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Correlation vs causation
Hi, I'm Dr Nic
In this video I am going to talk about causation and how it relates to correlation.
People like to find the causes for things. Sometimes the cause - effect relationship
is valid, but sometimes it is not.
Here's an example
When the wind blows from the northwest in Christchurch, the planes fly over the university as they come into land.
Nor-west winds are hot. This drew a colleague to the amusing conclusion
that the planes flying overhead make the temperature go up.
If you did analyse the number of planes flying over the university
and the daily temperature, I am pretty sure you would find a positive correlation.
But the planes are not causing the temperature to rise.
Nor is the higher temperature the reason for the flight-paths.
But the cause or indicator for both is a different thing altogether - the wind direction.
This is an example of where a third factor or variable is involved.
When phenomena are found to be statistically correlated or associated,
there is a temptation to conclude that one causes the other.
Here is another example
There have been studies that show that self-efficacy around mathematics,
and attainment in mathematics are positively correlated.
This means that on average, people who think they are good at mathematics
also get good results in tests of mathematics.
Should we then spend time convincing people that they are good at maths in order for them to get better results?
Possibly, but we would need more evidence of causation.
This correlation does not surprise me. When a person gets good results you would
think they are more likely to feel competent. It may be that there is a causal relationship,
but the direction is unsure, and may even be in both directions.
Another circumstance where causation can be claimed mistakenly is where
multiple factors interact. This is known as multicollinearity.
An analysis of house prices showed that 5 bedroom houses tended to sell for more than 4 bedroom houses.
At face value it might suggest that turning a living-room into a fifth bedroom
will increase the value of a house. But the fifth bedroom may instead be an indicator that
it is a more luxurious home, or have a larger total area which may tend to higher prices.
Or it may be that five bedroom homes tend to be in more desirable locations, thus increasing the price.
Though the relationship can be found, between the number of bedrooms and the price,
we cannot claim that the relationship is causal.
Correlations can be a result of increases in population and technology.
Just about any two sets of time dependent data can show a correlation.
The crime rate could well be correlated to the number of selfie sticks sold, but in reality
both are just related to population and technology growth.
It would be unwise to suggest that selfie sticks cause an increase in crime.
For some entertainment, search on "spurious correlation". This is where two events or sets of data are inferred to be
related when there is no logical connection. The sales of cheese and the films of Nicholas Cage
feature a surprising amount in these.
So what does this all mean for statistical literacy? Always beware of claims of causation.
Think - could the relationship go the other way - could doing well at maths increase efficacy?
Is there possibly a third factor in play, such as the wind direction or house location?
Is the correlation be due to increase in population or technology.
Generally we require a randomised controlled experiment to be able to claim causation.
You can see more about this in my videos about experiments.
It is possible to claim a causal relationship from observational or epidemiological data,
but the conditions are strict.
In the description below are links to further information
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