Block Design Matched Pairs Design Section 4 2

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 Assignment To Blocks Is not random Light Colored Clothing Random Assignment Cold Water Hot Water Compare Results Many Pieces of Dirty Laundry Cold Water Dark-Colored Clothing Random Assignment Compare Results 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