10/13/2025

Chapter 6 - One Way ANOVA

See GoogleDrive\Stat216-Nonparametrics-F2025\!Class Notes\Section6.1-Notes-BH.pdf

• Setting
• Model
• Hypotheses
  • General Alternatives (Section 6.1)
  • Ordered Alternatives (Section 6.2)
  • Umbrella Alternatives (Section 6.3)
• Kruskal-Wallis Procedure
  • If k=2 then the Kruskal-Wallis test is equivalent to the Mann-Whitney-Wilcoxon test.
  • Combine all N observations and rank them from least to greatest.
  • Find the sum of the ranks for each treatment.
  • Find the average of the ranks for each treatment.
  • What should the average rank for each treatment be close to if the null hypothesis is true?
  • Kruskal-Wallis Statistic (H)
  • Kruskal-Wallis Test
    • Use the R command kruskal.test(x, g) to compute the KW test stat and p-value.
    • Use the R command cKW(alpha, sample sizes, "Exact") to find critical values.
    • Use the R command pKW(x, "Exact") to find p-values.
  • L.S.A.
    • Use the R command qchisq(prob, df) to find approximate critical values
  • Dealing with ties (see H' on page 205)
    • Use a permutation test to get an exact p-value - See comment 7 on p. 209.
• Exercise 10 on p. 214
  • see Google Drive\Stat216-Nonparametrics-F2025\!Class examples and labs\pine.csv
  • see Google Drive\Stat216-Nonparametrics-F2025\!Class examples and labs\pine.R

Examples

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

Class time to complete our tenth lab activity - see GoogleDrive\Stat216-Nonparametrics-F2025\!Class examples and labs\Kruskal-Wallis - Lab Activity.RMD

Please read Section 6.2 for class on Wednesday.