of sin. But the actions and beliefs that various religious traditions classify as sinful exist along a spectrum. So does sin involve overlapping nominal/numeric data types?

  3. That's an interesting question that I almost went into in the post.

    As you note, for Protestants all sins are equal. But for Catholics there is this notion of severity, that some sins are worse than others. That notion of severity suggests that sin can be graded along a continuum from, say, driving +1 mile over the speed limit to genocidal rape and torture.

    And that's the thing that interests me. Any coherent view of sin should take the issue of severity into account, treat it as a numerical variable. And yet, most Christians don't think about it this way, doctrinally speaking. Which is an odd disjoint. Functionally, though, while a lot of Christians say all sin is equal, they recognize the differences in how they treat the sins.

    Shame, guilt and stigma varies across the sins, suggesting that practice and doctrine are divergent.

  4. This post made me laugh, Dr. Beck. I can tell that your statistics class must of rubbed off on me last year. I've been contemplating similar ideas lately on my blog.


  5. And salvation (which appears to be absolutely binary) hinges upon "sin".  Orthodoxy is funny in this manner - whether measured nominally or numerically, "perfect orthodoxy", like beauty, rests in the eye of its beholder. LOL.

    Thanks again Dr. Beck!
    Gary Y.

  6. Hello qb,

    As you probably picked up, I was making my usual jab at common churchianity's shallow take on salvation.  I should have done a better job to distinguish:

    justification (saved/not saved, alive/dead) vs
    sanctification (mentioned by Dr. Beck), a less holy to more
    holy continuum, the first seemingly nominal and the latter, numerical.

    What I think is funny about the life ring thing is the person drowning has to 1) be alive still, therefore not "spiritually dead",
    2) has to know he/she is perishing and 3) realizes the urgency / desperate need.

    I always appreciate your takes.  I'm frankly in over my head attempting to volley with you, but thanks for the feedback.
    Gary Y.

  7. Nonsense, I say!  when it comes to this stuff (and a wide variety of other kinds of stuff), qb is an ignoramus.  I'm just trying out some ideas like the rest of these Beck Groupies [TM].  Posts like the Lily Pad are the main reason I keep coming back to this blog.

  8. As a stats geek, this kind of post warms my heart to no end :)

    Brian McLaren, in his latest book, Naked Spirituality, talks about four stages of spiritual development (which he borrows heavily from psychological development).  In the first stage, which corresponds to early childhood,  we are characterized by seeing everything in binary (right/wrong, us/them, good/bad, etc.).  By the third or fourth stage (if we ever make it that far), we have come to the point where there are many more gray areas and fewer absolutes.  In the third stage this leads to despair and doubt, while in the fourth stage we learn to live with the uncertainties and learn to appreciate each person at whatever stage they are in.

  9. Oh, and here's another one for your list that lends itself well to statistical thinking: gender differences.

    For any given characteristic (including spiritual gifts, if we want to apply this to Christian practice) there are two normal distributions, usually with some degree of overlap, which represent the probability of having that characteristic.  For some characteristics/gifts, there may be more men than women, for others, vice versa.  In most (all?) cases, there will be a mix of genders displaying certain characteristics/gifts.  In this way, we can acknowledge that there are indeed differences between the genders, while at the same time allowing that few, if any, functions are restricted to one gender or the other.

    This is not exactly relevant to data types per se, but I couldn't help throwing it out there anyway...

  10. My old prof. J.D. Thomas used to say, "You can't pour God in a test tube." Does this involve lilly pads or rivers?

  11. I was getting all excited when you said "gender differences," but you didn't go where I'd hoped. I was /hoping/, see, that you would point out that most people take biological sex to be nominal when it's not. I don't think it's really quite numerical, either, since trying to place someone on a sex spectrum makes little sense, either.

  12. Interesting! I wonder what they would have done if the psychologists had "cut the baby in half," with half the psychologists reporting the true findings, and half reporting the opposite, simply stating their findings/positions as opposite, without attempting to reconcile those differences. Which side might the chiefs have claimed to know already?

  13. Good question.  My initial temptation to take a cheap pop at the military chiefs led me to deeper reflection on the limitations of empirical research which all too often likes clean answers to messy problems.  Perhaps amidst the pressure to carve out reputations and secure grants psycholgocial research has lost something of the dialectic?


  14. Even though that wasn't where I was going, I would pretty much agree with you on that as well.

  15. Well, since you are the psychological stats geek, I have to ask a question that has plaguing me for over 30 years.  When I took my first statistics class, among the very first, and most repeated, "rules" was that statistics cannot be used to explain or predict a single event.  So, why is it that psychologists insist on using statistics when dealing with a single individual?

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