module 12

Causation

A relationship where one event (the cause) directly influences another event (the effect).

Explanation

Clarifies how and why a causal relationship exists, linking causes to their effects logically or empirically.

Causation difficulty

Causation cannot be directly observed; it must be inferred from patterns, correlations, and controlled experiments.

Common mistake in causation

Confusing correlation with causation, leading to erroneous conclusions about relationships between variables.

Probability and causation

Probabilistic reasoning can suggest causal relationships by showing how changes in one variable affect the likelihood of another.

Probabilistic causation

A concept where a cause increases the probability of its effect but does not guarantee it.

Probabilistic independence

Two variables are independent if the occurrence of one does not affect the probability of the other.

Probabilistic dependence

A situation where the probability of one event is influenced by the occurrence of another.

Correlation

A statistical relationship between variables.

Difference between correlation and causation

Correlation is statistical while causation implies a direct cause-and-effect link.

Reason why correlation does not imply causation

Correlation can arise from confounders, coincidence, or other indirect relationships.

Common cause principle

If two variables are correlated, there is often a common cause influencing both.

Importance of identifying common cause

It prevents misattribution of causation to one variable when another variable is the true cause.

Confounder

A variable that influences both the independent and dependent variables, potentially distorting the perceived relationship.

Association with the Independent Variable: A confounder is related to the independent variable. For example, if you're studying the effect of exercise on heart health, age might be a confounder because it is associated with both exercise habits and heart health.

Association with the Dependent Variable: A confounder also affects the dependent variable. In the same example, age affects heart health directly.

Controlling confounders

Through randomization, matching, or statistical adjustments in experiments.

Screening off

When a common cause makes two variables independent, the knowledge of one variable does not provide additional information about the other.

Example of screening off

If smoking explains both tar in lungs and lung cancer, knowing about tar does not add extra predictive value once smoking is known.

Spurious correlation

A correlation that arises due to coincidence or a hidden factor, not a causal relationship.

Example of spurious correlation

The correlation between ice cream sales and drowning rates linked by the hidden variable of hot weather.

RCT (Randomized Control Test)

A study design where participants are randomly assigned to groups to test causal relationships while minimizing bias.

Gold standard in causal inference

RCTs are considered the gold standard because they reduce confounders and ensure that observed effects are due to the intervention.

Simpson’s Paradox

A phenomenon where a trend appears in individual groups but reverses when data is combined.

Example: In a study, a treatment might appear effective within each subgroup (e.g., different age groups), but when all data is combined, the treatment might seem ineffective or even harmful.

Example of Simpson’s Paradox

A treatment appears effective in separate gender groups but ineffective when genders are combined due to differing group sizes.