Randomized Block & Matched Pairs Design (College Board AP® Statistics)
Study Guide
Written by: Mark Curtis
Reviewed by: Dan Finlay
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
Examiner Tips and Tricks
Exam questions may use the word pairing instead of blocking.
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
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