Chapter 10 page 3 Let’s investigate setting up a test where our hypotheses are the following: : H0: μ1= μ2= … = μcH1: At least two means are different Notation: c = number of groups or treatments nj= total number of replicates of treatment j (j = 1,..., c), n = total number of replicates for all treatments Assumptions: 1. c independent and random samples. 2. Each population has a Normal probability distribution. 3. The c population variances are equal. Chapter 10 page 4 or among) Consider the breakdown of the variability within our samples: How do we quantify this variability? Terms:
= Sum of Squares for Treatments (variability between or among) Consider the breakdown of the variability within our samples: How do we quantify this variability?
)= Sum of Squares for Error (variability within)
Total Variation = Treatment Variation + Error Variation Total Variation = Between Variation + Within Variation Total Variation = Explained Variation + Unexplained Variation