# Talk:Correlation does not imply causation

Could this article be put in the Logical Fallacy group, under a title such as "The Correlation = Causation Fallacy" --Remarcsd 18:59, 8 October 2007 (EDT)

- I agree with the cat, but not the title change. For these reasons:

- It is actually what it is called (this phrase is how people bring it up)
- "weird" characters in titles can cause unepxected problems. In fact, I think the "=" sign is not permitted. (We had an article with "&" in the title that required database access to delete...)
- It is much more likely that someone will type the existing title as a link in an article or talk.

- I'll check the cat and see if I can go add it to the logical fallacy article.
**human**21:22, 8 October 2007 (EDT)^{be in}

## Contents

## Latin phrases[edit]

You mention *post hoc ergo propter hoc*, but omit the phrase *cum hoc ergo propter hoc*, which refers precisely to the topic of this article...^{— Unsigned, by: 77.186.140.134 / talk / contribs }

## Title?[edit]

I've always heard this as "correlation does not **imply** causation", which I think is a little more applicable than "equal." **Uke** **Blue** 19:29, 24 January 2013 (UTC)

- That is the name of the WP article so move I guess. Ty
^{JFBANBSRADA}19:31, 24 January 2013 (UTC)- Yes. Wėąṣėḷőįď
^{Methinks it is a Weasel}19:42, 24 January 2013 (UTC)

- Yes. Wėąṣėḷőįď

## Is the convers/inverse true?[edit]

When taking a look at the correlation-causation fallacy, it seems that correlation is needed for causation, but does not imply it. To that end, I was wondering if it would be a valid assertion that a *lack* of correlation (or even a *negative* correlation) definitively *disproves* causation.

Take, for example, that old moral panic about the Super Mario Bros. video game franchise supposedly normalizing violence and animal cruelty by allowing players to throw cartoon turtles at enemies, which could alter and distort kids' views and turn them into violent killers when they get older. About 25-28 years after the first Super Mario Bros. is released (i.e. around the present day), a study is done (I'm not referring to an actual study, just a hypothetical one) evaluating the popularity of the Super Mario Bros. franchise over the previous 25 years and how it compared to the rates of murder and other violent crimes over the same period of time.

Now, even if the increasing popularity of Super Mario Bros. *were* correlated with an increase in violent crime rates, drawing a causal relation would obviously still be incredibly dubious. Nevertheless, let's say this hypothetical study actually shows either a *lack* of correlation or a *negative* correlation between the popularity of Super Mario video games and violent crime rates, with the rates of murder and other violent crimes actually *decreasing* over the 25-year period in areas where Super Mario video game sales were consistently high. Of course, this doesn't mean that Super Mario Bros. actually decreases violent crime, but that's not what I'm asking.

My question is this: Would this information definitively *disprove* a supposed causal link between Super Mario Bros. and violent crime, or am I missing something? Could the converse and inverse of the correlation-causation fallacy be said to be true, or is it just as uncertain? 208.40.167.249 (talk) 07:38, 22 May 2013 (UTC)

- A "negative" correlation is still a correlation, it means that one goes up and the other goes down. The thing with correlation that you might need to look into is the fact that there isn't so much a "there is or there isn't" style approach to them. You measure it statistically as how likely a change in one variable results in a change in the other. It's extremely unlikely to produce entirely uncorrelated data just as much as it's unlikely to get 100% correlation. They're reported as confidence intervals, which are effectively arbitrary.
- If you demonstrate a lot of scatter, and a very low correlation, or a very low confidence in the correlation being genuine, then it doesn't necessarily disprove causation
*for individual cases*. Someone could still shout "Ah, Mario! I hate this fucking game it's so frustrating!!" and storm outside and shoot someone.*But*a lack of statistical significance in the correlation demonstrates that even if an individual case can have a causal link between your two measures, it cannot hold true statistically as a general rule.^{d hominem}14:24, 22 May 2013 (UTC)- I see. Thank you for taking the time to reply. I guess my example of the Mario Bros. moral panic, which was intended to be a "simplified" example (it was also intended as an allegory for some more recent moral panics, but I digress), still doesn't escape the complex nature of actual statistics.

- Would it be more apt to say that a
*lack of statistical significance*in a correlation definitively*disproves*a purported causal rule?

- Would it be more apt to say that a

- Even if it doesn't necessarily rule out a causal link in individual cases (such as the rather hilarious example you gave of the frustrated Mario player shooting someone), would it be accurate to say those hypothetical statistics in my example would conclusively prove the wingnut wrong? 208.40.167.249 (talk) 16:59, 22 May 2013 (UTC)
- Correlation is necessary, but not sufficient, to demonstrate causation. No correlation, no causation. (But as ADK points out, it is very rare that there is
*zero*correlation as opposed to statistically insignificant correlation.) However, the hypothetical study does not disprove the connection between Mario and violence levels. For example, the study could be low-power and result in a type II error (i.e., false negative). This could still occur even with a high-power study -- that's why replication is so important. Consider the alleged link between vaccines and autism. We can say pretty definitively that there is no link because the lack of correlation has been replicated over and over, among other things. Nebuchadnezzar (talk) 18:11, 22 May 2013 (UTC)- IIRC, there is precisely zero correlation between x and y when they conform to x
^{2}+ y^{2}= 1. Happens all the time, for obvious cause, in rotating machinery such as electric generators. Implications are left to the readers' imaginations. Sprocket J Cogswell (talk) 19:24, 22 May 2013 (UTC)

- IIRC, there is precisely zero correlation between x and y when they conform to x

- Correlation is necessary, but not sufficient, to demonstrate causation. No correlation, no causation. (But as ADK points out, it is very rare that there is

- Even if it doesn't necessarily rule out a causal link in individual cases (such as the rather hilarious example you gave of the frustrated Mario player shooting someone), would it be accurate to say those hypothetical statistics in my example would conclusively prove the wingnut wrong? 208.40.167.249 (talk) 16:59, 22 May 2013 (UTC)

## Is this good enough for bronze?[edit]

I think it is. Proxima Centauri (talk) 18:26, 26 May 2014 (UTC)

- No, Close perhaps, but not there. Keep trying. It
*should*be, sad that it's not.**ħuman**00:45, 27 May 2014 (UTC)

## Wouldn't Bible prophesy be a VERY good example of this?[edit]

- The bable stated in the last days people would sin, and since people are currently sinning, bible prophesy is true. Is this a (blatant) example of this?--TemplarJLS (talk) 07:16, 10 September 2014 (UTC)

## Murky example is not murky; just bad[edit]

Yes, obesity is not the *cause* of diabetes. But it is a probable risk factor unto itself, as the "Risk factor" section notes. Adipose tissue triggers insulin resistance and inflammation, which are themselves causative factors for diabetes. Drawing a distinction between central obesity and other forms is just a red herring.

The "risk factor" section covers the obesity-diabetes overlap better (and I improved it further). However, the talk about risk factors being symmetric is a classic causation boner: even if A causes B, B does not necessarily cause A.--Fire Me Boy (talk) 05:21, 3 November 2014 (UTC)

- Ah, beat me to it! I was trying to find a different murky example to take its place. Noir LeSable (talk) 05:58, 3 November 2014 (UTC)

## Nitpicking: (P&Q) ≠ (P→Q) ٧ (Q→P)[edit]

Technically the above is correct, but a bit more accurate formula for the implication would be:

(P&Q) → (P→Q) ٧ (Q→P)

And it just happens to be a tautology. Which mostly proves that one can't really discuss causality via propositional logic. I suppose there is a certain aesthetics in decorating article about a logical error with some erroneus logic, but I'm not sure if it was intended? 95.221.194.28 (talk) 18:51, 9 December 2014 (UTC)

- Yeah, but see, there's a reason we use ≠, right? Because the notions themselves aren't logically identical. You can't just go through a proof and replace all instances of (P&Q) with (P→Q) ٧ (Q→P), and still prove the same things. It's
**one**of the classes of errors people make in using the idea. Ikanreed (talk) 19:01, 9 December 2014 (UTC)- So, for someone a little less conversant with PQ style statements, is it that the article version is a literal statement of the title while the BoN version shows what one would conclude after making the error? It's not necessary that I understand, but I want to! MarmotHead (talk) 21:49, 9 December 2014 (UTC)
- (P→Q) ٧ (Q→P) causes the truth value of Q and P to be the same. (P&Q) causes the truth value of Q and P to be both true. They are therefore not equivalent, but if "(P&Q)" is true, then "(P→Q) ٧ (Q→P)" will also be true. The more limited case is also an example of the general case, but this relationship only goes one way.--TiaC (talk) 22:14, 9 December 2014 (UTC)
- Thanks! I was trying to parse it linguistically, but your explanation (from programming?) is much more straightforward. MarmotHead (talk) 22:21, 9 December 2014 (UTC)
- No guys, you're wrong. The BoN had it right. (P→Q) ٧ (Q→P) is a tautology, because if P is false, then the former statement is true, if q is false, the latter statement is true, and if both P and Q are true, then both sides of the or statement are true. It doesn't ascribe equality to P and Q, it's just a universally true logical statement. Like (P v ~P). Ikanreed (talk) 17:49, 10 December 2014 (UTC)

- Thanks! I was trying to parse it linguistically, but your explanation (from programming?) is much more straightforward. MarmotHead (talk) 22:21, 9 December 2014 (UTC)

- (P→Q) ٧ (Q→P) causes the truth value of Q and P to be the same. (P&Q) causes the truth value of Q and P to be both true. They are therefore not equivalent, but if "(P&Q)" is true, then "(P→Q) ٧ (Q→P)" will also be true. The more limited case is also an example of the general case, but this relationship only goes one way.--TiaC (talk) 22:14, 9 December 2014 (UTC)

- So, for someone a little less conversant with PQ style statements, is it that the article version is a literal statement of the title while the BoN version shows what one would conclude after making the error? It's not necessary that I understand, but I want to! MarmotHead (talk) 21:49, 9 December 2014 (UTC)
- At
*any*rate, the fact that it's the summary quote is misleading, and the logic isn't sound. I'm gonna take BoN's advice and scrub it. Ikanreed (talk) 20:15, 10 December 2014 (UTC)- Why not just change it to (P&Q) ≠ (P→Q)? People don't use the fallacy to claim bidirectional implications.--TiaC (talk) 20:18, 10 December 2014 (UTC)
- Because as the anon explained, the notion of logical "and" isn't the same as the observational idea of co-incidence. Nor is the theoretically application of causation the same as the logical notion of implication. You can't actually express the true notion without first order logic, and even then, it wouldn't be intuitively meaningful. It's probably best to save the formal logic where it is strictly applicable. Ikanreed (talk) 20:23, 10 December 2014 (UTC)

- Why not just change it to (P&Q) ≠ (P→Q)? People don't use the fallacy to claim bidirectional implications.--TiaC (talk) 20:18, 10 December 2014 (UTC)

## Images[edit]

- http://theamericangenius.com/wp-content/uploads/2011/12/causation-correlation.jpg (there may be a better version of this)
- https://www.google.com/#q=correlation+causation+pirates&tbm=ischUser000name (talk) 06:08, 21 January 2016 (UTC)

## Another example[edit]

This is an example from real life. There was an article in 2013 in Denmark about a guy who'd "discovered a wonder-remedy" against snails in his garden. He'd discovered that the snails wouldn't invade any flowerbeds he'd put dead moss in, so after this discovery, and this is seriously what it says in the article, he used ironsulfate to kill the moss in his lawn, removed the moss and tossed it into his flowerbeds.
The expert who was consulted, said that she'd never heard of this before, but couldn't deny there *could* be something in dead moss that kept snails away.
So following this article, the advice of course spread to various gardeners and forums. Use dead moss against snails.

The funny thing is, I found another article posted five years earlier... About how somebody coincidentally discovered that snails are killed by ironsulfate.