# The truth about correlation studies!

Greetings fellow bloggers!

This week I am going to look at the subject of correlational studies and ask the question “Can a correlation ever prove a causality in a relationship?”

So let’s start with the basics, a correlation study is a type of study used to determine whether there is a relationships between any and all variables used. A correlation is described by the APA as “Interdependence of variable quantities.”

So what forms of correlations can you get? There are positive correlations, negative correlations. A positive correlation is where one variable will either increase or decrease and the second variable will increase or decrease along with the first (not to be misunderstood as a causality I might add, this effect could be caused from either variable). A negative correlation, on the other hand, occurs when one variable increases and the second variable decreases (or vice versa) at the same time. And of course, there are “no correlation” results, when, as the title suggests, has no discernible pattern to it. Correlations can also be obtained via such techniques as observations, archival study and questionnaires/interviews.

Correlation graphs sound great! They take all of your data and compare them, to look for traits/relationships and then explain them all to you! From this you can see what happens(ed), how it happened, and why it happened! But wait.. can a correlation really tell you how and why an effect happens(ed)?  Let’s create a scenario to envision this idea… Imagine there is a study conducted on school children and it’s discovered that at dinner time the students who pick the healthy options tend to score above average on tests in the afternoon, compared to the students who do not pick the healthy options. Now what this statement would appear to say is that eating healthily at dinner time would seem to increase how well a student performed afterwards, but this is not the case! For here, we only have a correlation, this is not a causality. There may be many factors that interfere with these statistics, maybe certain types of classes, or attentional span and so on. This is the main disadvantage of using a correlational study, you can never assume a causality from a correlation, whether positive or negative, you must only determine thatthere is a relationship between one variable and another.

Let’s try with a real world example instead. A study run by Buss (1984) looked at the correlation between the choosing of a spouse in marraige and that persons’ qualities, and also whether or not the length of a relationship/marriage affected the cohesion of a couples’ interactions. The study found that indeed there was a correlation regarding the qualities a spouse had and their being chosen by their partner (particularly with domain such as quarrelsomeness, dominance, and extraversion). The study also found that the cohesion between a couple does increase (and subsequently correlate with,) the increased length of a relationship/marriage. These finds seems to be pretty conclusive don’t they? Couples form a tighter, more on track, relationship with a partner the longer the relationship lasts, and partners pick people who rate highly with particular traits of their spouse. But once again, with these correlations, we can only assume that there is a relationship, we cannot determine which direction the effect is going.

So to conclude, when conducting correlational studies, although very useful in terms of determining relationships, we must be very careful to avoid the urge of applying causality to our data as they cannot be used to determine causality.

This pretty much sums it up.

## 11 thoughts on “The truth about correlation studies!”

1. Very good blog, I like the fact you made up your own example, then used a real life one 🙂
I quite like correlations myself, but this may be because I find them easy, simple and quick to do (one of the advantages of correlations)!
Because we can’t infer cause and effect from correlational studies, I think they should be used as a pre-research test. There could be something you want to investigate, so you carry out a correlation to see if there’s a possible relationship between the two variables. If there’s no relationship, you know not to bother carrying out a big experiment, whereas if there is a correlation; you could be onto something!
For example, if you want to see whether parental income affects a child’s school grades, you could carry out a correlation on this, and if you find, say, those with lower parental income score lower on a test than those whose parents’ have higher income, then you can do some deeper research into the theory.
The scores on the test could be caused by diet, the relationship between a child’s parents, or how much TV they watch per day on average, but the deeper research is what should find this out.

2. I’m going to agree with the comment above; I quite like correlational studies too as they’re interesting and not too complicated 🙂 however there are so many negatives to the use of them that it is hard not to get bogged down by the vast number of negative points. But one of the things that is interesting to me is how correlations can show a relationship between to variables, but what about those extra variables? The ones that we don’t think about….
Well the third variable problem proposes that there may be an unknown third variable involved in a study that you have absolutely no idea about! So A cause the effect we see on B? Well we might originally think that but what if C (our third unknown variable) is controlling A or B or even both! One correlational study aimed to discover which variables were the best predictors of birth control use in Taiwan (Li, 1975)*. Taiwan had severe problems with overpopulation you see so researchers wanted to find out why… And what they found next was completely baffling (and also slightly amusing).
The variable that correlated the most highly with the use of birth control was the number of electrical items there was in the home. So things like toasters, and televisions! But of course that’s ridiculous; surely owning a toaster or a television cannot seriously increase the use of birth control right?! No. Of course not. And this is where the third variable I mentioned above comes into play. People who did better at school probably paid more attention when learning about the use of contraception, those that did best at school probably got higher paid jobs, and those that got higher paid jobs could probably afford more electrical appliances. See where I’m going with this? Education was the third variable in the correlational study. People with higher socioeconomic status can afford more things and are more educated about the use of birth control. Therefore it wasn’t really the toaster (A) sat in the kitchen causing the use of contraceptives (B) but education (C) which the researchers didn’t immediately link in.

So the third variable problem can cause issues and sometimes the correlation that’s found isn’t as obviously wrong as the example above, but still correlational research does provide us with lots of information about variable relationships 🙂

*Li (1975) in S. L. Jackson’s Research Methods and Statistics: A Critical Thinking Approach (Page 155)

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4. A very comprehensive blog which I believe explains very how correlation does not prove causality. I would like to state that although causality cannot be assumed simply through correlation, this doesn’t make correlation studies redundant. Correlation studies are extremely useful when an area of research hasn’t received a lot of attention as correlation studies can identify variables that may need further investigation. Also correlation studies are useful at looking at variables which we cannot ethically manipulate, for example we could look at correlations between health and environmental pollution, as these variables exist but they are variables which we cannot ethically change in an experimental research study.

If one wanted to infer causality from a correlation one would have to use more complicated statistics such as Path Analysis, but even then researchers make very limited causation claims
and if one wanted to infer causation then there are conditions that need to be met. These are:

Time precedence – Variable 1 must precede Variable 2 if 1 causes 2.
Relationship – There must be correlation
Non-spuriousness – Which is pretty much the third variable problem

Kenny, D. (1979). Correlation and Causality.
Gravetter & Walnau – Research Methods for the Behavioral Sciences
http://psychcentral.com/blog/archives/2011/07/18/the-importance-of-correlational-studies/

5. I would like to point out that correlation has more usefulness than the comments above have made out, because correlation is the basis of causation (Gravetter & Forzano, 2009). A correlation is where variable A has a relationship with variable B. Causation is where variable A causes something to happen to variable B, this is a relationship and therefore variable A and B have a correlation. Say you found a significant result from a t-test, if you were to run a correlation analysis it would also be significant (http://www.statisticalmisconceptions.com/sample1.html). The statistical analysis proved causation which proved that there’s a relationship between the two variables, so the correlation analysis will show that there’s a relationship. I know I’m just repeating myself but the point is that correlation is the basis of causation, and if you have causation then you will also have a correlation between your variables and therefore correlation is important.

References
Gravetter, F. J., & Forzano, L. (2009). Research methods for the behavioral sciences (3rd ed.). Belmont, CA: Wadsworth Cengage Learning.

6. You make a very good point, I didn’t look at this from that point of view, yes indeed, we must consider the fact that if there is a causation, it’s basis will be derived from a correlational study. I should have worded my argument more appropriately, what I meant to say was that correlations do not definitevly prove causation, but it can indeed indicate if there is any.

7. Very good blog 😀 and of course we all know not to fall into the trap of assuming that correlation equals causation, though we can use the strength of the correlation to determine whether further into a causal relationship is necessary. One other thing I’d like to point out is that a problem with the pearson correlation is that it leads us into assuming linearity.
Anscombe (1973) pointed that correlations may not give a fair reflection of the relationship, as he shows here with 4 scatterplots that share the same mean, standard deviation, correlation, and regression line. However, all 4 are clearly distinctly different sets of data.

Anscombe, F. J. (1973). “Graphs in Statistical Analysis”. American Statistician 27 (1): 17–21.

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