Relationships

We are often interested in determining if cause and effect are present in natural, environmental, and social phenomena.

This usually means determining if there is a mathematical relationship between quantitative measurements of our world.

• Does increasing fertilizer increase the amount of harvest of a crop? Is there a limit to this increase?
• Does presenting citizens with facts about global warming lead to changed behaviors?
• Does early childhood education improve educational and economic outcomes much later in life?

If these relationships are present and significant, we can make decisions that improve human and environmental health.

Types of Data

• Continuous
• Binary
• Categorical
• Interval Data

Dependent and Independent Variables

• can think of as cause and effect

Relationships and Associations

• continuous, continuous (linear regression)
• continuous, binary (logistic regression)
• binary, continuous (t-test)
• binary, binary (???)

Proxy Data

Sometimes we do not have direct data on something we want to observe.

In those cases, we may use proxy data. Proxy data are other directly measureable things that have some relationship with the item we want to observe.

For example, tree ring widths are used as a proxy for rainfall and temperature.

Intuition and Quantitative Relationships

We often have strong convictions that certain relationships do exist or should exist. However, some of these convictions are not based in evidence (they are pure vibes).

While our intuition can be correct, it is important to check that our convictions rest on a strong empirical base.