1/30/2008

Paired Replicates Data

Two sets of observations, typically referred to as "pre-treatment" (X) and "post-treatment" (Y), are obtained on n experimental units. We are interested in assessing the effect of the treatment.
Let (theta) refer to the "typical effect" of the treatment.
- All of the information about (theta) in the pair (Xi, Yi) is contained in the difference Zi = Yi - Xi.
Model: Let Zi = Yi - Xi, i=1, ..., n and assume that:
- The n Zi's are mutually independent;
- Each Zi has a continuous distribution with median (theta).
We want to make inferences about (theta).
- Three ways to use the information in the Zi's
  1. Use all of the information (paired t-test)
  2. Use minimal information on whether Y is larger than X (sign test)
  3. Use the information on whether Y is larger than X and the relative magnitudes of the Zi's. (signed rank test)
Example - Does aspirin increase bleeding time?
- Aspirin.sas
- Aspirin.mtw

Two sample z test and confidence interval for means (not very useful)
Two sample t test and confidence interval for means
Pooled t test and confidence interval for means
Example - Do the data present sufficient effidence to indicate a difference between the mean ultimate strengths for two different plastics?
- See plastic.sas