Section 1.2

Observational Studies vs. Designed Experiments

The "Golden Rule" of Statistics: Correlation does not apply Causation. But why? And how do we prove causation?

The Causation Barrier

We often find two variables that move together. Ice cream sales go up when shark attacks increase. Does ice cream cause shark attacks?

LogicLens: The Confounding Trap

Observational Study

We just watch. We record ice cream sales and shark attacks. We see a pattern (Association).

Result: Association ONLY

Designed Experiment

We interfere. We force one group to eat ice cream and ban another group from eating it.

Result: Causation Allowed

In the shark example, there is a third variable (Lurking Variable) driving both:

Summer Heat

Heat → More Ice Cream
Heat → More Swimmers → More Sharks

In any study, we are trying to see if one thing changes another. We give them distinct names.

The "Cause"

The variable that we think explains the change. Also called the Independent Variable.

The "Effect"

The outcome we measure. Also called the Dependent Variable.

Concept	Definition	LogicLens Insight
Lurking Variable	An explanatory variable that was NOT considered in the study, but affects the Response.	The "Ghost". It's not in your data set, but it's ruining your conclusion (e.g., "Summer Heat").
Confounding	When the effects of two or more explanatory variables cannot be separated.	The "Mix-up". Did the Fertilizer improve the plant, or was it the Extra Water? If you did both, they are confounded.

Focus: The Present

Collecting data at a specific point in time. Like a 'Snapshot'. Fast but limited.

Focus: The Past

Retrospective. We look back at records. Good for rare diseases, but relies on memory/records.

Focus: The Future

Prospective. We track a group over time. The most powerful observational method, but expensive.

A Census is a list of all individuals in a population along with certain characteristics.

Pros: 100% Accurate (No statistics needed)Cons: Expensive, Time-consuming, Impossible

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