A Beginners Guide to Causality

We will answer the questions:

  • What is causality?

  • What are the interrelationships among 'simple causality', correlation, and causal networks?

  • How is causality assessed via noisy experimental data?

What is causality?

Our goal in analyzing data is usually to compare hypotheses, because different hypotheses propose different causal relations among variables. Thus, ultimately, we want to infer causal relationships among variables.

In a causal relationship, there is a mechanism by which changes in one variable have an influence on one or more additional variables.

Causality is interesting for multiple reasons: 

  1. Knowledge of the mechanisms underlying causal relationships gives us a greater understanding of the natural world

  2. Understanding causal relationships allows us predict when and how future events will unfold 

  3. We can manipulate and/or short-circuit known causal relationships, allowing us to control when and how future events will unfold

What are the interrelationships among 'simple causality', correlation, and causal networks?

When we see causality discussed in a lay (and oftentimes even in a scientific) context, there is generally the implicit assumption that we are discussing the most straightforward type of causality, which I will refer to as 'simple causality'.

  • Simple causality is like an applied force, wherein a force applied to a mass causes that mass to accelerate.

  • This type of causal relationship is usually represented graphically as in Fig. 1a. 

FIG 1

Simple causality is certainly an important

causal networks

correlation may occur in any, all, or none of these causal relationships

How is causality assessed via noisy experimental data?

When causality is assessed, you will inevitably hear someone repeat the tired old slogan: 

- 'correlation does not equal causation'

As with most slogans, it hides the important subtlety of the true state of affairs:

Two issues:

repeatability

complexity