4.2 (Day 2) 10.19.2017

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

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

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

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

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

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

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

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

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

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

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

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

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

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