The example below is a larger data set that exhibits interaction between two factors.

Hay fever relief

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

The diagram below initially shows the data, plus the overall mean hours of relief for the 36 subjects.

Click the checkbox Main effect for Ingredient A to show the mean hours of relief for this ingredient. Increasing the amount of this ingredient gives longer relief.

Click Main effect for Ingredient B to show the 'best' fit of a model with no interaction between the ingredients. The vertical red lines are 'residuals' for the model — they show whether the no-interaction model over- or under-estimates yield for each patient. In particular, 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.