There are a number of different aspects of statistics that make it inapplicable to discussions of God's influence. Many of its limitations render it rather agnostic. (...)
Firstly, one basic requirement for probabilistic statements in statistics is of course some aspect [or model] of repeatability. This does not mean we have to repeat the whole thing. Repeatability can be found in throwing multiple coins, testing multiple patients, drawing multiple samples for carbon dating, comparing multiple gene sequences, measuring multiple time points, [running multiple simulations] et cetera. But we cannot [model or] take multiple samples of the precise circumstances that led to the origin of the first cell(s) or that of the universe, leaving us without a robust basis for making probabilistic statements.
Secondly, a much more fundamental limitation of statistics is that it can only be used to compare the relative merits of multiple specific scenarios. This has to do with Bayesian statistics. Suppose that, given the data, scenario A is found to be extremely improbable, but still much more likely than scenarios B and C. That does not tell us that A is true or false, just that it looks better than C and D. For all we know, there could be another unknown but specifiable scenario D that would look a bit better. Also, showing that scenarios A, B, and C are all extremely unlikely does not make scenario D more likely if it remains unspecified.
A common mistake in many psychology studies is to assume that rejecting the null hypothesis (e.g., scenario A) on the basis of some probability criterion (usually p < 0.05) automatically leads to the acceptance of the alternative hypothesis (e.g., scenario B based on some pet theory). However, that reasoning is false because there could be many other alternative scenarios much more likely than B. I know a professor from my university who built half of his career on demolishing other people's conclusions just based on Bayesian statistics!
So here's the connection to Intelligent Design. Assigning an extremely low probability to a certain scenario A (e.g., DNA code arising through specified natural processes) does not automatically make alternative scenarios more probable. If a proposed alternative scenario B (e.g., "design") is not formulated in terms of specifiable predictions, the calculated probability of A does not have any meaning. Or, applied to fine-tuning, assigning an extremely low probability to the parameter settings of the universe does not mean anything without specifiable predictions to compare it with.
Thirdly, there is something deeply disingenuous about employing probabilities in arguments for God. If the natural explanations turn out to capture all of the data, someone might say "wow, look at those underlying regularities, those patterns point to a Creator!" If the natural explanations appear to be unlikely, the same person might say "wow, that low probability points to design!" I think that's fundamentally flawed. We can't have it both ways.
(...) choice and randomness lead to indistinguishable results in formal statistical terms. I wish everyone would acknowledge that and stop using probabilities as pseudo-rational arguments to bolster the case for (or against) God's existence. I want to be fair here but I can't think of a softer way to put this clearly.