9/29/2025

Review exercises - see Exam1-F2021

General Location-Scale Model

See GoogleDrive\Stat216-Nonparametrics-F2025\!Class Notes\Section5.1-Notes-BH.pdf

Ansari-Bradley Statistic for Scale Differences

• Another scoring function
  • Order the X's and Y's from least to greatest
  • Assign Scores:
    • 1 to the smallest and largest observations
    • 2 to the 2nd smallest and 2nd largest observations
    • 3 to the 3rd smallest and 3rd largest observations
    • ... continue this process until you meet in the middle.
  • Let Rj denote the score assigned to Yj, j=1, ..., n.
  • Ansari-Bradley Statistic: c=sum of Y scores
• Null distribution (when m=3 and n=3)
• Large Sample Approximation
• Ties Correction (see p. 156) - overall recommendation is the same as before

Demonstration

• See GoogleDrive\Stat216-Nonparametrics-F2025\!Class examples and labs\Ansari-Bradley - Examples in R.RMD

Class time to complete our seventh lab activity - see GoogleDrive\Stat216-Nonparametrics-F2025\!Class examples and labs\Ansari-Bradley - Lab Activity.RMD

Please read Section 5.2 for class on Wednesday.