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Category: Statistics

The general theory, methods, and philosophy of the Science of Guessing What Is.

January 18, 2019 | 8 Comments

Another Proof Statistics Cannot Discover Cause

We discussed this before, but since it has come up recently in personal discussions, I wanted to offer this clarification.

Suppose we’re in a standard epidemiological situation, or even a planned experiment, where we have two groups, (a) exposed to some horrid thing, and (b) not exposed. It should be clear that the people in group (b) were not exposed. Where by “not” I mean “not”. We track the incidence of some dread malady, or maybe even maladies, in the two groups.

We collect data and “submit” it to some software, which spits out a wee p-value for whatever “test” you like between the groups; and where we can even grant—and upon this I insist—group (a) shows the higher rate of whatever dis-ease we track. It also shows a healthy predictive probability difference between the groups.

Lo, all statisticians would say the exposure and malady are “linked”, by which all of them would at least secretly mean “cause”. Whatever it was those in group (a) were exposed to caused the malady or maladies.

If you press them, and tell them they will be quoted and held accountable to their judgement, the statisticians may well lapse into “link”, and shy away from “cause”. But they will secretly believe cause.

Now here is what happened. Not everybody in group (a), the exposed group, will have developed the malady (or maladies; after which I use the singular to save typing), and some people in (b), the not exposed group, will have the malady.

It thus cannot be that the people in group (b) had their disease caused by the exposure. It then necessarily follows that their malady was cause by something other than the exposure. This is a proof that at least one more cause than the cause of the exposure exists. There is no uncertainty in this judgement. Not if it is true none of the people in the not-exposed group were not exposed.

Of course, it could be that every person in the not-exposed group had a different cause of their malady. All that we know for certain is that none of these causes were from the exposure.

Wild, right?

It’s worse, because even though we have proved beyond all doubt that there must exist a cause that was not the exposure, we have not proved that any people in the exposed group had their malady caused by the exposure. Why?

Because it could be that every person in the exposed group had their disease caused by whatever caused the disease in the not-exposed group—or there could even be new causes that did not affect anybody in the not-exposed group but that, somehow, caused disease in the exposed group.

It could be that exposure caused some disease, but there is no way to tell, without artificial and unproven assumptions, how many more maladies were caused by the exposure.

It’s worse still for those who hold statistical models—in which I include all artificial intelligence and machine learning algorithms—can discover cause. For what about all those people in either group who did not develop the disease?

Even if exposure causes disease sometimes, and the other (unknown-but-not-exposure) cause which we know exists only causes disease sometimes, we still do not know why they exposure or non-exposure causes disease only sometimes.

Why did these people develop the malady and these not? We don’t know. We can “link” various correlations as “cause blockers” or “mitigators”, but we’re right back where we started from. We don’t know—from the data alone—what is a cause and what is not, and what blocks these (at least) two causes sometimes but not in others.

Once again I claim over-certainty in medicine, and in epidemiology in particular, is rampant.

This is why I insist that cause is in the mind and not the data.

January 17, 2019 | 9 Comments

Another Proof Against P-Value Reasoning

This isn’t so much an extra proof, but a clarification on one of the proofs used in “Everything Wrong With P-values Under One Roof” (the first two arguments).

Calculation of the p-value does not begin until it is accepted or assumed the null is true: p-values only exist when the null is true. Now if we start by accepting the null is true, logically there is only one way to move from this position and show the null is false. That is if we can show that some contradiction follows from assuming the null is true. In other words, we need a proof by contradiction in the following way:

  • If “null true” then some proposition Q is true;
  • Not-Q (Q is false in fact);
  • Then “null true” is false; i.e. the null is false.

Yet there is no proposition Q in frequentist theory consistent with this kind of proof. Indeed, under frequentist theory, which must be adhered to if p-values have any hope of justification, the p-value assuming the null is true is uniformly distributed. This statement (the uniformity of p) is the only Q available. There is no theory in frequentism that makes any claim on the size of p except that it can equally be any value in (0,1). And, of course, every calculated p (except in some circumstances to be mentioned presently) will be in this interval. Thus we have:

  • If “null true” then Q = “p ~ U(0,1)“;
  • p in [0,1] (note the now-sharp bounds).

We cannot move from observing p in (0,1), which is almost always true in practice, to concluding that the null is true. This would be the fallacy of affirming the consequent. On the other hand, in the cases where p in {0,1} (the set with just elements 0 and 1), which happens in practical computation when the sample size is small or when the number of parameters is large, then we have found that p is not in (0,1), and therefore it follows that the null is false. But this is an absurd conclusion when p=1.

Importantly, there is no statement in frequentist theory that says if the null is true, the p-value will be small, which would contradict the proof that it is uniformly distributed. And there is no theory which shows what values the p-value will take if the null is false. There is no Q which allows a proof by contradiction.

Think of it this way: you begin by declaring “The null is true!”; therefore, it becomes almost impossible to move from that declaration to concluding it is false.

There is no justification for use of p-values other than will or desire of the user.

January 15, 2019 | 27 Comments

Science Without God Is Incomplete

Either God exists or He does not.

If He does not, then science does not matter. Nothing does. Anything anybody does is mere prejudice, whim. There is no good, there is no evil. There is no point in doing science, or in anything else.

Of course, you can claim that science is necessary (we’re still assuming God does not exist), but that is, like, your opinion, man. To quote a higher authority. My opinion is that it doesn’t matter. You may say that your opinion (joined with many others) outweighs mine, which is surely true. More people agree with you. But that “truth” is determined by vote is not itself true. Not that that matters. Nothing does.

It does not matter if everybody starves, or no one does. It does not matter if we make no new invention, or all old ones are destroyed. You may say that saving lives is the very purpose of science, but that is just so much hot air. All existence means nothing. The universe, since God is not there, is all there is, and the universe is nothing. It doesn’t feel remorse or pity—or any emotion. It does not even not care that you exist. It can’t care, one way or the other, since there is nothing there to care.

Any findings made by science—to use the most technical and terse word—are bullshit. So is this opinion, and so is your opinion. So is everything.

Do I make myself clear?

You say the economy should be high. I say, why? High or low, what’s the difference? You’ll be dead and gone and forgotten soon. See ya.

You say mass starvation is bad. I say, to whom? People live, people die. What possible difference can it make (now) or how? Let them die. Let them live. It’s only molecules bouncing back and forth acting according to deterministic rules. You technically don’t even exist. Only electrons and some other who-gives-a-damn particles do.

You say you don’t like pain? I say, stuff it, Nancy. Like the man said, Without God, everything is permitted. Maybe I like giving you pain. And I’m bigger than you, and way meaner. That you don’t like pain doesn’t mean squat. It’s just another opinion. Pain is just nerve impulses, or whatever, which are meaningless. And the universe can’t even not care.

If you or everybody dies in great pain tomorrow, so what? What’s the big deal?

There is no deal. There is nothing. If God doesn’t exist.

Now suppose God exists (the God of Thomas Aquinas, Aristotle, and the other greatest minds of all time). Therefore a science that does not account for this most important, fundamental, crucial, consequential fact is at best a weak science, a lacking science, a science filled with holes. A science that pretends not to see its base, or that suddenly feigns deafness when hearing “God”, is, in a word, incomplete.

This applies as strongly from the hard sciences as all the way down to those who dwell in the intellectual slums of academia.

Physics is operating only one leg suspended in space if it can’t answer what is happening at base, because that base must be supported by pillars designed by God, or by God Himself. Scientists are increasingly starting to realize the role metaphysics must play if any future work is to progress. If physics doesn’t meet metaphysics, it dies or becomes desultory.

The so-called mind-body “problem”—why qualia? what is intellect?—cannot be solved without references to what it means to have a mind, and that science by itself cannot provide. Not if that way is determined to ignore God. Which, you will remember, we are now assuming for the sake of argument, exists.

Why are people the way they are? How reliant is their intellect, which is non-material, on the body, which is? Psychology without God will never solve their fundamental puzzles either, not if they ignore the reason there is a reason for psychology. And this includes the evolutionary psychology beloved of reactionaries and (curiously) so-called scientific atheists.

There will never be such a thing as “hard” AI—not without the cooperation of God. For the kind of thinking that leads to thinking like us needs God.

All materialism is a dead end, if God exists. All so-called “ultimate” answers will be failures, frauds, and fallacies.

If God exists, and science says He doesn’t, that science must fail eventually.

January 14, 2019 | 8 Comments

Pick A Random Number From 1-10

I’m picking a number between 1-10. What is the probability of you guessing it correctly?

It doesn’t exist. No probability exists.

“C’mon, Briggs. It’s one outta ten. Don’t play games.”

Well, the whole setup is a game. But ignoring that, no. It’s not “one outta ten”. It’s not anything.

“What BS. It’s ten percent. Anybody can see that. What kind of statistician are you, anyway?”

Well, I’m the Statistician to the Stars!, so I have that going for me. Still, I insist. There is no probability.

“Do I really have to do this? Look, you coulda picked 1, you coulda picked 2, and so on up to 10. That’s 10 choices. That makes one outta ten.”

Nope. Tell you what. Have a go a guessing and I’ll prove that you’re wrong.

“Funny man. Okay, I read most people pick 7, so I’ll say 7.”

Nope.

“Fine: 6.”

Nuh uh.

“This is getting tedious. 1? 2? 3? 4? 5?”

Keep going.

“8? 9? 10?”

None of those.

“Bull! It has to be. You’re reminding me why I stopped reading you.”

My number was 6.3.

“What!? Hold on. You didn’t say anything about fractions. Always cheating.”

You’re misinformed. I’ll repeat what I said: I’m picking a number between 1-10. Last I checked. 6.3 is between 1-10. You didn’t get it, and you got the probability wrong, too.

“I see what you did there. You’re trying to say that all probability is conditional, and if you don’t specify the conditions, you can’t have a probability.”

That’s right.

“And part of those conditions was the meaning of the words ‘I’m picking a number between 1-10.'”

Yep.

“I assumed an integer as one of my premises, and you defined it as any number. Meaning the words and grammar of any probability problem matter.”

They always do.

“Funny man. Hang on. You said 6.3, so I assume you could have picked any number, any real number. Right?”

Right.

“But there’s an infinite number of those numbers! If that’s what you meant, then there’s no probability of you picking. How could you even pick if you had to first select from an uncountable number of numbers?”

Good question. I can’t, not if I’m presented with an uncountable number from which I have to select one. I don’t even know how to define “picking one” when the number of numbers is so huge I don’t even know how to comprehend them all, except by the fiction of pointing to a symbol.

“Ha! Hoist meet petard.”

I blush.

“Wait, though. You did pick one.”

I did.

“Meaning you had to have some mechanism for picking. Meaning you couldn’t have been picking from some hugely impossible uncountable number, but from some smaller set.”

That follows.

“There’s no way I could have known what that set was, or the mechanism of picking was.”

True.

“Best I could do was to suppose your behavior was similar to other people’s. I could’ve used that as a premise, and then deduced a probability from that.”

That’s it, all right. Which is what you did when you guessed 7.

“But you, you have to be different. Funny man. So you have to pick a non-integer, just to be a funny man.”

My jokes are world famous.

“Yeah, sure. But there was no way I could’ve guessed exactly what you were going to do. And even if I did, I’d have no way of knowing how many digits you were going to throw out.”

Very true.

“Which means there was no way I could really deduce a quantitative probability—not unless I accepted premises which were too concrete.”

That’s because not all probability is quantifiable. That’s what the man said in this award-eligible book. That not everything has a number is a hard equation to swallow for some, growing up as they do, devoted to scientism. Still, it’s true. The only proof there is that everything has a number is hope.

As in so many things, Thomas Berger has the best thing to say about our obsession with numbers. Here’s Jack Crabb, returning to the company of whites after having lived with plains Indians for many years (start of Chapter 8).

That’s the kind of thing you find out when you go back to civilization: what date it is and time of day, how many mile from Fort Leavenworth and how much the sutlers is getting for tobacco there, how many beers Flanagan drunk and how many times Hoffmann did it with a harlot. Numbers, numbers, I had forgot how important they was.

As important as they are, they are not the most important things. Quality triumphs over quantity.