Randomized Block & Matched Pairs Design (College Board AP® Statistics)

Randomized block design

What is a block?

• A block is group of experimental units who have something in common (are similar) that may affect how they respond to a treatment

  • e.g. a group of participants who are smokers

• Blocking is the act of dividing up the experimental units into different blocks

  • e.g. separating participants out into smokers and non-smokers

    • 'smoking or not' is the blocking variable

• Blocking should only be done if the researcher believes the blocking variable could affect the results

Why is blocking used?

• How experimental units respond to treatments varies naturally due to many different factors (variables)

  • e.g. age, diet, weight, ....

• Blocking allows natural variations in responses to treatments to be distinguished from those variations that were due to the blocking variable

  • It removes the blocking variable from the list of interfering factors

    • which gives a clearer picture of the effectiveness of the treatment

    • and makes any differences between treatments more distinguishable

What is a randomized block design?

• An experiment that has a randomized block design is one in which

  • experimental units are separated out into blocks

    • based on an identified blocking variable that could cause an issue

  • then experimental units are randomly assigned the different treatments within each block

    • Common methods for randomly assigning treatments can be used in each block

    • e.g. using random number generators

• If an experiment has more than two treatments

  • each block needs to be randomly assigned all of the treatments

Is a randomized block design better than a completely randomized design?

• In general, a randomized block design is better than a completely randomized design

  • making it easier to distinguish the effectiveness of the treatment

    • from any differences caused by the blocking variable

• However, completely randomized designs should be used

  • if blocking variables are unknown

  • or if the sample size is very large

    • because larger samples tend to introduce more blocking variables

    • which means more blocking is required

    • which ends up reducing the sample size within each block

Matched pairs design

What is a matched pairs design?

• A matched pairs design is a special type of randomized block design

  • The blocks have only two experimental units each (a pair)

  • which are matched either naturally or by the researcher based on some common factor

    • e.g. matching pairs of individuals who have similar heights

    • The blocking variable here is height

• The experiment has two treatments

  • These are randomly assigned within each pair

    • One of the pair receives the first treatment, the other receives the second

How do I randomly assign treatments to each pair?

• One way is to use a random number generator as follows

  • Label one of the pair as 1 and the other as 2

  • Use a random number generator to generate a number between 1 and 2

  • Give the first treatment to the experimental unit whose number is selected

  • Given the second treatment to the experimental unit whose number was not selected

Is a matched pair design better than a completely randomized design?

• A matched pair design is better than a completely randomized design

  • as it makes it easier to distinguish the effectiveness of the treatment

    • by removing any effects due to the blocking variable