-Conditional Probability 
- What is the probability of Z happening given the event of X? This is also written as P(Z|X)

-Correlation/Regression 
        -Shows how the data is related or Associated with eachother 

 -Machine Learing and Deep learning occours at this level because they only predict outcomes they dont reason why things are occouring 
 
 -Statistics occurs on the association rung on the ladder (what data tells us about the result)

University of Michigan - Ann Arbor

Association refers to linking variables together solely based on their perceived outcomes and is not influenced by reasoning. 

Association

Association Examples

A real life example of a question that can be answered through association is: "How likely is a customer who bought toothpaste to also buy dental floss?"

What does a symptom tell you about a disease?

What does wearing glasses tell you about a person's eyesight?

Real life example of association questions/application

In the context of Berkeley's admission paradox, Bickel contends that bias is to do with a pattern of association between a particular decision and particular sex of the applicant.  The words "pattern" and "association" are indications that bias belongs to the rung one of the Ladder of Causation, association.  

Bickel's Definition of Bias

A genome-wide association study (GWAS) is a statistical genomic analysis technique to associate specific genetic variations with particular diseases by looking for patterns and frequencies so that certain genetic variations can be identified to associate with and predict disease.  It is important to note that GWAS cannot tell causality since it can only be used to make associations between variables, -hence the first ladder of causation, Association.  

Genome-Wide Association Study (GWAS)

A Bayesian network's structure is made up of nodes (which can be multi-variate), edges between paired nodes, and a conditional probability distribution in each nodes. The nodes in a Bayesian network represent random variables and edges represent the conditional dependence of these nodes. We try to use this structure to model the conditional probability distribution of outcome variables (which are often causal) after observing new evidence.

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