9/6/2023

My solutions are available for the One Proportion Lab - See Stat216-Nonparametrics-F2023\!Class examples and labs\One Proportion - Lab Activity - Solution.RMD

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 (Sections 3.4 - 3.6 and 3.8)
    3. Use the information on whether Y is larger than X and the relative magnitudes of the Zi's. (Sections 3.1 - 3.3 and 3.7)

The One Sample Location Problem

• Sign Test (Competitor to the one sample t test)
• See GoogleDrive\Stat216-Nonparametrics-F2023\!Class Notes\Section3.4-6 and 3.8 - Notes-BH.pdf

Examples

• See GoogleDrive\Stat216-Nonparametrics-F2023\!Class examples and labs\Sign Test - Example in R.RMD

Large Sample Approximation for the sign test

Dealing with ties

• If there are zero Zs (note that these have zero probability), discard the zero values and redefine n to be the number of nonzero Zs. ***{Do NOT use the sign test if you have a lot of zero Zs.}
• An alternative and recommended approach

Point estimators associated with the sign test

Confidence intervals and confidence bounds based on the sign test

Our second lab activity - see GoogleDrive\Stat216-Nonparametrics-F2023\!Class examples and labs\Sign Test - Lab Activity.RMD

Please read Sections 3.1, 3.2, 3.3, and 3.7 for class on Friday.