Randomization and Causality
Chapter 7

Key Definitions

• Observational study: can show the correlation between two variables but difficult to show causation. This is because there could be a confounding variable causing both to happen (e.g. voluntary assignment).

• Randomized experiment (Gold Standard): avoids the issues with confounding variables by comparing two groups (treatment and control) that look on average the same.

• Confounders: alternative explanations for differences between the experimental groups. Confounding variables correlate with both the experimental groups and the outcome variable.

Example

Does eating ice cream cause drowning?

Experiment:

• Control group: do not eat ice cream

• Treatment group: eat ice cream

• Scenario 1
• Scenario 2

We randomly divide a population into the treatment and control groups and compare the number of drownings between groups.

• Type of experiment: randomized experiment
• Types of conclusions can we make: causal conclusions

We have survey data of the number of monthly ice cream sales and number of monthly drownings and calculate a correlation of 0.85.

• Type of experiment: observational study
• Types of conclusions can we make: correlation only conclusions (possible confounding variables)

Key Ideas

 

• Randomized assignment helps separate causation from correlation.

• Additionally, randomized assignment helps rule out confounding variables.

Using randomization in R

Bernoulli trial = randomized experiment with exactly two outcomes.

• In R: rbernoulli(n = ____, p = ____)

It can be framed as a “yes or no” (success or failure) question.

Examples:

• Whether or not flipping a coin results in heads

• Whether or not you roll a 1 when rolling a die