Ahhh yes, the age-old stats question…. to which I shall now give my view and explain why I have this view.
If, like me, you have always been taught that ‘correlation DOES NOT MEAN causation’ , you are not alone! In my opinion this statement is correct, and I’ll explain why I think this is later on.
But the question in the title of this blog is whether or not correlation can show causality. Which, in my opinion, it can. I’ll explain why now… Take an example, with 2 variables, where a set of results show positive correlation. Looking at a graph, this is what it would look like.
This graph shows a positive correlation, I’m sure you would all agree. Let’s assume that in this example, the 2 variables have causation. In other words, the variable represented on the bottom of the graph (let’s call it variable 1, original I know) directly affects the variable represented on the side of the graph (variable 2). The positive correlation shown in the graph demonstrates that the 2 variables both increase in number together; as variable 1 gets bigger, so does variable 2. Therefore it can be said that this positive correlation has illustrated – or shown – the causality.
However! I’m going to emphasize that in this example, the relationship between the 2 variables was already there, but that the positive correlation helped to show the causality….. I hope you understand this!
So now I shall make my point that although correlation can show causality, it DOES NOT MEAN causality. Just because 2 variables are positively correlated, it does not necessarily mean that one causes the other to occur. There may be other reasons for the correlation, for example a third variable which affects both.
Let’s take the same graph as before.
Again, you can see the positive correlation. Now, what if I told you that in this example, the variable along the x axis (along the bottom) represented the number of shark attacks during the year, and the variable along the y axis (up the side) represented the number of ice cream sales during the year? Yes, both numbers increase (as it heads to summer). So they are positively correlated. BUT one is not causing the other! You don’t see people after being attacked by a shark think, “oh, I’d like an ice cream now…” Maybe a silly example but you get my point.
In case you got lost in all that, what I’m saying is that I completely agree with what we’ve been brought up being taught, and that just because there is a correlation between 2 or more variables, it does not mean that there is causation. However, as explained above (or attempted to explain!) positive correlation can show (or illustrate) a causality between variables.
suuzblog 
Feb 21, 2012 @ 18:46:08
Really good blog, at first I thought you were going to argue that correlation cannot ‘cause’ causality. However, I had to go back and reread the title, like you I was also brought to believe well strongly influenced to believe that correlation does NOT cause causality. However, I was never asked the question does correlation ‘show’ causality. In the example you have given, I agree with you that it does. However, I can also see why many would hesitate to agree with you. The media has often taken scientific research and manipulated it. The most common is arguing that correlation causes, causality. However, these assumptions made by the media are not on minor things, but on new medicines and life threatening diseases. So many do not want to see a link for fear of being seen to be taking things out of proportion. But does correlation ‘show’ causation? Well i would say in some cases yes.
http://www.cut-the-knot.org/do_you_know/misuse.shtml
Feb 22, 2012 @ 10:46:08
You have raised a good question here and have challenge the way we think about correlation and causality however i have something to add to this. Although you say at the end of your blog that correlation can show causation i would say that even in those cases there can be an outside force
for example, while looking around the internet for help with this comment i came across a description that illustrated this well. the example was, say we are looking at the link between breastfeeding and higher IQ- a correlation could be showed and this could even be strong enough to lend itself to looking like a causation however is there another factor?- it could be that it’s actually parental involvement that causes both the increased breastfeeding and higher IQ
http://ask.metafilter.com/80526/How-do-we-establish-causation
Feb 22, 2012 @ 12:03:11
I may not prove causality but it does give you an indication. you can NOT have a Causation without a relationship and a correlation is the first indication of this. Similar to the way you can’t have validity with our reliability. A lot of what we do in research is falsification, you can’t prove any thing but you can falsify it. if you run a correlation and find nothing then its not necessarily a bad thing.
Feb 22, 2012 @ 17:05:40
i agree with what you are saying and if i saw that graph i think i would go ‘well x must cause y… its obvious’ but as usual we have to be a bit more scientific and cover all angles just to make sure we dont make a mistake. as other comments say it gives and indication to what has occured and it is always useful to have a picture of what your data looks like
🙂
Feb 22, 2012 @ 18:40:10
You’re right in saying that correlation does not mean causation but that correlation shows (or maybe suggests) causation. In trying to think of an example that shows that there is a definite causal relationship between two variables…I couldn’t, I could always think of something else! Which makes me think that maybe we can never be 100% certain of causation. It may seem pretty obvious that one thing causes another (like in the typical example of ‘the more work you do the better grade you get’), but there can always be other variables involved. for example, i might do loads of work and get really good grades (wishful thinking), but the amount of work I did might not be a direct cause of the grades i got. it could be that I did lots of work, got lots of sleep the night before the exam, ate healthily and enjoyed the topic that the exam was on; all of these variables would have interacted and resulted in me getting a good grade. so, I still completely agree that correlation can show/suggest causation, but i’m not entirely convinced that it can ever truly mean causation (despite how strong the evidence might be).
Feb 22, 2012 @ 21:22:38
I disagree completely with what you have said.
The reason being is that you are already working off the assumption that there is a causal relationship between variable 1 and variable 2 in Figure 1. Naturally, this would show causation. Relationships only portray the way data have occured at the same time. I feel as though you are just using technicalities to try and justify your claim.
Mar 09, 2012 @ 21:10:39
^ you clearly haven’t read the whole blog! Thanks for that btw, not taking the time to read everything which I worked on but instead jumping on and criticising one idea which you have misunderstood because you have not read it all and therefore not seen it in context. I used the assumption in the blog to illustrate clearly and help explain what I meant. ‘you are already working off the assumption that there is a causal relationship between variable 1 and variable 2 in Figure 1’ of course I am, that’s what I said in the blog… In the future I suggest you 1) read all the way through blogs and understand what the author is trying to say before jumping onto one thing which you misunderstand, and 2) use comments to make constructive criticism and a valid point with research evidence and not just to be rude.
Apr 17, 2012 @ 12:47:07
I enjoyed reading your blog and was refreshed when you concluded that just because correlation doesn’t mean there is causation, correlation can indicate a causative relationship. Or to put it another way you can have correlation without causation but you cannot have causation without correlation. This is, of course, because a correlation is a relationship between two variables (Gravetter & Forzano, 2009), and if one thing causes another thing then they share a relationship! Although, from a number of other blogs on this subject, many students do not seem to appreciate this fact. Additionally, as well as indicating a potential causation, correlation can also help to produce more research questions (Rogers and Nicewander, 1988), leading to further research and ultimately the advancement of the scientific field. So don’t knock correlation!
Gravetter, F. J., & Forzano, L. (2009). Research Methods for the Behavioral Sciences (3rd ed.). Belmont, CA: Wadsworth Cengage Learning.
Rogers, J. L., & Nicewander, W. A. (1988). Thirteen ways to look at the correlation coefficient. The American Statistician, 42(1), 59-66.