Block Design Matched Pairs Design

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Block DesignMatched Pairs Design

• Section 4.2 Part 3
• Reference Text
• The Practice of Statistics, Fourth Edition.
• Starnes, Yates, Moore

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Lets 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 theres 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, well see if you are a
  winner or a loser!

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Activity

• Are girls better than boys at playing this game?
• Does training improve ones ability to play the
  game?
• To find out, lets 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 (authors definition)
  element

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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.

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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.

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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!

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Diagram of Block Design Example TB pg. 246
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
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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.

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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

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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

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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.

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Homework