Model without interaction

The additive model for two factors, X and Z, is


yijk  =  µ

 + 
(explained by X)
βi

 + 
(explained by Z)
γj

 + 
(unexplained)
εijk

The β-parameters and γ-parameters are called the main effects for X and Z.

In this model, the effects of the two factors on the mean response can separately described by the two sets of β-parameters and γ-parameters. This can be done because:

Since the effects of the two factors can be separately described, it is said that the two factors do not interact in their effect on the mean response.

Bait Acceptability by Feral Pigs

In order to assess whether feral pigs were beginning to avoid feed baited with 1080 poison, an experiment was conducted in which trapped feral pigs were given a wheat diet on Day 1 then five different feeds on Day 2, some of which contained 1080 poison with other addtives. Ten male and ten female pigs were used so each feed was was given to two pigs of each gender. The response analysed was the difference in feed intake from Day 1 to Day 2.

The diagram below shows the changes in feed intake of the pigs and the best-fitting model with no interaction.

Rotate to y-z. The coloured lines show how mean change in feed intake differs for the five feed types, both for males (purple) and females (green). Observe that the fitted lines are all parallel.

Similarly, rotate to y-x. Again the three fitted lines (corresponding to different feed types) are all parallel.