2024-01-01
Score
stratified by Sex
Salary
stratified by Sex
Salary
stratified by Sex
Creative writing study was a randomized experiment.
Salary dataset was an observational study.
Differences in strength of conclusions: randomized experiments like creativity
can admit causal conclusions
Generalizability: what population are the data from?
salaries
represents a sample of starting salaries.creativity
The observed difference (i.e. treatment_effect
) is not 0. Is there a real difference?
We need a (statistical) model to draw statistical inferences!
t.test
Score
between the groupssalaries
The difference is not 0. Is the difference real?
We need a model to draw statistical inferences!
Male
and Female
salariesMale
and Female
salariest.test
We used the same method even for these different studies… does this make sense?
Terminology:
Parameter: a property of the probability model (often written \(\theta\))
Estimate: a function of the sample data (often written \(\hat{\theta}\))
Goal of statistical inference is to learn about the parameter \(\theta\) from the estimate \(\hat{\theta}\)
Experimental design:
Randomization: individuals were randomly assigned Treatment
in creative
study
Simple random sample: a way of sampling \(n\) from a population such that every \(n\) points are equally likely.
Other sampling mechanisms: systematic sampling, cluster sampling.