Homework 1 - Granger causality¶
The following relationships are consistent. Left to right:
- $A$->$B$: this is obvious. Example: A is flare, B is eye closure.
- $A$-|$C$-|$B$: a chain of two repressions leads to activation. Example: A is the number of students in class, C is the amount of instructor's attention received by each student, B is the average amount of distraction per student.
- $A$<-$C$->$B$: a confounder preceeding both outcomes. Example: A is whether your house is flooded, B is whether your neighbor's house (higher than yours) is flooded, C is the amount of rain.
The examples are not unique.
Homework 2 - Imperfect perturbation¶
Q1. Scenario 2 with $A$->$B$ will show $P$->$A$ and $P$->$B$ but with biased estimation of effect $A$->$B$:
Q1. Scenario 1 without $A$->$B$ will show $P$->$A$ and $P$->$B$, becoming a false positive of $A$->$B$:
Q1. Scenario 2 with $A$->$B$ will show $P$->$A$ and $P$->$B$ but with biased estimation of effect $A$->$B$:
Q1. Scenario 2 without $A$->$B$ will show $P$->$A$ and $P$->$B$, becoming a false positive of $A$->$B$:
Q2¶
- By giving double-blinded placebo-controlled treatment, the group assignment cannot affect the outcome through means other than the treatment. Without placebo, the patient knows whether they receive the treament, so the patient's psychological expectation of the treatment can have an effect on the outcome. Without double-blindedness, the doctor or prescriber can unconsciously or consciously be more optimistic to patients who receive the treatment, similarly affecting their psychological expectation.
- By randomizing the group assignment, nothing would affect the group assignment. Otherwise, disease severity or other factors can lead to preferential assignment of patients to the treatment group, therefore becoming a confounder that simultaneously affects the outcome.