STAT 541: Randomization

# Statistics 541: Randomization

• Any questions on the homework
• Importance of statistics: Keeping people from overstating their claims. Like a "blessing." So wider is better, less significant is better since they are more likely to be correct.

## Randomization

### The Ecological fallacy

• Before the "blocks" project we did "find your own data" projects.
• People found census data on states
• Y = murders, X = education, Y positively related to X
• Its negatively related if you add % urban. But its positively related if you add %urban, and income.
• Bummer--we should outlaw education instead of handguns!
• Draw several pictures of how X could be related to Y

### Observational studies

• (AZ library project yet again) Suppose 15 out of 200 librarians do the "new reading program."
• X = 1 if new, 0 if old, Y = reading level of students
• This is better than the state-by-state level analysis since at least the covariates have to be within each subject
• Start controling in a regression sense is the only way
• Once we add "ordering books for new reading program" we will get an infinate SE on our variable of X of interest
• (This is as it should be!)
• So people leave such variables out

### Intutive analysis of a multiple regression

• People look at a multiple regression and see all the choices that are made
• They say to themselves, couldn't they have done many other regressions before they found this one?
• So people intuitively do Bonferonni and ignore such studies
• Hence people can't publish them and can't do them

### Controlled experiments

• By only doing Y vs X we eliminate the "intuitive Bonferonni problems."
• But, we have all the X --> Z --> Y like diagrams
• So randomize assignment, now X is independent of Z FOR ALL Zs!
• Ok, not all. We have anything that is post randomization could be an interesting Z.
• Hence don't tell the subjects (called single blind).
• But merely telling say teachers/doctors that group A are treated and group B are untreated is enought for group A to get better results
• So don't tell the doctors (called double blind).