One-way ANOVA is a linear model with one factor as a predictor. One-way ANOVA has two equivalent formulations: the means model and the effects model. Suppose that we have a factor $\tau_i$ occurring at $j = 1, \dots, J$ levels with $i = 1, \dots, n_j$ observations per level. The means model states $Y_{ij} = \mu_j + \epsilon_{ij}$ The effects model states $Y_{ij} = \mu + \tau_j + \epsilon_{ij}$ where $\tau_j$ is the difference between the grand mean $u$ and the mean for group $j$ and the $\epsilon_{ij} \overset{iid}{\sim} N(0, \sigma^2)$. ## assumptions 1. Observations are [[independent]] 2. The response has the [[normal distribution]] 3. The [[variance]] across observations is constant.