This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Unit 2: Experiments with a Single Factor: One-Way ANOVA Sources : Sections 2.1 to 2.3, 2.5, 2.6. One-way layout with fixed effects (Section 2.1). Multiple comparisons (Section 2.2). Quantitative factors and orthogonal polynomials (Section 2.3). Residual analysis (Section 2.6). One-way layout with random effects (Section 2.5). 1 One-way layout and ANOVA: An Example Reflectance data in pulp experiment: each of four operators made five pulp sheets; reflectance was read for each sheet using a brightness tester. Randomization : assignment of 20 containers of pulp to operators and order of reading. Table 1: Reflectance Data, Pulp Experiment Operator A B C D 59.8 59.8 60.7 61.0 60.0 60.2 60.7 60.8 60.8 60.4 60.5 60.6 60.8 59.9 60.9 60.5 59.8 60.0 60.3 60.5 Objective : determine if there are differences among operators in making sheets and reading brightness. 2 Model and ANOVA Model : y ij = + i + ij , i = 1 ,..., k ; j = 1 ,..., n i , where y ij = j th observation with treatment i , i = i th treatment effect, ij = error, independent N ( , 2 ) . Model fit: y ij = + i + r ij = y +( y i y )+( y ij y i ) , where . means average over the particular subscript. ANOVA Decomposition : k i = 1 n i j = 1 ( y ij y ) 2 = k i = 1 n i (...
View Full Document
- Fall '08