Killing people is the best solution.

@Nick Ashley,

Nick Ashley wrote:

4. Correlation isn't a binary thing. Its not a matter of either they are correlated, or they aren't. There are levels. This is important, because the higher the correlation between 2 things, the greater the probability that there is causation.

This I have to disagree with. There are some very strong correlations that are not causal.

1 Reply

@Robert Gentel,

Robert Gentel wrote:

Drew, pony up to this already so that we can get to Bill's graph. There's easier ways to argue against his conclusion than the whole "imply" logomachy.

I've tried to move the debate along several times.

0 Replies

@DrewDad,

Key word "probability".

When you know there is no causation, of course you know the greater the correlation there is, there is no greater probability of causation. But probability can only be calculated by what you know. And if you don't know whether there is causation, then an increase in correlation reasonably increases the probability evaluation.

That doesn't mean it's always the case, but c'mon, "probable" doesn't mean "always" in any definition.

1 Reply

Correlation
Lyrics by Alan Reifman
(May be sung to “Revolution,” John Lennon)

You say you’ve got a correlation,
Well, you know, it says nothing about cause,
You’ve got to do experimentation,
Well, you know, to fulfill science’s laws,

With a correlation between B and A,
Causal direction could go either way,

A correlation cannot be,
Airtight!
Airtight!!
Airtight!!!

You say you’ve got a correlation,
Well, you know, A and B are only linked,
You need further investigation,
Well, you know, to show the pathway that you think,

There’s another option, and this is key,
There could be a third variable called C,

A correlation cannot be,
Airtight!
Airtight!!
Airtight!!!

0 Replies

@Robert Gentel,

No, Robert, it does not make it more "probable." It does not make it even .01% more probable.

1 Reply

@DrewDad,

DrewDad wrote:

If the letter "A" is always followed by the letter "B", and you see a letter "B", what can you assume about the letter preceding "B"?

Every played with cryptology (the basic spy kid stuff)? As a kid I'd crack simple codes with this kind of data (combined with trial and error). I'd memorized the most common words and common combinations, eyeballed the code for correlations and tried the most likely letters first.

Sure, the correlations didn't always give me the answer, but they were the most probable answers.

So what it would tell me is:

That based on the information available the most likely preceding letter is A.

If I had more information (like the language and the most common letters, combinations for that language) I'd have more to go off of. So as a kid doing this for an encrypted English text, the first thing I'd try would be A, then E, T, O and so on.

A comes right after O in probability in English, but based on the data you provided I'd find A to be the most probable preceding letter. I would not know that it is A, but given the information provided it's not unreasonable to find it the most likely answer, and to try it first.

1 Reply

@DrewDad,

DrewDad wrote:

No, Robert, it does not make it more "probable." It does not make it even .01% more probable.

Now the new logomachy is about "probability".

Nothing changes the real probability of anything, but the calculatable probability is what real world scenarios are based on when calculating the likelihood of an unknown prior event like these examples. Here's another poker analogy.

After all cards are dealt, nothing changes the probability that my opponent has an Ace or not. He either does or does not.

But I do not know this all I know is that I have an Ace so there's about a 70% chance that he doesn't (depending on how many players on the table), so if I see the dealer peel off an Ace on the flop, I estimate the probability that he has a Ace to be lower with the additional information.

That doesn't change the real probability, but the overwhelming majority of times you calculate probability you are just estimating based on what you know, and as information comes in you change this estimate even though the actual likelihood is not changing.

1 Reply

@Robert Gentel,

I was not describing an English language text, or a cryptographic exercise. That's your bias.

I can produce a stream of text that follows the simple rule "A" is always followed by "B". Based on this rule alone, what information do you have about the preceding letter when you run across a "B"?

1 Reply

@DrewDad,

DrewDad wrote:

I was not describing an English language text, or a cryptographic exercise. That's your bias.

That's new information.

Quote:

I can produce a stream of text that follows the simple rule "A" is always followed by "B". Based on this rule alone, what information do you have about the preceding letter when you run across a "B"?

That it is (not probably is) preceded by an A. But I think you may have misspoke because I don't think that is what you are trying to ask.

1 Reply

@Robert Gentel,

No, Robert. No logomachy.

My stance has always been: No conclusion made regarding the existence or the direction of a cause and effect relationship only from the fact that A and B are correlated.

A correlation by itself does not make causation any more probable. It does not suggest, imply, or hint at a causal relationship. A correlation gives no information about causality at all.

1 Reply

@Robert Gentel,

BBBBBBBBBBBBBBBBB

This follows the rule the an "A" is always followed by a "B".

This is to illustrate that one cannot reason backwards from "A" implies "B" and get "B" implies "A".

1 Reply

@DrewDad,

DrewDad wrote:

A correlation by itself does not make causation any more probable.

This really does depend on your operating definition of probable.

Quote:

A correlation gives no information about causality at all.

We already went through this and you needed to soften your absolutism, remember?

If there is no correlation, causality is not possible. So if there is a correlation at all, it at the very least gives the information that there is a possibility of causation.

Of course there's causation or there isn't, and nothing changes that. But when dealing with possibility and probability you can be talking about what you can calculate based on the information you know or the binary "it is, or it isn't" that an omniscient person can know.

The only way to interpret your absolutism logically is using a different definition of probability than I am using.

--------

Link drop that I forgot to add earlier:

http://www.scientificblogging.com/seth_roberts/what_should_correlation_does_not_imply_causation_be_replaced_with

2 Replies

@Robert Gentel,

Robert Gentel wrote:

Quote:
A correlation gives no information about causality at all.

We already went through this and you needed to soften your absolutism, remember?

No, Robert. "A correlation" means you have a correlation. If you find there is no correlation then you wouldn't have a correlation.

1 Reply

@Robert Gentel,

Robert Gentel wrote:

DrewDad wrote:
A correlation by itself does not make causation any more probable.

This really does depend on your operating definition of probable.

How can it possibly depend on a definition of probable?!?!?!?

1 Reply

@DrewDad,

DrewDad wrote:

BBBBBBBBBBBBBBBBB

This follows the rule the an "A" is always followed by a "B".

This is to illustrate that one cannot reason backwards from "A" implies "B" and get "B" implies "A".

Doh!

I should have added the rest of what I'd intended to type ("or I am interpreting it wrong") because in reality I read it wrong and I needed that additional caveat.

Ok, so now that I have got reading comprehension temporarily conquered:

1) I have no way to determine what letter preceeds a random B. It is either an A or it is not.

2) But based on the information available to me, the most likely letter is A. I'll explain the logic:

The baseline probability with no additional information is that it can be one of X possibilities (using the English alphabet this would be 1/26 for random non-English text). With the additional information about that correlation I know that there is a greater probability that it is an A than any other letter.

The reason is because you established that an A in this text is always preceded by a B. Now sure, your random text (I have to assume randomness for the missing information) may not even contain an A, and that might just be a maverick B hanging out there, but as long as that rule exists there is a greater probability that an A precedes the letter than any other letter.

This, again, refers to the calculatable probability. So if you run this simulation, generating a random set of letters following only that rule a million times A will be the most probable answer to the question.

I don't remember if you are a programming guy, or a networking guy but if you are a programming guy give it a try.

0 Replies

@DrewDad,

DrewDad wrote:

No, Robert. "A correlation" means you have a correlation. If you find there is no correlation then you wouldn't have a correlation.

So the fact that you have a correlation changes the available information to you by not allowing you to rule out causation based on the absence of the correlation.

1 Reply

@Robert Gentel,

Quote:

- We all know that correlation doesn't imply causation, as long as you are using a statistician's meaning of "imply".

I agree.

Quote:

- The colloquial meaning of "imply" is to suggest, and yes correlation can suggest causation. This is what is in dispute.

Ok. But the trouble begins when you start drawing conclusions from these non-statistical suggestions.

Quote:

That's where we are stuck, the very different meanings of "imply" are confusing the issue. Correlation isn't causation, we all know that. But it does give us information about causation. It's not a binary thing, and the differences between correlation coefficients can give us information about causation (even if it's not infallible).

The highlighted phrase is what brought me back into this thread. Again, colloquial interpretations is one thing. Conclusions drawn on inferences that don't have statistical meaning is another. Just don't start using the word "significant" and I'll go back to my corner.

Quote:

I also haven't seen convincing data from Bill in regard to the murder/capital punishment correlation and don't agree with that either. This puts me in the odd spot of agreeing with Drew about the graph not being very meaningful, but agreeing with Bill to the effect that correlation can reasonably suggest causation.

Precisely!

1 Reply

@Robert Gentel,

Robert Gentel wrote:

DrewDad wrote:
No, Robert. "A correlation" means you have a correlation. If you find there is no correlation then you wouldn't have a correlation.

So the fact that you have a correlation changes the available information to you by not allowing you to rule out causation based on the absence of the correlation.

But it still gives you no information about whether causality actually exists, or if it doesn't exist. Finding a correlation does not change the available information in regard to causality.

1 Reply

@DrewDad,

DrewDad wrote:

How can it possibly depend on a definition of probable?!?!?!?

I don't see any way your statement can be accurate unless you are thinking about probability differently than I am.

Past events don't have probability. They are or they aren't.

If you don't know, you can calculate a probability based on the meaning "run this enough times and some answers are more often correct than other answers".

Under this definition of probability (which is the one used the overwhelming majority of the time) your statements are not accurate. But yes, if you mean that it changes nothing about the relationship that already does or does not exist that is true.

Look, now we are into demonstratable territory. We can run simulations for your A/B scenario to test this if you'd like. I'll even hack out the code (or entice Nick to "hey Nick... you know what really awesome programmers can do?").

Another option is to take a huge sample of correlation and causation data, and see if the greater the correlation coefficient the more often we hit causality.

Are you game for either scenario? I'll do the work if it's the former (or bribe Nick).

1 Reply

@Robert Gentel,

I see immediate problems with both scenarios. I don't think this is something that lends itself to empirical testing.

This is an information theory problem, not a statistical problem.

1 Reply

Killing people is the best solution.

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