Review of Christian and Humanist Foundations for Statistical Inference

Andrew Hartley: Christian and Humanist Foundations for Statistical Inference

I realize that this post will have a limited sphere of interest, but I felt the need to record my reactions to this book for my own sake (so I have a record of it for my sabbatical review) and let others read it if they want to.
I recently finished reading Andrew Hartley’s Christian and Humanist Foundations for Statistical Inference: Religious Control of Statistical Paradigms. I did not agree with the primary conclusions of the book. There are several reasons for this, which I’ll list and elaborate on briefly.

  • Hartley overly simplifies the breadth of statistical perspective. He considers two frequentist views and two Bayesian views. There are far more nuances than this among statisticians, which Hartley only briefly acknowledges before trivializing these differences away.
  • Hartley views two different forms of Humanism, but only one Christian philosophy. Worse, the view he chooses is clearly not broad enough to include all statisticians. Hartley acknowledges that his Christian philosophy, the so-called “Philosophy of the Law Idea” was developed by two Dutch Calvinist scholars, and seems biased against the many whose philosophy reflects the Arminian/free will view of Christianity. This biased view of Christianity limits the ability to view his conclusions as decisive. In fact, the only mention of freedom of choice or freewill is in connection to humanism.
  • Hartley’s view of humanism is defended by many quotes, but most of these come from secondary sources. It is interesting to note what others have said about humanism, but not in place of direct quotes to convince me that these secondary opinions accurately reflect the views of humanists themselves.
  • Hartley’s choice for the only Christian perspective is what he terms “Subjective Bayesianism”. Many Christian statisticians would be extremely concerned about this view. Since the Bible is clear that human beings are fallen and imperfect, why should a view that relies on subjective perspectives be endorsed as most Christian? It seems to me this view is possibly most susceptible to abuse by humanists.
  • On the other extreme, Hartley’s Direct Frequentism is unfairly maligned on two fronts. First, Hartley makes the claim that Direct Frequentists often confuse the probability of the data given and assumed hypothesis with the probability of a hypothesis given the data. I have read this claim several times, and it is beginning to drive me crazy. This is a first semester stat course mistake that I have never heard a trained statistician make. I warn my students about this all of the time, as well as explaining how to correctly understand what the P-value really is telling them. This critique holds no water with me.
  • Second, Hartley assumes that Direct Frequentism is only consistent with mathematically slanted versions of humanism. He never tells me why I, as a Christian who worships a God that created an orderly world, cannot trust the mathematics behind the conclusions of Direct Frequentism. Just because some humanists like it, does that mean I can’t? Hartley never addresses this. I agree with him that ultra-rationalist humanists should support Direct Frequentism or Objective Bayesianism, but those both seem consistent with Christians who trust the orderliness of mathematics (is there anyone who posits that math is fallible and fallen?) over the fallen nature of humans as well.

In all, I find that what he has to say is reasonable, for the most part. His logical tracing of the effects of religious belief are helpful in understanding perspectives on these particular views of statistics, but they are limited. The limitations of not further addressing nuances within statistics, as well as nuances withing Christianity, limit the usefulness of this book. I am not a philosopher, and would not be surprised if Dr. Hartley is a better statistician than I am, as well as a better philosopher. However, this does not excuse the limitations of his work, at least in my mind. I would love to see an expanded work that addresses these issues. The issues that Hartley begins to address here are very important for Christian statisticians to consider, and I appreciate his contribution to the larger discussion.


8 comments on “Review of Christian and Humanist Foundations for Statistical Inference

  1. […] the introductory chapter, and do not foresee myself doing so in the future. If you read my previous review post of Andrew Hartley’s Christian and Humanist Foundations for Statistical Inference, you may […]

  2. NoLongerNormal,
    I appreciate your taking the time to read my book & post comments about it. As you seem concerned about issues involving how Christian faith might influence practicing statistics, I’m confident we can learn something from each other. So, I encourage you to check out the Christian Statisticians’ Informal Discussion Group at http://groups.yahoo.com/search?query=csidg, & the Association of Christians in the Mathematical Sciences, http://www.acmsonline.org/. Maybe you would have a “chance” to contribute to 1 or both of these orgs. Many other good orgs exist, too, of course, on interrelating faith & science.

    Rather than attempting to address all your comments at once, let me talk briefly, & solely, about your first point, concerning the “views” of statistics my book considers. Indeed, even though statistics is a young science, its schools of thought have indeed proliferated. I knew I would never have time to discuss all of them, so I limited my attention to those most commonly adhered to. I tried to substantiate the ones I chose using the works of both early & recent thought leaders, & both secondary & primary sources. Additionally, I have dealt only with statistical inference, as stated in the book’s title & in its content. This constraint did, in fact, put me in a slightly uncomfortable spot, because when a statistician considers another area of statistics, decision theory, the argument for a subjective bayesian attitude becomes, in my opinion, even stronger than it is with respect to inference. In any case, I do believe still that most statisticians performing inference do so following the methods & attitudes of the 4 paradigms I discussed. This does not mean that many statisticians stay in 1 camp exclusively; in fact, as I argue, most statisticians try, at least occasionally, to interpret frequentist (deductive) results bayesianly (inductively), which obviously complicates the analysis of trends in the practice of our science.

    You bring up many interesting points, some of which do suggest to me opportunities for improving my book in the future. Consequently, I hope you will indulge me with at least a little more discussion on them. Thanks for your time. Andrew.

    • Andrew,

      I do appreciate your reply. I am a member of the CSIDG and the ACMS. I teach at Messiah College (I believe you are familiar with my retired colleague Gene Chase, and may also know Marlin Eby, my fellow statistician). I appreciate that what you were attempting had necessary, though perhaps unfortunate, limitations. My biggest concern philosophically was the lack of recognition of the serious issue some of us Christian statisticians have with the effect the fallen human nature might have upon the subjective priors. While it is certainly advantageous to include “pre-scientific” information, as you say, might not personal bias work its way in, as well? This could be unintentionally done, as with a Christian or humanist who is unaware of the bias that they possess, or intentionally by someone hoping to sway the conclusions, yet seem less subjective than the indirect frequentist. I don’t pretend to be a philosopher of any substance, so feel free to correct my errors if you see any more!

      – Sam

  3. Sam,

    Sorry also for my slowness in replying…am writing a paper now & busy other ways too. It’s great that you are working already with CSIDG & ACMS. Sorry not to have met you yet at the CSIDG sessions at JSM or anything; I don’t often go to JSM. I do miss corresponding with Gene; he gave me some good advice & perspectives.

    A partial response: I agree that, in our science, we need to account for fallen human nature. In fact, on my shelf is a book saying the very same thing, though about technology rather than science. Putting the right tool into the wrong hands can, indeed, result in great harm. The tricameral US Government, in this spirit, accounts for that nature, by its system of checks & balances between the 3 branches.

    Speaking in the terminology of the philosophy of the law idea: I’m not convinced, however, that relying on 1 or 2 aspects of creation (logical & quantitative, because they seem to be “trustworthy” or “objective”), as direct frequentism does, at the expense of others (which would come in to our stats inference thru subjective bayesian priors) such as the biological or physical aspects, is the way to avoid the deleterious effects of that fallen nature. That would constitute relying on part of creation to save us from ourselves.

    I think rather that we need to bring many (all, where possible) aspects into play in our stats inference. The social aspect, for instance, should have a role, as we rely on communities of experts to help us form our priors honestly & fairly (much as the US Govt relies on the checks & balances). The economic aspect should come into play, as we choose the stats methods that yield reasonable inferences without undue computational efforts. And so on.

    Relying exclusively, or even only primarily, on the logical & quantitative aspects, is exactly the spirit underlying direct frequentism. It portrays those aspects as more trustworthy than the others.

  4. Hey, NoLongerNormal,
    any thoughts on my responses to some of your notes concerning my book?

    • Andrew,

      I appreciate your reply, and I think I can understand your perspective. Unfortunately, I have never had the privilege of a dedicated philosophy course. I feel a bit out of my league debating this type of thing with you. However, I would say that I am not yet convinced that Christian statisticians must all agree on this point, any more than I think that all Christians must be Calvinist in regards to determination/free will. I wonder how much the Calvinist thinking behind the PLI affect the conclusions that you draw. Would someone, like myself, from an Arminian view be philosophically compelled to the same conclusion? I do appreciate your continued willingness to discuss this, and help me think through this. Reading your book was recommended by Gene, and I put it high on my list of things to read during my sabbatical. I do find this discussion stimulating, so please don’t think that you are talking to someone who refuses to listen.

      – Sam Wilcock

  5. Sam,
    I think I can understand your concern. Calvin may be known best for double predestination, but neither Dooyeweerd nor the current leaders of the PLI go along with it. It’s not even relevant to the PLI. Calvin’s greatest contributions were 1. the rejection of the scholastic nature/grace dichotomy & 2. the recognition that everybody has religious beliefs & that these beliefs regulate everything we do & say (including our scientific theorizing). I don’t see why an Arminian would have a problem with these contributions. The PLI developed them into a theory of knowledge & reality, which has (I think) guided the development of my book. I could email you much more information on this, if you like.

    More closely related to predestination/free-will & their impact on statistics, I think, would be Bartholemew’s “God of Chance,” indexed at
    The full book was made available on the internet for a time; I don’t know if it’s still there.

  6. Sam,
    sorry our discussion seems to have lost some steam; any thoughts on my feedback above? Andrew.

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