Correlation does not mean causation, or does it?

Maths aside, we cannot ever truly know anything. Science does not prove things – it disproves things. This keeps us all in jobs, of course, arguing about what we think we know and don’t know. (Maths is different – mathematicians can prove things to be true. I don’t know whether mathematicians will still have jobs when they have proven everything that can be proven.)

Environmental scientists often face the problem of “causal inference”, which Wikipedia defines as the process of “inferring the cause of something”. Beyers (1988) notes that it is very difficult to justify claims of cause-and-effect in environmental impact studies because of the lack of randomization and replication, which strictly invalidates the use of inferential statistics. In other words, the real world is not our personal laboratory, and we cannot manipulate it to obtain perfect data to use in statistical tests. Of course, even then, we are not truly proving anything with those statistical tests.

Correlation is not causation

Seebacher and Franklin (2012) say that we mostly rely on correlations in arguing cause-and-effect in environmental science; think of those graphs that show matching trends in global temperature and atmospheric carbon dioxide concentration. This is where the problem arises, because we all know the old chestnut: correlation is not causation. We’ve all heard the amusing stories about spurious correlations; there are books about them, there is even a spurious-correlation generator and (of course) Buzzfeed will give you a list of the 10 Most Bizarre Correlations.

At some point, “correlation is not causation” is usually hurled into arguments about cause and effect. OK, but let’s go back and think about why we find those spurious correlations so amusing in the first place. For one thing, they are incongruous, which is thought to be a source of humour. (For example, in what possible way could a “pirate shortage” be linked to global warming – #2 on the Buzzfeed list?) It is when correlation is matched with a good physical explanation that things can start to get more convincing. It turns out that Svante Arrhenius (1859–1927) provided that physical explanation between temperature and the presence of heat-absorbing gases such as carbon dioxide a long time ago, which leads us to take rather seriously those graphs I mentioned above.

Models

We often use models to demonstrate cause and effect: we “hindcast” observations and, when they match, we claim the model has “explained the data”. What we really mean by that is that the cause-and-effect relationships embodied in the model (usually expressed as sets of equations that the model solves) are true. We then feel justified in using the model to predict the future.

Assessing cause-and-effect in environmental studies

Formal methods have been proposed for assessing cause-and-effect in environmental studies. For example, Norris et al. (2012) propose an 8-step process, called “Eco Evidence”, in which the evidence for and against causation is systematically reviewed and weighed. The Eco Evidence approach draws from the field of epidemiology, in which Hill (1965) first proposed the minimal conditions needed to establish a causal relationship between two items. Amongst the “causal criteria” proposed by Norris et al. are:

• Plausibility: is there a plausible mechanism that could explain the relationship between the causal agent and the potential effect?
• Evidence of response: are the causal agent and the potential effect associated (for example, do they occur at the same site)?
• Dose–response: does more of the causal agent cause more of the potential effect? (I am paraphrasing here.)
• Consistency of association: does the causal agent result in the potential effect in all or most studies?

Norris et al. conclude that:

“Stronger studies contribute more to the assessment of causality, but weaker evidence is not discarded. This feature is important because environmental evidence is often scarce. The outputs of the analysis are a guide to the strength of evidence for or against the cause–effect hypotheses. They strengthen confidence in the conclusions drawn from that evidence, but cannot ever prove [emphasis added] causality.”

Telling stories

I like this approach: we acknowledge our fundamental inability to know things, but we find a way of weighing and evaluating all the pieces of information that we have anyway. In essence, we tell a story. Don’t discount this: Beyers (1998) argues that the difficulty of demonstrating cause-and-effect in environmental studies “place[s] special demands on descriptive arguments for causation”, and that causal inference “by means of argument is consistent with the scientific method of strong inference and increases the likelihood of correct conclusions”.

Let’s tell more stories, and ease up on the old chestnuts that get us nowhere.

Malcolm Green

Beyers, D.W. (1998) Causal inference in environmental impact studies. Journal of the North American Benthological Society, 17(3): 367–373.

Hill, A. B. (1965) The environment and disease: association or causation? Proceedings of the Royal Society of Medicine, 58: 295–300.

Norris, R.H. et al. (2012) Analyzing cause and effect in environmental assessments: using weighted evidence from the literature. Freshwater Science, 31(1): 5–21.

Seebacher, F. and Franklin, C.E. (2012). Determining environmental causes of biological effects: the need for a mechanistic physiological dimension in conservation biology. Philosophical Transactions of the Royal Society B, DOI: 10.1098/rstb.2012.0036.