Wuchap_02a_09fall

# Wuchap_02a_09fall - Unit 2 Experiments with a Single Factor...

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
This is the end of the preview. Sign up to access the rest of the 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 = η + τ i + ε ij , i = 1 ,..., k ; j = 1 ,..., n i , where y ij = j th observation with treatment i , τ i = i th treatment effect, ε ij = error, independent N ( , σ 2 ) . Model fit: y ij = ˆ η + ˆ τ 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

{[ snackBarMessage ]}

### Page1 / 5

Wuchap_02a_09fall - Unit 2 Experiments with a Single Factor...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online