# The one-way ANOVA model

The statistical model can be written as in the equation above.On the left hand side of the equation we have the response variable (y_{ij}) that identifies each observation with the corresponding treatment and replication.

*i *=1… *t, t* is the number of treatment levels.

*j* =1…* n _{t}, n_{t}* is the number of replications of treatment level

Note that the number of replications per treatment level do not necessarily has to be the same. The total number of observations is: N = ∑_{ t} n _{t}

On the right hand side, a linear combination of model parameters:

μ is a constant

τ* _{i}* the effect of treatment

ε_{ij }a random effect attached to treatment and replication called the error.

We typically assume that ε_{ij } are independent and identically distributed *(iid)*, following a Normal distribution with equal variance, in short: ε_{ij}~N(0, σ^{2}).