Hay fever relief

This example gives another illustration of what is meant by interaction between two factors.

Click the checkbox Main effect for Ingredient A and Main effect for Ingredient B to show the 'best' fit of a model with no interaction between the ingredients. From the residuals (red lines),

The model under-estimates the relief when both ingredients are at the High level.

Click the checkbox Interaction. The best model with an interaction between the ingredients fits the data much more closely.

The combination of high levels of the two ingredients has a particularly good effect.


A study was conducted to investigate the effect of a drug compound in providing relief for hay fever. In the experiment, two active ingredients (A and B) were each varied at 3 levels in a factorial design with 4 replicates. There were 36 hay fever sufferers available and they were randomly allocated to the 9 treatment combinations. The table below shows the hours of relief that the subjects reported.

  Ingredient A
Ingredient B Low Medium High
Low
2.4
2.3
2.7
2.5
04.6
04.9
04.2
04.7
04.8
04.4
04.5
04.6
Medium
5.8
5.5
5.2
5.3
08.9
08.7
09.1
09.0
09.1
08.7
09.3
09.4
High
6.1
5.9
5.7
6.2
9.9
10.6
10.5
10.1
13.5
13.3
13.0
13.2