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.

=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).