# Peter Lux

## Correlation Does Not Prove Causation

One of the statements that is often quoted is ‘correlation does not prove causation’. That means just because two things seem to go up or down together it does not prove that one causes the other.

For example the record of CO2 concentration in the atmosphere is correlated with temperature – for example the graph below:

However, this is a complicated situation. Does the temperature cause the CO2 to go up or does CO2 cause the temperature to go up. Or perhaps there is some other factor that is varying that causes both of them to go up.

That is a very valid argument.

However, although such arguments have been put forward it is not the scientific basis for the belief in climate change.

In such situation we need to do a controlled experiment. One in which we can change only one variable to see what the effect is.

One such experiment was done by John Tyndall in the 1850s:

You have a heat source, a tube that various gases can be introduced and then a heat detector.

If you have a vacuum in the tube it is possible to get a reading of the heat transfer with ‘nothing there’.

Now introduce oxygen or nitrogen into the tube – not much difference.

Next you introduce CO2 or water vapour into the tube – there is a big drop in the amount of heat being transferred from the heat source to the heat detector.

In this cause there is a correlation between what gas is in the tube and what the heat transfer is.

Since we are changing nothing else we can safely say that the CO2 causes heat to be absorbed. In this case correlation does prove causation.

If we go back to our original diagram then we now know that if the CO2 is increasing will cause temperatures to rise. However, it could also be true that increasing temperature will increase the amount of CO2 in the atmosphere – what is called a positive feedback.

Well what could cause that – back to the lab where we can do controlled experiments.

One possibility is that water holds less CO2 as temperatures increase (cold fizzy larger or warm flat beer) and since a lot of CO2 is absorbed by sea water this could be an important factor.

It is not difficult to see how we could do a controlled experiment where we measured how much CO2 is release when you heat up water with CO2 dissolved in it.

## When Correlation Does Not Prove Causation

As I said earlier just looking at the first graph does not prove a causation between CO2 levels and temperature although such correlations were proved over 150 year ago in controlled laboratory experiments.

Now what some climate ‘skeptics’ do is try to prove causation incorrectly from correlation. They will say that the CO2 increase lags the temperature increase therefore it proves that only temperature causes the CO2 increase and that an increase in CO2 does not increase temperature.

Such over simplistic attempts are linking correlation and causation are wrong. We can prove in carefully constructed experiments that CO2 causes temperature increase AND temperature causes CO2 increase.

We would expect a lag between temperature and CO2 in the past since we believe that it was the initial warming that increase CO2 levels. There is some evidence from that in some ice cores (Vostok) it is not so evident in others.

At present we know that we are pumping vast quantities of CO2 into the atmosphere (6.5tonnes per year per person in the UK). This will cause a temperature increase which we (rather worryingly) expect to lag behind the CO2 increase – which is what we are seeing.