Block Design Matched Pairs Design Section 4.2 Part 3 Reference Text: The Practice of Statistics, Fourth Edition. Starnes, Yates, Moore

Let’s Make A Deal! There are three doors at the front of the room. Behind one of the doors is a prize! Choose the right door and you win!!! Behind two of the doors is nothing. Choose the wrong door and you lose. But wait… there’s more! After you make your choice, I will show you one of the loser doors and let you switch doors if you want. After your FINAL ANSWER, we’ll see if you are a winner or a loser!

Activity Are girls better than boys at playing this game? Does training improve one’s ability to play the game? To find out, let’s divide the class into gender groups, and within each group, randomly choose a group to be trained and a control group. Notice the control and randomization elements We will then play the game many times and compare winning percentages within each group Notice the replication (author’s definition) element

Objectives Describe what is meant by a “block design experiment” and draw a schematic diagram of such an experiment. Describe what is meant by a “matched pairs experiment” and draw a schematic diagram of such an experiment.

Block Design Experiments In some cases, we may expect different responses to an explanatory variable by different subjects based on some identifiable difference (such as age, gender, geography, etc) Block: is a group of experimental units that are known before the experiment to be similar in some way that is expected to affect the response to the treatment. In that case, divide the subjects along those lines, then take an SRS within each block to establish treatment groups.

Randomized Block Design The random assignment of experimental units to treatments is carried out separately within each block. Blocks are another form of control. They control the effects of some outside variables by bringing those variables into the experiment to form the blocks. Lets look at an example and diagram to put this all together!

Diagram of Block Design: Example TB pg. 246 Cold Water Light Colored Clothing Random Assignment Assignment To Blocks Is not random Compare Results Hot Water Many Pieces of Dirty Laundry Cold Water Compare Results Dark-Colored Clothing Random Assignment Hot Water

Things to Note about Blocking: Many students confuse blocks and treatments groups Blocks are not formed at random Blocks should be very different from one another, we then take a randomized treatment group within that block. Students confuse stratified random sampling with a random block design Stratified is done only when taking a sample from a population Blocking happens only when assigning units to treatments in an experiment. Moral of the story is: Control what you can, block on what you cant control, and randomize to create comparable groups.

Matched Pairs Experiments Choose treatment and control groups by pairing like subjects and assigning one to each group Another approach: Let each subject be his/her own control Measure before and after data on each person Let each person evaluate two treatments and compare responses

Activity! Get your heart beating! Are standing pulse rates generally higher than sitting pulse rates? We will preform two experiments to try to answer the question! 1) Completely Randomized design 2) Matched Pairs Design

Objectives Describe what is meant by a “block design experiment” and draw a schematic diagram of such an experiment. Describe what is meant by a “matched pairs experiment” and draw a schematic diagram of such an experiment.

Homework