Chapter 13: Part III
AP Statistics
Blocking
• Blocking is used instead of randomizing subjects
to treatments.
• Blocking is used if it is believed that there will be
differences in how set groups of subjects will
respond to the explanatory variable(s)
• Blocking may be used if we suspect that some
issue we cannot control may introduce variability
in the response. (maybe gender will produce
variability in the response, therefore, we will
block by gender)
Blocking
• Randomization is introduced when we randomly
assign treatments within each block.
• By blocking, we isolate the variability attributable to
the differences between the blocks, so that we can see
the differences caused by the treatments more clearly.
• We block to reduce variability so we can see the
effects of the factors
• When we block, we are not usually interested in
studying the effects of the blocks themselves (no need
to compare the results between/among the blocks)
Blocking
Example: Suppose that the drug we are testing
works effectively. That should show up as a
difference in response between the
experimental group and control group.
However, if both groups are mixed gender and
men and women respond differently to the
drug, then the variability between the genders
can drown out the true effect of the drug in
each gender. We won’t see that the drug is
effective.
Blocking
Example (cont.): We cannot cope with this
variability problem with randomization (can’t
randomize by gender). Instead, we block by
gender to reduce this variability.
Blocking Design
Matched Pairs Design
• Subjects are sometimes paired because they are similar
in ways not under the study
• When we match subjects in this way we can reduce
variability in much the same way as does blocking
• If we have study that is trying to determine if playing
sports increases mathematical achievement, we might
want to pair a subject that has a high IQ and plays a
sport, with a subject that has a high IQ and does not
play a sport (this would be an observational study).
• The matching would reduce the variation due to IQ
differences.
Matched Pairs Design
• When we have a matched pairs design that is an
experiment, we need to introduce randomization
• If we use a matched pairs design in an
experiment that looks at whether or not children
can determine the difference between the facial
expressions of fear and anger. In this situation,
we could match subjects and then randomly
assign the order in which the pictures of facial
expression are shown. One part of pair will get
anger and then fear, the other part of the pair will
get fear and then anger.
Matched Pairs Design Diagram
Confounding and Lurking Variables
Confounding and Lurking Variables
Confounding and Lurking Variables
Confounding and Lurking Variables
• Lurking variables are most common in
observational studies
• Confounding are most common in
experiments