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 (yij) that identifies each observation with the corresponding treatment and replication.
i =1… t, t is the number of treatment levels.
j =1… nt, nt 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
τi the effect of treatment
εij a random effect attached to treatment and replication called the error.
We typically assume that εij are independent and identically distributed (iid), following a Normal distribution with equal variance, in short: εij~N(0, σ2).