Chapter 5 Analysis of Two-Factor Experiments Based on Additive Models

• additive model: $y_{ijk} + \mu + \alpha_i + \beta_{j} + \epsilon_{ijk} \quad(i = 1,2; j = 1,2,3; k = 1,2)$, factors do not interact
  • simple effect = main effect for additive model
  • test for main effects: $\alpha_1 = \alpha_2$, $\beta_1 = \beta_2 = \beta_3$, no main effect for first level $\Leftrightarrow \alpha_2 = 0$, no main effect for second effect $\Leftrightarrow \beta_2 = \beta_3 = 0$