Now the simple answer to this question is no. Causality cannot be established just because there is a correlation.
When a researcher conducts a correlational study they are measuring variables that already naturally exist, such as height and IQ, to see whether there is a relationship between the variables. These types of studies cannot explain the relationship between variables, the research has no control of the variables and they are not manipulated in any way, like in a laboratory experiment.
So, the aim of the research is purely to see whether there is a relationship. This relationship can be either positive, as one variable increases the other tends to increase too i.e. as the height of individuals increase their IQ tends to increase too; or negative, as one variable increases the other tends to decrease i.e. as the shoe size of individuals increase their IQ tends to decrease.
A correlation can lie anywhere between 0 and 1 (or minus 1 depending on the direction of the relationship); 0 meaning that there is no relationship between variables (see first graph below for an example of no correlation); 1 (or minus 1) meaning that there is a perfect relationship between variables, so as one variable increases the other will always increase too (or decrease depending on the direction of the relationship. See second picture below for an example of a perfect correlation). Generally a good correlation is shaped like an American football when plotted on a scatterplot, at 0.7 (see third picture below).![no_correlation 1](https://prpklm.wordpress.com/wp-content/uploads/2012/02/no_correlation-1.gif?w=529)
![perfect correlation 1](https://prpklm.wordpress.com/wp-content/uploads/2012/02/perfect-correlation-1.gif?w=529)
However, as briefly mentioned above laboratory experiments can establish causality, due to the high control the researchers have the ability to manipulate the independent variable and measure the dependent variable. This allows the researcher to compare scores and establish cause and effect, by manipulating a variable they can see the changes this may have in another variable. So a lab experiment only measures one variable where as a correlation measures two (as they naturally occur).
So, if correlations cannot establish cause-and-effect why are they so useful?
Correlations allow you to make predictions. For example, Berman, Jobes & Silverman (2006) found a relationship between specific behaviour and imminent suicide attempts. While this research is not able to say whether it is the specific behaviour that causes suicide attempts or whether the imminent suicide attempts causes the specific behaviour, it does allow clinicians, psychiatrist etc to spot the warning signs. If they know what types of behaviours are linked to imminent suicide attempts then they can potentially prevent it from occurring.
Furthermore, correlations are useful as a starting point in areas that have not been previously studied. The researcher can first of all establish whether there is a relationship between the two variables of interest and, if there is, lead onto an experimental study in order to see which variable causes the effect in the other. Also, sometimes it is unethical or not possible to manipulate some variables therefore correlations are handy as the researcher measures naturally occurring variables. An example would be if you wanted to study whether there was a relationship between criminal recidivism and IQ.
The main reason for why correlations cannot show cause-and-effect is because of the third-variable problem. Due to the lack of control it is unknown to the researcher whether a third variable is causing the negative or positive relationship between variables; therefore it may be an indirect relationship.
Berman, A.L., Jobes, D. A., & Silverman, M. M. (2006). Adolescent suicide: assessment and intervention. Washington, DC: American Psychological Association.