# A Statistics Question for Barry Arrington

• If you came across a table on which was set 500 coins (no tossing involved) and all 500 coins displayed the “heads” side of the coin, how on earth would you test “chance” as a hypothesis to explain this particular configuration of coins on a table?

Even if the observer was not party to the information that there was “no tossing  involved”?

The reason I ask, is that you seem to have revealed an conceptual error that IMO bedevils much discussion about evolution as an explanation for the complexity of life.

Chance is not an explanation, and therefore cannot be rejected, or supported, as a hypothesis.

Some explanatory hypotheses are stochastic, meaning that they invoke a mechanism that is indeterminate in some way.  One such hypothesis might be “fair coins were fairly tossed”, where “tossing” is itself a stochastic process with a known probability distribution – but we can reject this hypothesis in this case, either because we know, a priori, that there was “no tossing involved”, or because the pattern is vanishingly unlikely under the hypothesis of “fair coins, fairly tossed”.

This is not because we “reject chance as a hypothesis” but because, under the null hypothesis of “fair coins, fairly tossed”, there is a very small chance aka probability that they would all land heads.

So can we please jettison this canard that “Darwinists” propose chance either as as an explanation for the complexity of life, or even as the explanation for an unfeasibly long string of tossed heads?

Statistics is all about chance and chance is crucial to hypothesis testing, but it is never an explanatory hypothesis.  In fact, it’s to what we attribute the portion of the variance of the data our model does not predict.  It is also intrinsic to the probability distributions we propose for our data both under our null and under our study hypothesis.

And it is also crucial to the concept of sampling: if sample data as, or more, extreme than our data are very unlikely i.e. have a very slim chance, under our null we can reject our null.

But chance itself explains nothing. It is the exact reverse: Chance is what we call the part of our data we can’t explain.

What we can use to explain our data are processes with a specific probability distribution, whether those processes are intelligent, intentional, or the results of physical and chemical interactions.  The more complex the processes (e.g the forces acting on a spinning, arcing coin), the greater the combinatorial possibilities, and so the the greater the spread of the probability distribution.

And if I say “I met so-and-so by chance yesterday”, in no sense do I mean that either of us was acting in a non-intentional, or non-intelligent manner (though we might have been).  All we mean is that we did not predict that our intentions would result in our meeting.  What caused that meeting was a highly complex multiplicity of events and processes, many of them intelligent and intentional.

What was chance about our encounter was not its cause but its unpredictability.

## 157 thoughts on “A Statistics Question for Barry Arrington”

1. William J. Murray: Frankly, Liz, I wouldn’t want to have a mind …

Richardthughes: Ignorance is Bliss, Mindpowers. And ID and IDists have never *really* been about understanding, have they?

FIFY 🙂

2. My hunch is that there is a huge amount of baggage attached to the word “chance” (or “random”). For many, it means “unintended” or “unintelligent” or “meaningless”. And so the idea that life is “due” to “chance” is equivalent to saying that life is “meaningless” and therefore must be wrong.

Precisely. That’s a key difference between Catholicism’s acceptance of evolution and the support of ID theory by certain segments of Protestants — chance does not negate intention.

Father Edward Oakes: I also object to the way the ID Movement conflates the Thomistic distinction between primary and secondary causality. The advocates of this movement claim that if it can be proved scientifically that God must intervene on occasion to get various species up and running, then this will throw the atheist Darwinians into a panicked rout.

I disagree. My view is that, according to St. Thomas, secondary causality can be allowed full rein without threatening God’s providential oversight of the world.

Q: But aren’t you making God recede from the world, just as the deists did with their concept of the clockmaker God?

Father Oakes: Actually, no. Remember that for Aquinas God’s primary causality does not refer to an initial moment of creation, after which secondary causality kicks in and runs things from then on out.

No, God must sustain the world in each moment of its existence. God keeps the world in being because God is “He Who Is.” God is Being itself; and because of God’s self-sufficient Being, the universe “is,” albeit derivatively.

3. William J. Murray:
Liz said, all in the same post:

Frankly, Liz, I wouldn’t want to have a mind that could “get the point” of the mush you present as an argument.

See William, the problem here is that what you see as “mush” is some very rigorous logic that you do not apparently have the background to follow, although I would gladly explain it to you (it is well within your cognitive powers to understand). But because you dismiss it as “mush”, never will.

It’s a bit like someone looking at Arabic and dismissing it as gibberish, or, for that matter, math equations.

Null hypothesis testing is a very precisely defined procedure, in which we define a null hypothesis about phenomenona, then define what we expect to see, with what probability, in a random sample of such phenomena, if the null hypothesis is true. If what we observe in our sample is extremely improbable if our null is true we can reject the null hypothesis, i.e. include that it is probably false.

But the “random” or “chance” part is the sampling part – “chance” is not the hypothesis. This is not “mush” – what is “mush” is to vaguely, mushily, say that the results are due to “chance”.

But that doesn’t mean that chance was any kind of hypothesis.

4. See William, the problem here is that what you see as “mush” is some very rigorous logic that you do not apparently have the background to follow …

Yes, I would assume that it does take years of indoctrination to to be able to say the things you say with a straight face and with all sincerity.

5. But the “random” or “chance” part is the sampling part – “chance” is not the hypothesis.This is not “mush” – what is “mush” is to vaguely, mushily, say that the results are due to “chance”.

“For example, the origin of new genetic variation by mutation is a process that involves a great deal of chance. Genetic drift, the process I referred to earlier, is a matter of chance.”

6. William J. Murray: See William, the problem here is that what you see as “mush” is some very rigorous logic that you do not apparently have the background to follow …

Yes, I would assume that it does take years of indoctrination to to be able to say the things you say with a straight face and with all sincerity.

So what is your objection to my claim? Are you disputing that the null hypothesis in the case of the 500 coins is “are fair coins that were fairly tossed”?

Because simply telling me that you think that what I am saying is “mush” and not saying what is wrong with it, or what the correct state of affairs is, is not very persuasive.

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