1. 4.2 (Day 2)

2. New Experimental Designs
Today we will talk about two new ways to design an experiment
Instead of the completely randomized design
Blocked Design (“Blocking”)
Matched Pairs Design

3. Example (page 246 in textbook)
Researchers are testing a new formula for laundry detergent
They want to know whether it is more effective in cold water or in warm water
However, they have a problem: not all clothes are the same
Light-colored clothes tend to get cleaner in warm water
Dark-colored clothes tend to be better off in cold water
So the answer MAY depend on what type of clothes we’re washing

4. Completely Randomized Design Randomized Block Design
We randomly assign some groups to be washed in cold water, and some in warm water
If we wanted a true “control” group, we may have some clothes not washed at all
We then compare the cleanliness after washing
If we do this, we HOPE that the randomness of the design will make the distribution of light/dark clothes fairly even in each treatment
First we split up all the clothing into a “light” category and a “dark” category
These are called “blocks”
This is NOT done randomly
Then, within each block, we randomly assign the warm/cold treatment
We then compare the results, for each block

5. When to use Blocking
For assigning treatments, blocking behaves similarly to how stratified sampling does for sampling
We block based on some characteristic of the individuals/subjects
Typically because we think that individuals with different characteristics may respond differently to the treatment
Notice, it is not just that “some individuals are different than others” but that some individuals will respond differently to the treatment

6. Another Example
Recent medical research has asked the question: “what is the effect of receiving a blood transfusion from the blood of a pregnant woman?”
Or in other words, is it any different from receiving a blood transfusion from someone who is not pregnant?
Do you think that the blood from a pregnant woman would affect men and women differently?
If no, then a completely randomized design is fine
If yes, then that would be useful information, so we probably want to use a blocked design

7. Blood Transfusions
So, if we wanted to design a study to test this, we would first separate our subjects into males and females
Then within each group, we randomly assign the treatment
The treatment group gets blood transfusions from a pregnant woman
The control group gets blood transfusions from other people

8. Blood from Pregnant
Males
Random Assignment
Compare
Other Blood
Subjects
Blood from pregnant
Compare
Random Assignment
Other blood
Females

9. Results
Real study
Just came out recently in the Journal of the American Medical Association
Results showed that receiving blood from a pregnant woman was fine for women
NOT for men: They were 6% more likely to die as a result of the transfusion
Researchers not sure exactly why, but presumably something having to do with differing hormones that male bodies can’t process

10. Matched Pairs Technically, a specific type of blocked design
More often thought of as its own type of design
The idea is to create pairs of very similar individuals/subjects
So each “block” has a size of 2
Then one receives the treatment, and the other doesn’t, then we compare
If the individuals are REALLY similar, but have different values for the response variable, then it is almost definitely due to the treatment

11. Matched Pairs—the perfect match
Oftentimes, the best match for an individual is that individual himself/herself
If our goal is to create pairs that are as similar as possible, the closest we can get to you is….you!
This is not always the case—sometimes we choose others that are similar to us

12. Example Use the table to create matched pairs University
Highest Degree
# of Students
Wisconsin-Milwaukee
Doctorate
26,073
Northcentral University
10,093
North Dakota State
14,358
University of Iowa
33,334
Cal State Channel Islands
Masters
6,611
Henderson State
Bachelors
3,981
Metro State
23,948
Colorado College
2,000
Idaho State
13,569
University of South Dakota
9,971
Use the table to create matched pairs

13. Example Somewhat subjective UW-Milwaukee & Iowa
University
Highest Degree
# of Students
Wisconsin-Milwaukee
Doctorate
26,073
Northcentral University
10,093
North Dakota State
14,358
University of Iowa
33,334
Cal State Channel Islands
Masters
6,611
Henderson State
Bachelors
3,981
Metro State
23,948
Colorado College
2,000
Idaho State
13,569
University of South Dakota
9,971
Somewhat subjective
UW-Milwaukee & Iowa
North Dakota St & Idaho St
CC & Henderson
South Dakota & Northcentral
Metro State & Channel Islands

14. After matching
Now that we have our matched pairs, we would randomly choose which one gets the treatment, and which one doesn’t
We then compare results
So if our treatment was giving every student a free laptop, and our response variable was GPA
We would look at the average difference between the two members in each pair

15. Matched Pairs
So if our treatment was giving every student a free laptop, and our response variable was GPA
We would look at the average difference between the two members in each pair
A DIFFERENT WAY TO DO THIS USING MATCHED PAIRS
Treat each school as its own matched pair
Compare before treatment and after treatment