The one-way analysis of variance model can be specified in several ways. The cell means model is:
All observations for the factor level have the same expectation, μ i . Because μi is a constant, all observations have the same variance, regardless of factor level.
In analysis of variance, least squares estimation is used to fit the model and provide estimates for the parameters, μi .
The hypothesis test for one-way analysis of variance is:
H0: μ 1 = μ 2= … = μ r
H1: At least one mean is not equal to the others
| μ i || parameters or the true mean of observations at the i th factor level|
|ε ij || error that is independently and normally distributed with mean 0 and constant variance σ 2|