If the correlation coefficient has a positive value above 0 it indicates a positive relationship between the variables meaning that both variables move in tandem, i. Where the correlation coefficient is 0 this indicates there is no relationship between the variables one variable can remain constant while the other increases or decreases. While the correlation coefficient is a useful measure, it has its limitations: Correlation coefficients are usually associated with measuring a linear relationship.
For example, if you compare hours worked and income earned for a tradesperson who charges an hourly rate for their work, there is a linear or straight line relationship since with each additional hour worked the income will increase by a consistent amount.
If, however, the tradesperson charges based on an initial call out fee and an hourly fee which progressively decreases the longer the job goes for, the relationship between hours worked and income would be non-linear , where the correlation coefficient may be closer to 0.
Care is needed when interpreting the value of 'r'. It is possible to find correlations between many variables, however the relationships can be due to other factors and have nothing to do with the two variables being considered. For example, sales of ice creams and the sales of sunscreen can increase and decrease across a year in a systematic manner, but it would be a relationship that would be due to the effects of the season ie hotter weather sees an increase in people wearing sunscreen as well as eating ice cream rather than due to any direct relationship between sales of sunscreen and ice cream.
The correlation coefficient should not be used to say anything about cause and effect relationship. By examining the value of 'r', we may conclude that two variables are related, but that 'r' value does not tell us if one variable was the cause of the change in the other.
However, there are a variety of experimental, statistical and research design techniques for finding evidence toward causal relationships: e. Beyond the intrinsic limitations of correlation tests e. For example, imagine again that we are health researchers, this time looking at a large dataset of disease rates, diet and other health behaviors. Suppose that we find two correlations: increased heart disease is correlated with higher fat diets a positive correlation , and increased exercise is correlated with less heart disease a negative correlation.
Both of these correlations are large, and we find them reliably. Surely this provides a clue to causation, right?
In the case of this health data, correlation might suggest an underlying causal relationship, but without further work it does not establish it. Imagine that after finding these correlations, as a next step, we design a biological study which examines the ways that the body absorbs fat, and how this impacts the heart. Perhaps we find a mechanism through which higher fat consumption is stored in a way that leads to a specific strain on the heart.
We might also take a closer look at exercise, and design a randomized, controlled experiment which finds that exercise interrupts the storage of fat, thereby leading to less strain on the heart.
These statements could be factually correct. However, with these statements, we need evidence from a properly completed study to factually state there is a causaul relation between the two variables.
If someone states a potentially spurious casual statement like this, I'd encourage them to perform research on independent studies to gather official evidence. Studies are often done by research-driven institutions and universities. Here is a paper published by the Journal of Obesity that cites several studies that provide evidence that high-intensity intermittent exercise may be effective to cause people to lose abdominal body fat. Tyler Vigen has an interesting page on his website that visualizes spurious correlations.
Below is an example that shows a strong positive linear correlation with U. However, do you think U. My hypothesis is that there's no evidence to support a causal relationship between these two variables.
While this example from Tyler's website seems extreme, it's poking fun at how people can immediately visualize a relationship between two numerical variables and naively jump to the conclusion that there's a causal relationship. The joke is that the guy on the right feels he doesn't have strong evidence such as through a study to prove his statistics class caused him to believe that fact is true.
Perhaps you freelance for a magazine that pays by the word. The longer the story and the more words it contains , the more you get paid. So there's a direct correlation between how many words you write and how much you get paid. But there's also causation because you wrote more, you got paid more. Why is it so easy to think that correlation implies causation? Well, if two things seem related, we tend to associate them and assume they impact each other.
When the weather's cold, people spend more time inside. Around the holidays, shopping malls are packed. When you take some ibuprofen, your headache goes away.
While these circumstances certainly are related - and some might even imply causality - they don't necessarily stand up to scientific analysis. First of all, you might have a confounding variable in the mix. This is a variable that affects both the independent and dependent variables in your relationship - and so confounds your ability to determine the nature of that relationship.
For example, if a new family moves into a neighborhood, and crime goes up, the residents in that area might assume it's because of that new family. But what if, at the same time, a detention center opened nearby?
That's the more likely cause of the increased crime. Second, you might be dealing with reverse causation. This happens when, instead of correctly assuming that A causes B, you get them mixed up and assume that B causes A. It might be hard to imagine how this happens, but think of how solar panels work. They produce more power when the sun is in the sky longer. But the sun isn't in the sky longer because the panels are producing more power.
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