STAT 541: Design Of Experiments

# Statistics 541: Design Of Experiments

• No book for the rest of the semester

## Design Of Experiments

### Do students give higher evaluations in the morning?

Suppose we are interested in whether students give higher class evaluations in the morning than in the afternoon. (Theory is based on anectodotal studies.) How can we test this claim?
• Exp 1: Abba teaches morning classes for next 10 years. Bob teaches afternoon classes for next 10 years. n=30, m=30.
• Exp 2: Abba does 5 years in morning (while Bob does 5 years in afternoon) then then switches with Bob. n = 30, m =30.
• Alternative theory: n = 2, m = 2. (Maybe Bob is completely tiard after his noon bike ride and hence doesn't teach well in the afternoon.)
• Exp 3: Abba teaches both morning and afternoon classes each semester. So does Bob, Charles, Dean, Edward, Fred, George. Look at bob_afternoon - bob_morning and abba_afternoon - abba_morning. One sample: n = 7.
• Alternative theory: morning students grade easier than afternoon students.
• Aside: do we care?
• Under this theory we would still choose to teach in the morning.
• BUT, the deparmtnet can't do it on mass since that will drive the afternoon students to the morning.
• Exp 4: Randomly assign students to classes. Solves all problems but practical ones! (Ethics, scheduling conflects, adminstration not liking it.) n = 1000s. m = 1000s.
• So what are the control variables of the deparment? When classes are taught.
• Exp 5: Run only morning classes for 5 years, then run only afternoon classes for 5 years. See difference.
• Alternative theory: Students are getting grumpier/easier with time.
• Exp 6: Randomly decide each semester to run only morning classes or only afternoon classes. See difference. For 10 years we would get an n=10, m=10.

## Handout on DOE

• Key items in design
• H0, H1 as science
• Xs, Ys
• what is a "row"?
• randomization, controls, data collection
• models
• H0, H1 as statistics
• n
• bad things: missing data, costs, time, interium analysis for stopping
• Some examples
• plan, model, key statistical question
• Rogaine vs. Gro-againe
• Science: prevention of balding
• what to measure?
• randomization/data collection
• statistical hypothesis (beats rogaine, equal to or different than?)
• Missing data. Bored with poor results, moving out of area, etc.

## Sample size calculations

• signficance, power, sample size, signal/noise are key properties
• Goal: determine sample size from other items
• One sample problem
• Alpha says how far away x-bar has to be to be significant
• Beta for some delta says how far away x-bar has to be from interesting point
• n determines ratio of two scales
• Ah, now the details begin