Statistics

Statistics

So far we have learned how to estimate or model a single thing or event. Statistics gives us tools to understand multiple measurements from a group of objects.

We will focus on the application of statistics to problems of environment and environmental justice. Particularly, statistics allows us to elucidate patterns and provide evidence of the causes.

We will be using two data sets from California to ask questions and gather evidence.

• CalEnviroScreen 3.0

• Cal Adapt

We'll start with a brief discussion of causality.

Causality

Here are a few questions that require the establishment of causality:

• Does pollution cause health problems?

• Do green taxes reduce pollution?

• Is discrimination contributing to health problems?

Establishing Causality

To establish evidence of causality, we need to establish three factors

• Association

• Time order

• Non-spuriousness and mechanism

Association

The association between two measured quantities is quantified by correlation. This correlation is a key tool provided by statistics.

Time order

The cause must occur before the observed effect.

Mechanism

The association must have some mechanism that explains how the cause could lead to the effect.

If we do not have a mechanism, it is possible that we have a spurious (false) relationship.

Spurious relationships

Spurious relationships can have associations and time order but no mechanism to link them. They often are both related to another more important variable.

Examples:

• Ice cream and violent crime.

• Breath mints and lung cancer.

Causality Revisited

So statistics provides evidence of a time-order and an association, but we must often rely on a branch of science to suggest a mechanism.

Biochemistry might show that a chemical damages human tissue in a way that could lead to disease.

Types of Studies

Field Work

These are studies in the "real world".

Laboratory Studies

These are studies in laboratories that attempt to simulate parts of our world or environment.

Cross-sectional Study

A study that looks at a number of individuals (population) at a specific point in time.

Usually tries to use random methods to reflect the entire population.

Longitudinal Study

A study that measures something over a long period of time.

These studies often look for changes that can be related to an event or change in an environment.