I’d like to share a great blog post by Adam Mastroianni at Experimental History. Entitled “There are no statistics in the Kingdom of God“, it naturally caught my attention, and held it even once I realised that it wasn’t seeking an authentic Christian perspective. No stats in the Kingdom of God? I’ll come to that later. What I find so striking about Mastroianni’s piece is his claim that using statistical methods to detect phenomena is often a concession to ignorance. He argues that it belongs only to the earliest stages of progress in a modern science.
Before going further, I’d urge you to read the article, enjoying its playful humour and rich insights. What follow are my reflections on the wisdom of Mastroianni’s arguments in the context of a realist biblical Christian faith. I do believe that the Kingdom of God is advancing towards the day when the Earth shall be full of the knowledge of the glory of the Lord, as the waters cover the sea (Habbakuk ).
We’ve had posts before here on Faith-in-Scholarship critiquing the ideas that data can speak to us and that scientific discoveries are a form of ‘general revelation’, and about epistemic humility. The main target in those posts around epistemology for the sciences has been forms of positivism. I recall a postgraduate statistics lecture where a professor essentially told us: “Because the world of biology is complicated, we can’t prove things, but at least we can put probabilities on them”. But later on in the same course, another lecturer introduced us to the principles of Bayesian inference, where it becomes clear that, properly, we can only revise probabilities (or prejudices); we can’t conjure up probabilities about reality just from data.
When it comes to drawing conclusions from noisy data, then, it’s hard to disagree with Mastroianni’s view that statistical inference is often exploring the answer “sometimes” to simple questions that we would ideally refine to the point where we can answer “always” or “never”. To give some ecological examples: “Does biodiversity increase ecosystem stability?”; “Do invasive species succeed by escaping their natural enemies?”. Mastroianni then illustrates how “things seem random until you understand ’em“: the history of sciences is partly about people speculating about surprising phenomena until effective prediction becomes possible. At that stage, statistics are no longer needed – although, of course, statistical methods weren’t available until the last hundred years or so, and Mastroianni makes the intriguing suggestion that our obsession with stats may now be hindering progress towards mechanistic understanding.
But the world is incredibly complex (avoiding the reductionistic undertones, we should say it is rich, mysterious and exciting). Indeed, the pre-20th century history of physical sciences, corresponding to the period when statistical methods weren’t much in use, is peculiar for being focused around geometry and kinetics (optics, motion and waves), and abstract physical relations such as gravitation, electrical phenomena and thermodynamics – areas where most phenomena can still be treated deterministically (Dick Stafleu shows how determinism is strictly only relevant where we focus on geometric and kinetic phenomena, as in Newtonian physics). Once we take a scientific interest in how individual things function (from particles to people), various kinds of indeterminacy (from quantum effects to human spontaneity) have a bearing on what happens. And this makes statistical description invaluable. Statistics are needed to help us measure things and quantify laws of nature.
So statistical methods can be indispensable to scientific progress. The young science of ecology (where I was trained) perhaps has more than its share of laws recently elucidated through statistics. Species – area relationships, physiological scaling laws and universal patterns among plant functional traits are three examples where exciting progress has come from large-scale analyses of global data sets, revealing biotic laws that could not have been fully discovered in other ways. Some of this has been facilitated by the definition and cataloguing of functional traits, a project that represents a breakthrough in the application of scientific objectivity.
Yet I agree strenuously with the central thesis of Mastroianni’s article. Key problems begin with the project to use frequentist statistics to deliver yes/no answers (or strictly, “yes/don’t-know” answers) to simplistic questions. The development of the null-hypothesis test was a major achievement with important applications, but it was also a triumph of 20th-century positivist thought. And such tests and their P-values have now overrun the literature in the human and social sciences; too few people are trying to conceptualise and measure quantities objectively. A common short-cut is to ‘theorise’ about notions that might be related to each other, run a survey yielding relevant Likert scores, and then proceed to test null hypotheses about these Likert scores (or customised constructs based on them). This has become a quick route to generating large numbers of articles that are, too often, not replicable or even reproducible. Positivism, as part of the larger secularisation project, eventually cuts off the branch on which it sat.
So my overall view is that the social sciences need more real statistics and fewer P-values. ‘Real statistics’ means discovering useful quantities and estimating values for meaningful parameters, rather than yes/no answers.
What about the Kingdom of God? Many Christians have been brought up to assume that there’ll be nothing like research in the age to come, but I disagree. Perhaps God could give us accounts of how everything works that would satisfy all possible research questions, but I doubt we’d be able to understand them. Much like a child asking “why” questions to an academic parent, I think we’d fail to grasp advanced explanations without embarking on an extended programme of study. I can even imagine that, asked about exactly why there are more species towards the Equator, what explains memory loss, or the factors that make for a successful business, our Creator would prescribe some of us a data-gathering programme, followed by a bout of really serious statistical modelling.
[Views expressed here are his own.]
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