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