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Block Design Matched Pairs Design

Learn about block design and matched pairs experiment schemas in statistics, with practical examples and applications. Explore control elements and randomization in experimental setups.

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Block Design Matched Pairs Design

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

  2. 21

  3. Another Explanation

  4. Consider This!“Let’s Make A Deal!” • There are three doors at the front of the room. Behind one of the doors is a prize! Behind the other two doors, nothing. • Choose the correct door and you win!!! • 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…

  5. Statistical Questions Regarding“Lets Make a Deal!” • 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

  6. Today’s Objectives • Describe what is meant by a “block design experiment” • draw a schematic diagram of such an experiment. • Describe what is meant by a “matched pairs experiment” • draw a schematic diagram of such an experiment.

  7. 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) • In that case, divide the subjects along those lines, then take an SRS within each block to establish treatment groups. Definition A 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 treatments.

  8. Randomized Block Design Definition In a 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! Hand out: “Doing the Laundry” • …do not go to next slide till done with diagram…

  9. Diagram of Block Design: “Doing the Laundry” Cold Water Light Colored Clothing Random Assignment Compare Results Assignment To Blocks Is not random Hot Water Many Pieces of Dirty Laundry Cold Water Compare Results Dark-Colored Clothing Random Assignment Hot Water

  10. Things to Note about Blocking: • Many students confuse blocks and treatments groups • Blocks are not formed at random, it’s the 1st step before randomizing. • 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.

  11. Matched Pairs Experimentstwo types! 1st type: Choose treatment and control groups by pairing like subjects and assigning one to each group “brown hair and 6 foot guys together” 2nd type: 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 Allow me to demonstrate an example… Muhahaha

  12. Activity!Get your heart beating! The Question: • Are standing pulse rates generally higher than sitting pulse rates? • To find out… We will preform an experiment to try to answer the question! (lucky you...I’ll show you 2 modeled designs) 1) Completely Randomized Design 2) Matched Pairs Design

  13. Example: Standing and Sitting Pulse Rate • Consider the Fathom dotplots from a completely randomized design and a matched-pairs design. What do the dotplots suggest about standing vs. sitting pulse rates? Experiments

  14. 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.

  15. Homework • 4.2 Part 3 Homework Worksheet • Continue working on Chapter 4 Reading Guide

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